Military & Maritine DISCIPLINE IN THREE BOOKS. BOOK I. Military Observations or Tactics put into PRACTICE for the Exercise of HORSE and FOOT; the Original of ENSIGNS; the Postures of their Colours: With Sir Francis Vere's Directions for Officers; And a small Treatise of INVASION. By Captain Thomas Venn. BOOK II. An exact Method of MILITARY ARCHITECTURE, the Art of FORTIFYING TOWNS; with the ways of Defending and Offending the same. Rendered into English by John Lacey, out of the Works of the late Learned Mathematician Andrew Tacquet. Together with Corrections made by the Count de Pag'an and St Sam. Mor●land's Methods of Delineating all manner of FORTIFICATIONS. BOOK III. The COMPLETE GUNNER in three Parts, Showing the Art of Founding of GREAT ORDNANCE; making Gunpowder; the taking of Heights and Distances either with or without Instruments; with the nature of Fireworks. Translated out of Casimir, Diego, Vssano and Hexam, etc. To which is added the DOCTRINE of PROJECTS applied to Gunnery by Galilaeus and Torricellio. And Observations out of Mersennus and other Authors. LONDON, Printed by E. Tyler and R. Holt for Rob. Pawlet at the Bible in Chancery Lane, Tho. Passenger at the three Bibles on London Bridge, and Benj. Hurlock over against Saint Magnus' Church, 1672. Military Observations, OR THE TACTICS PUT INTO PRACTICE, Collected and Composed for the EXERCISE BOTH OF Horse and Foot, To our present mode of Discipline. WITH The Original of ENSIGNS their duties, and Postures of their COLOURS. Hereunto is added Sr. FRANCIS VEARES notes of Direction for Officers. By Capt. Thomas Venn. LONDON, Printed by E. Tyler and R. Holt, for Robert Paulet at the Bible in Chancery Lane, Tho. Passenger at the three Bibles on London Bridge, and Benjamin Hurlock over against Saint Magnus' Church. 1672. TO THE Right Noble JOHN DUKE OF SUMMERSAULT, MARKS and EARL OF HARTFORD, VISCOUNT BEAUCHAMP AND Lord Seymour. May it please your Grace. IN vacant hours my Genius guiding me to some thoughts upon Art Military, and having made some Collections of part thereof, out of the chiefest Authors both Ancient and Modern, but finding in them many Motions to be of little use, and may well be spared according to our present Mode of Discipline, which is to Exercise and fight our Horse but three in File, and the Foot six. I have according to the several Commands for the Exercise thereof, drawn the platforms, and directions for the performance of the same, and now they want nothing but your Grace's protection, for which, being your Servant and Tenant, I have presumed to implore; knowing that there is in your Right Noble self, Wisdom and Potency enough to allow hereof for the use of the young Souldrie of this Kingdom: Sir, next to my Sacred KING be assured of my dutiful affections, and Command the Life of him who is in all humlity Your Grace's most obliged Servant Tho. Venn. TO All such of the Deputy Lieutenants For the County of SUMMERSAULT That have faithfully managed his MAJESTY'S affairs in the well ordering of the Militia of the said County. Right worshipful, and truly Honoured. I Am to crave your pardons for my boldness, that (being Comissionated to obey your Commands) have presumed thus far without them; but your Honour's love to this Art, and my own experience of you, is the cause thereof; and as the Country can testify the same, so it is my endeavour (if it were possible) the whole world should know it: But your splendid carriages in the activeness of your proceed in the Militia, do shine most glorious in your effectual managements; for your diligence hath drawn obedience, your wisdom reverence, your virtuous education makes a willingness in all to serve you, and a readiness in your Honours (in all your actions) to equalise the same. These Collectives are but shadows your Noble minds are adorned withal, being but little more than the Accidence of Military Discipline, yet useful in this Warlike age. My Lord Duke's Patronising hereof I hope may not be denied by you to suffer these to march and quarter within the precincts of your Honour's Commands, assuring that in quality I am Your Honour's Servant to be Commanded. Tho. Venn. A List of the names of those worthy Gentlemen as are concerned in the affairs of the County of Somerset, as Deputy Lieutenants, and Colonels, both of Horse and Foot. The Lord Fitzharding, Colonel of Horse. Lord Pawlett, Colonel of Crewkerne Regiment, 1. Sir William Portman. Sir John Syddenham. Sir William Wyndham. Sir Thomas Bridges. Sir Hugh Smith. Sir George Horner. Sir Edmond Windham Knight Martial. Sir John Coventrey Colonel of Taunton Regiment, 2. Edward Phillip's Esq Ralph Stawell, Esq Colonel of Bridgwater Regiment. 3. Peregrine Palmer Esq Henry Roger's Esq George Speak Esq Francis Windham Esq Colonel of Wells Regiment, 4. Samuel George's Esq Robert Hunt Esq Thomas Peggot Esq Colonel of Bath Regiment, 5. TO THE Right worshipful, and truly honoured Sir COPLESTONE BAMPFIELD Knight, And one of the Knights of PARLIAMENT For the County of DEVON, etc. SIR, ALthough I am a stranger to you, yet the Gallantry of your Virtuous inclinations, together with the nearness of affections to my never to be forgotten Cammander Sir Hugh Wyndham Knight, late deceased, forceth me to present you with a Lively Portraiture of his worth. As to his Military concerns, he made his Soldier's Commanders of the chiefest principles of War (that is) to be Faithful, Obedient, Resolute to fight, loving to their Country, and loyal to their Sovereign: So likewise in the private Exercises of his Troops, those under his Command were as Ornaments in peace, and a guard in War: This only was not the height of his ambition, for he made it a principle to himself in Warlike combats, not to have many names, but many hands: And for his deportments, I am sure none was more beloved in his Country, nor could command more able and stouter Soldiers for his Majesty's service than himself: And I hope the Heavens have most largely rewarded him for his blood spilt in his late Majesty's service (of ever blessed memory.) Sir, I humbly beg I might by your favour indicate to the world my Obligements to his deceased person, which was accepted of by him when he was alive, as an Epistle to my Observations for the Military Exercise of Horse and Foot. And what I have truly said of him, your own worth falls not short; in your Paternal affections to your Country, which hath of late appeared (notwithstanding great opposition) in their clear affections to you again, especially in that unparallelled Election of you for Knight of the Shire: And give me leave to declare to the World your Countries further Esteems of you, to be one of his Majesty's chiefest Citadels (or fort Royal) for their safety: Not that I declare this to lessen any of the beams of those other worthy Heroes that shall join with you, when ever his Majesty shall Command. Sir, I crave your Pardon for my boldness, and conclude (with my desired wishes for your Worship's tranquillity, the increase of Honour here, and what may be merited for you, to make you glorious in the world to come) subscribing in the quality of July 29. 1671. Your Humble Servant Tho. Venn. TO THE Truly Generous Gentlemen and CITIZENS of LONDON Practising Arms in the Artillery Garden. Gentlemen, ALthough I am a stranger to you, I must declare to the world that what I know in this Art Military, I received, as it were from your breast; from some who were Leaders in your ground: And 'tis a grief to me that I live at such a distance from you, as not to be of your number; the least amongst you being of ability to be Commanders in Chief, when ever his MAJESTY may require it. There is in you strength enough to shield a just cause; and a Royal cause is able to advance your power: give me leave to tell you there can be nothing done by you without it; it is that which giveth strength and sinews, to all your motions. Gentlemen, you may see, by my other Epistles, what Authors I have made use of, Elton. and if you find some of the words of Command, one and the same with others late before me, I could not help it, for this was finished as to the Commands and directions above four or five years now last passed, and in all that time I never saw any thing of the Gentleman's, nor his latter piece as yet. This you'll find to be but methodical collections for the young Country Soldier; and in our rural exercises they can draw up but twelve files, in which I am stinted to a very small number for so great a work; if there were a proportionableness in the Arms, the figures would have been better; yet not in the least presuming to teach you; but I hope with your favourable constructions you will allow it useful for us in the Country, although your abilities may teach the world ten times more. I aimed at nothing but to show how necessary the readiness and use of Arms is, and of men to be well exercised in them. Which hath been a benefit to Republics, as History and experience hath made to appear; for what Nation hath not found safety in the expert use of them, and in the neglect thereof ruin? I hope there are none of you so disloyal, as not to obey your Prince's Commands; in Order to which I cannot but Commend your close order to his Religion, (and not to be at open distances); it is that which will make your obedience free, your affections settled, yourselves renowned, and as I may in some part say, the peace of the Kingdom secured. I humbly crave your pardons for my boldness, and grant me not only to be in the number of the well wishers to this Art, but also to the prosperity of your ground, and I shall always subscribe, March, 1671. Yours Tho. Venn. TO ALL MY FELLOW-OFFICERS SOLDIERS AND LOVING COUNTRYMEN To whom the Exercise of ARMS Is delightful. Gentlemen, and Fellow Soldiers. Although there are discouragements enough to make you negligent in the exercise of Arms, not only to see this Art so little countenanced, but our late Enemies by sitting still, grow rich, and the Royal Sons of Mars, in all their labours not able with one hand to wash the other; yet this one thing, in making ourselves capable to do our Gracious King and Country service, should be the chiefest motive to labour after the Theoric part of this Art, by which we shall be the better able to perform the Practic when we shall be called thereunto. But lest these few Collectives might meet with some objections, why that I should treat of the Horse in the first place, when Antiquity alloweth the precedency thereof to the Infantry; It was not to raise a dispute amongst the Novists, but I leave such to inquire of the precedencies in a Council of War, and who taking place there will resolve them: And it is well known to most of you I was a Commander of Horse myself; and then having finished my weak thoughts as to the Exercise thereof, which being viewed by some Gentlemen of our Country, I was desired by them to set out likewise some few Collections for the young foot Soldier. It is true there have been many Books printed of this Art in our past ages, and some in our present; and as Solomon saith of making many Books there is no end; yet if it had not been for Books this Art might have been buried in oblivion. And if I should set out at full how all that we practise is not only borrowed from Antiquity, but most of the very words of Command are kept still in use, it would be too large, and it being not my business, I shall acquiesce with what I intended for my private use, but being (as I have declared) requested hereunto, When London was burnt, 1666. Sept. 3d. etc. and now fearing that most of our books are consumed by fire, I am further persuaded to put these introductives to public view. Let me persuade, you fellow Soldiers, although you meet with many discouragements and scoffs in your Country, although taxes lie heavy upon you, and your allowances do not answer your moderate expenses, nay although not your due for your time spent herein, yet go on; for I will boldly tell you that practical knowledge in this Art is the highest step to preferment. We read among the Romans of Lucullus, and in our latter age of M. Spinola, who through maturity of judgement and great Learning became Generals as soon as Soldiers: Intimating that it is the Prerogative of Princes to be born leaders of Armies; But others must expect to ascend this Mountain of Honour by many and difficult steps. Therefore first lay a foundation of honest fame, labouring after the practice of private virtues; Then orderly proceeding to signalise thyself by some public achievements (which I doubt not, but every generous spirit will endeavour the ascension thereof) you may be assured that passing once the brunt of it, even to the hazard of life itself, you'll find delightful pleasures in following the exercises of this Art Military. Who is it that shall think so despicably of a Soldier, or his profession so base, as some have so accounted them? When they that are the sons of Mars and have the true form of Military Discipline, are highly to be esteemed as honourable, and as necessary members in a Kingdom; such as no Kingdom can be without. It is honourable, because it is compassed about with such reasons as that the contemners thereof by the judicious are much reproved; for that State that is not able to stand it out in Arms against the rage of intestine, and foreign violence, is sure to fall into the hands of the destroyer. How can any particular interest preserve itself without it? I will boldly say that the Despisers of the use of Arms, are not only disloyal to their Prince but destructive to themselves. What are the Laws and Civil Orders without defence for the maintenance of them? I may truly term them like a Ship without a Rudder, which being let at liberty to every gust of Wind will be ruined upon the Rocks of Rebellion: Or like some curious Edifice erected without a roof, which cannot withstand the violence of any storm. Constantine the Great, by the persuasions of some peaceable Subjects cashiered his ancient Legions, by which he overthrew the best of his Military Discipline, and so left an open gap for the barbarous Nations to invade the Empire. Solomon in the time of Peace provided for War. What Nation dare to meddle with that People who are prepared, and well exercised in this Art of War? Therefore let every one, Gentlemen and Farmours, Rich and poor, that intent to approve themselves true English men and Loyal Subjects, not only embrace, honour and cherish Arms, but also exercise (and be exercised) and diligently learn this Military Art: that in case any Rebellion or treachery may arise, they may be fit to defend His MAJESTY'S person, with all his rights and Prerogatives: That such as our late intestine ruins may be for ever hereafter prevented: That the Armed servant may no more command the unarmed Master: Nor the Rebellious armed Subject his unarmed Prince. Let us not be overwhelmed in security, but when any sudden Alarm may sound in our ears, there may be always found such ready and fit both to command and obey. Solomon doth in effect tell us, that it is not the great number of untrained men that are sufficient for defence when he saith, A wise man is ever strong; Pro. 14. yea a man of understanding increaseth in strength; for with Wisdom must War be taken in hand; and where there are many that give Counsel there is victory. It is impossible for any Kingdom or Dominion to live in peace, without the use of the Sword: As Idleness and the neglect of Warlike Discipline hath been the ruin of many States; so the Order of the ancient Romans resolved not to lie as sluggards, nor to delight in Idle, or wanton pastimes, but at certain times allotted them in a year for the bettering of their experience in Warlike Exercises, they did it with delight and pleasure, so that no labour herein was burdensome to them: and being become by the practice thereof most ready and expert in the same, became at last, as History hath declared, great and mighty Conquerors. I wish the same of us, that our reputation may not scornfully be laid aside, as if we minded more our Carpets, and the following products thereof, than the Musquett; That through the Exercise of this Military Art, we may become so mighty and Valiant, as that we may be able to withstand any opposition both Foreign and Domestic. Thus wishing prosperous success in all Martial affairs that may be for the good both of King and Country; I conclude and subscribe not only to be a wellwisher to all Military Arts, but in the quality of Your fellow Soldier and Servant Tho. Venn. Introductive Collections; OR INSTRUCTIONS For the Young Soldier, IN Art Military. CHAP. I. Military Observations for the Exercise of Horse. NOtwithstanding what these late Rebellious Times have made to appear, yet there is so much of selfwilled Ignorance, with more than the common sort of people, not only to think, but to say, that in all services and Exercise of Arms, there needeth no more Action, but by these words of Command; Make ready, Present; and Give fire: All other words of Command to be but as tendances to them; and all other postures are by them judged to be but superfluous, and may well be spared; or but trifles of small consequence: Whereas the life and well being of every well ordered Troop of Horse, and Company of Foot, consisteth wholly of form; and those received Ceremonies belonging to every Posture, cannot in the least, in the prime of Exercise be neglected, but with the hazard of Confusion; Matth. 15.14. Quod si coecus coecum per viam duxerit ambo in foveam cadent. The crooked deformity of the bones is covered with the flesh, for the better adorning of the body; so are Ceremonies which by experience (the Ancient have made Reverend) are the life and being of a Kingdom: And here by way of digression, give me leave to say, that which is but truth, that the neglect of Ceremonies formerly used and commanded, proved most injurious to this Kingdom, and yet to this day is an evident demonstration of Faction and Rebellion. It is the ambition of many men striving to be Captains before they be Soldiers, labouring after Command, before they know how to obey; and being well considered, what more is the Mother of Error, but Ignorance? It is well scited out of Vegetius, That knowledge in all things belonging to War, giveth Courage; Nemo facere metuit quod se bene didioisse confidit; No man feareth to do that which he hath well learned how to do: Without a true knowledge in the single Accidence, in this Art Military, (as I may term it) you will never be able to judge of the Syntaxis thereof; without experience in all the Postures belonging to Horse and Foot, none can be capable of exactness in that which is most of use in this Art; for Military Discipline (where with care it is observed) is but a true confirmation of Soldiers in their Valour and Virtue, and in short is performed By Exercise, Order Compulsion, & Example. 1. By Exercise: Good Instructions are nothing without they be followed by care and diligence; for what breeds more strong and resolved gallantry in Gentlemen than Industry? It excelleth nature itself: All the labour and exercise of a Commander from time to time, is not of any value as to the Execution of this Art, either in courage or strength in their Soldiers, without he be industrious to teach, and they also willingly labour after a perfection in the exercise of such Instructions as shall be commanded them; for experience with Instruction is the best way to perfection. Vegetius saith, Paucos viros natura fortes procreate, bonâ Institutione plures reddit industria; Nature brings forth very few strong men, but Industry by good Instruction breeds up many: None ought to be called for to exercise this Art, but such, who are able to produce what they know to action; for that Soldier that is not well taught, can never expect the fruit of his labour (to be courageous in his Erterprises.) Exercitium, Importeth nothing else but exercising an Army, etc. And it is most certain that the Souldery, who are often and well exercised, are much the better; as Varro saith, Exercitus dicitur quòd melius fit exercitando: Thus being willing to be exercised begetteth knowledge, knowledge begets courage; courage obtained, makes perils contemned, calamities despised, and death itself conquered. 2. By Order: There hath been so much writ of this by many Authors, that I shall only say in short, Polybius, Vegetius, etc. It consisteth in dividing, disposing and placing of men so fit; that upon all occasions they may be apt and ready to be commanded, by their Superiors as they shall direct. 3. By Compulsion: That Soldier that makes not this Military Art his delight, but is given to other pleasures and pastimes, (and being accustomed thereunto) contracts an unmanly effeminacy, and degenerates from courage; as Tacitus saith, Degenerate à robore ac Virture miles assuetudine voluptatum: Now all such Soldiers, as are vainly given, and mind pleasure more than commands, aught to be bridled and governed by compulsion. 4. By Example, And they are either in Reward or Punishment. 1. In Reward: That Soldier that expects advancement from his Commander, must be so stout in his resolutions, as perfectly to perform what is commanded: And when he shall answer his Commander's expectation, in the execution of some singular service, he ought to receive Fame, Honour and Riches, as a reward for it. 1. And first, That Soldier whose care is, that at all times his behaviour be such as to endeavour after all virtuous habits, and being so adorned, he ought to have that which virtuous Soldiers most desire and labour after; That is Good Fame: for it is the food of his reputation, and nourisheth towards Honour in the highest Achievements. 2. There is a second reward; and that is Honour: It is not the nature of a true Soldier to hunt after Honour, or to buy it with Bribes; It is blood and not gold, that hath been the price of Honour: Therefore that Soldier that shall thus deserve, ought not to be voided of it, but according to his merits and quality, aught to have his preferment. 3. And lastly; but not the least, the good, saithful, and stout Soldier's reward is Wealth; that when they are preferred they may not be despised, but to be in ability, as to the greatness and smallness of place, to hold up to his Rank and advancement; without These a Soldier can neither perform nor continue the duty of his calling; M. D. 1. p. 27. and therefore the bestowing thereof deserveth great consideration, that the well deserving Soldier at no time should be neglected. It must be acknowledged that Rewards are seldom seen, for Offices are more often known to be bestowed for favour (if not for money) than for desert: What makes many brave spirits to give up their services; but when they see their way of Advancement cut off, and their pay it may be hard to come by; in regard that some Paymasters, or Treasurers have been corrupt, that the soldier shall not have his pay without some unknown fees? And rather than to commit any base action in his Country, he is forced to desert the service; or when their service is ended, without they'll give one part of their just deuce, that they may have the other, they shall be delayed. etc. And this is one reason there are so many unwilling hearts to serve their Country; and what makes a Soldier so despicable in his Country, as to be forced to use extremity even for necessity sake? How base a thing is it for some Deputy Chieftains that make it their study to rob Honour's Workmen of their hire? And if it be so in our Country affairs, and in times of Peace; What can be expected from such in times of trouble? Let such know that Honour's trumpet shall never sound their praises. But to such as shall not in the least debar it from the deserved, but (as I may term it) are rather willing to disburden themselves of their Soldier's stipend; to such, I say, not only remains the obsequious diligence of their Soldiers to serve them in all hazardous attempts; but also the glorious title of a faithful Steward, which draws after it both the affection of Prince and People. 2. There are also Punishments due to those that are Vicious and Cowardly; for nothing more holds a Soldier in his due obedience than the severity of Discipline. Soldiers (as Vegetius saith) ought to stand more in awe of their Generals, than in fear of their Enemies: Discipline being once infringed, either by a slightment of Reward, or neglect of a Soldiers just pay, will cause the Virtuous to desist, and to others 'twill prove a spur, to necessitate them to base Actions; which with other corruptions, when seen by superior Officers, and shall not according to Martial Law endeavour to punish such vicious Actions; I say the Soldier instead of submitting to the Commands of his Leader, oftentimes breaketh forth into Mutinies and Rebellions. I must confess when, and where Reward and Punishments are not slighted, the welfare of a Country will be so supported, that no Vice shall be able to stagger it: So in an Army, what maketh a Soldier to forget obedience, more than the want of Pay and the execution of good Laws? which being duly performed, the Soldier will undoubtedly, the better know his Duty and Discipline. Here, by the way, I cannot but infert some few things that are prejudicial to the Soldier, and Army, etc. First, When the Public Service of God is so neglected, that the whole Souldery, under a Christian Prince are not tied to be Exercised in the same Religion his Prince is of; for Faction amongst them will do more hurt, than bullets against them. Secondly, When high debauchery is not severely punished. Thirdly, When Gaming is not most strictly forbidden; because it is not only a waste of Maintenance, and an Introduction to Quarrels, but a Profanation of God's holy name. And Fourthly, When Muster-masters are so careless in their Office, as to suffer any Captain, upon wilful absence of Soldiers, to receive some out of other Companies, or hired men out of the Town and Country; this being well considered will prove prejudicial both to King and Country. And lastly, When those strict Laws against Duelling are not better observed, that for every trivial quarrel, the life of a stout spirited Gentleman must drop. Fol. 183. etc. For better satisfaction, read Ward's Discourse of unjust Valour against Duels. CHAP. II. Of the Soldier, and Officers in General. IT is not my intention to run through the description of every particular Officer at large, of his duty in his respective place; it being set forth at large in several Authors: I shall therefore briefly pass them over; hoping it will be the endeavour of all that undertake any Office Military, in the service of his King and Country, to labour after a true form of Discipline, that is now in exercise by Authority in general; That when it shall please our Gracious King to call for us, we may not be uncapable of Command: What greater dishonour can there be than for a Commander to be commanded by his inferior Officers? Therefore it behoves all in their several Capacities, who are willing to win Honour; not to be wanting in their endeavours after the Exercise of Arms. 1. Of the private Soldier. None were admitted Soldiers among the Romans, but such as were of an honest Tribe, (or Family, as being more likely to labour after Victory, not only for his Liberty, but for his goods, or estate.) As for those that were absolutely necessitous, they might have liberty promised by their Enemies, and so betray their Trust. Again, they would never take any Soldiers into their Armies, but such as were well exercised beforehand; and this did their work, and obtained them Victories against their Enemies, Vegetius, Lib. 1. Chap. 8. The private Soldier's duty is as followeth. Whensoever he is commanded for service, let him labour to be sober, and patiented, enduring all hardships and travels; To know and observe all Orders Military, Liv. Completely Armed, and expert in the use thereof; Horridum militem esse decet, non caelato auro argentóque, sed ferro. It becometh a Soldier best to appear terrible; not to be garnished with gold and silver, but with steel. And Soldiers ought not only to be obedient to their Captains; but chief to Love God, and Honour their King. This being the duty of a Soldier in general, there are two particular duties belonging to him, that is, as a Sentinel and a Scout. 2. Sentinels; The further any Sentinels are set from the body of the Guard, it is thought necessary two should be placed, and there they are to endeavour both to hear and see, thereby to learn of their Enemy, what may be intended, and what they have discovered; that whilst one goeth to certify the Captain of the Guard, the other may stand fixed, and observe what else might happen in his fellows absence. A Sentinel must not alight from his Horse unless it be for natural necessity, and but one of them at once. Near to the Body of the Guard there may be placed but a single Sentinel, to observe the moving of the double. If the distances be not too large, if there be any other Cross-ways or advenues, that each Sentinel may see the other, then there may be but a single set; for they must know that they are set there only to certify the Body of the Guard concerning the several occurrences that may happen: Suppose a Sentinel should be provoked by any advantageous affairs; It is resolved he must not stir a foot; for that Sentinel that shall by day or night, remove from the place where he was set by his Corporal, before he shall be by him fetched off (or relieved) shall he punished with death. Polyb. lib. 1. If the whole Troop be upon the Guard the Lieutenant is to set forth the first Sentinels with the Corporal, according to his directive Commands received, Directions. and to change them, conducting them to his Guard; (but the Cornet is not to forsake his Standard;) Then the Captain of the Guard is to go the first Round, to see not only that all things are safe, but also whether th●se Sentinels are vigilant: And upon his return, there are four other Rounders to be sent twice in a night, to discover round the Quarters. Observe, that no Sentinel is to have the Word, but Officers and Corporals. 3. Scouts; They are not only to discover the Highways, but also to scour them: they are to be of a number, answerable to the danger of the Guard; for the hazard of them, may prove dangerous, both to a private Guard or an Army in General. They are to give notice of the Enemy's motion, of his approach, and of the number of them, that all sudden surprises may be prevented. 4. A Provost Martial; For the badge of his Office he is to have in his hand a staff or Truncheon; and having the same in his hand, it is death for any Soldier violently to lay hands on him: All Delinquents are to be delivered to him, by the Chief in Command. He is not to enter any quarter without the leave of the Chief Officer for any Prisoner; He is to clear all byways of Soldiers, that no prejudice may be done by them in their March; He is to see all Orders published, be duly executed; He must be an honest man, and take no Bribes. 5. A Trumpeter, aught to be a man skilful in all the sounds of the Trumpet distinctly; He ought to deliver all Embassies, etc. He ought to observe the Enemy's Works, Guards, and Soldiers, that he may give a good account thereof at his return: And for the better performance thereof, he ought to be a man witty and subtle, and to manage it discreetly; He ought not in the least to discover any thing, as may prejudice his own party; He must not fail to sound the hours commanded: One Trumpet is to be with the Cornet, and he is to be allowed by the Captain for him; who is to receive a list of the Guards from the Cornet, and is privately to warn the Soldiers thereof. 6. Corporals, in a Troop of Horse, have been always allowed to be of great use; who ought to be of a civil carriage and stout spirit; they are to be three or more, according to the allowance of Horse, etc. They are to be assistant to the Lieutenant in placing of the Sentinels, each in their several squadrons when they are to perform duty: If any parties are to be sent abroad, either for discovery, or to scour the highways, a Corporal is to be sent with them; He is bound to keep a list of his Squadron. 7. A Quartermaster, aught to be a man of much fidelity in regard of distributing of the Word and Billets; He is to have the Command of the Troop in the absence of his superior Officers: Who in going to make his Billets is to have a Soldier along with him by the appointment of the Lieutenant, who is to return to the Troop to conduct them to their Quarters. 8. A Cornet, aught to be a man of gallant behaviour and undaunted courage; His place in the Troop upon a march is on the front of his own squadron; and to take the Standard himself, marching through any great Town or City (or when commanded) or into the field with it flying; and when any General shall appear in the field he is to drop the head of his standard towards the ground in obeisance to him. His Place when the Troop is drawn up (to the opinion of some) is for to exercise upon the left of the Captain, somewhat behind the Captain; But in fight or skirmish, he is to place himself in the first rank of his own squadron; with his staff sunkt or slopped; and in danger, it is more honour to break his Lance (or staff) himself, then to suffer his standard to be broken and taken from him: He is to keep a list of the Troop, and wait every day upon his Superior Officers; and such Soldiers as his Captain and Lieutenant shall appoint he shall send to the Guard: In the absence of the Captain and Lieutenant he is to command the Troop. 9 For the Lieutenant; The Rear is assigned him for his place, and was anciently called Tregidux, that is a Rear Commander: And Lieutenant is a French word signifying one which supplieth the place of another; for in the absence of the Captain he commands the Troop; appointing an Officer to be in the Rear: He ought to be a man well educated in Cavalry, and in the other parts of the Art Military. He ought to be strict to see the soldiers punctually to do their service, and to have a care to their Horses and Arms in the field and fight. He being in the Rear is not only to encourage the Soldiers, but to have his sword drawn, and to kill any that shall endeavour to flee, and not to fight. He ought to know the ability of his Soldiers, keeping the list of their names; that the Guards may be in a readiness, with the Captain's consent, and by him delivered to the Cornet. In the mounting of the Guard, he is to inform himself of the place for the Guard, and of the Sentinels for to set, the ways for to be scoured, and must go himself with the Corporal of the Guard, and see the first Sentinels placed; And when he hath the Guard himself, he must often visit them; always to be armed and to keep his bridle day and night upon his horse's head. When the Troop is drawn up to lodge the Standard; He is to see the Quartermaster deliver to the Soldiers their respective Billets for their quartering, upon that Alt before they move, for then the Soldier will know thereby the better where to wait on the Cornet upon any occasion. He ought to visit all Quarters, as to his list received, and see that the Soldiers be of civil bevaviour; and if any complaints be made of any disorder, he is to remedy it, by punishing the Offenders. When the Trumpet sounds to Horse, he ought to be first mounted, and to cause all immediately to do the same; He must punish all lingering and lazy Soldiers that are not presently mounted with him. The good Examples of a Leader have ever been observed to be of a marvellous efficacy with the Soldiers. 10. Every Captain ought to be obedient, valiant, and resolute in the execution of all Commands with Judgement, discretion and Valour; that with virtuous nobleness and generosity he may win the love of his Soldiers, to their King, Country, and himself; and that by his own experience in the knowledge of Military Discipline, he may be able to govern his Soldiers accordingly. 11. Colonels, They ought to have an high respect with all Obedience to their higher Officers, faithfully to perform their Commands, and that with care, valour, affection and diligence they govern their Regiments. 12. And when every General shall make his whole Army to love and fear God, and shall govern with prudence, care, order and Justice; and knowing how to prevent, remedy and execute, as occasions shall offer themselves, with great skill and dexterity, will make himself no less loved than feared. From these Officers, the Trained Bands of this Kingdom (with the Ships) are the defence thereof (or aught to be;) but to speak of the choice of the Soldiers, or of their being armed, or well disciplined, (as in many places is much neglected,) and where the fault is, as I am an inferior Officer I must be silent: Pardon me to say it would be much better if his Majesty's Deputies would cast their eyes and commands oftener amongst them. I could wish that our Militia instead of celebrating their Feasts to Mars, did it not too much to Bacchus with carousing and drunkenness; which folly and detestable vice is an Enemy to all Virtues, both of soul and body; (and to all Military Discipline.) It is the very Nurse of Effeminacy, of Cowardice, of Sensuality, of Rebellion, and of all other Vices that can be imagined. This was a Foreign Vice brought in amongst us by our Neighbour Commanders, quaffing and carousing, until as the Fleming say, Do't Drunken. It is a sad thing that any that bears affection to Military Affairs, should make such fruits the merchantable effects of that Discipline; I am sure he is no true Soldier (nor Subject) that shall follow such beastly ensamples; when it is the Command of our Sovereign to the contrary: All must know they are bound to obey Authority; and let all true hearts take that for his Card to steer the course of his Loyalty by. CHAP. III. Of the Arming of the Cavalry. THe Cavalry are required in their Persons, Arms, and Horses, to be suitable to their several ends and Employments: There were among the Grecians and Romans two bodies of Horse, a light-armed body, and a heavy-armed body; the light-armed were to give the first onset to the Infantry, to make way (as I conceive) by disordering the Enemy; then the heavy-armed Horse were to take their advantages for Victory. There were and are to be taken notice of five several kinds of men at Arms for the Horse service Lanceirs, Cuirasiers, Harquebuziers, Carabiniers, Dragoniers. 1. Lanciers, they were offensive, but chief defensive, and were armed Capa pe, with Swords and Peternels, somewhat longer than our ordinary Pistols now in use, with a Lance of about sixteen or eighteen foot long. It hath been adjudged by our Royal Generals, and found by experience of late years not so serviceable, because not so nimble for any sudden erterprises, or field services as our light-armed Horsemen are; therefore wholly laid aside: Besides they were not always of effectual use in a body, for execution, but in a strait line, upon a Career, and where they must have both leisure, and room enough to work their designs; which I leave to the Judicious to give their Verdicts herein: for if men in our days should be laden with such Arms, how would they be able to command a Lance at that length: If there were such inconveniences in the weight of the Armour and Weapons as the then after experienced found many; yet our men are much weaker, and wholly unable to undergo the burden thereof; upon these considerations the use of the Lance was then left off; so that the Horse were called 2. Cuirassieers, who were both for Horse and Arms in no wise inferior to the Lanciers (his Lance excepted) and are also offensive but chiefly defensive; but not subject to those inconveniences as the former with their Lances: He is to have under his Armour (which is Capa pe) a good Buff coat, and good Peternels with a Sword whose point must be stiff, and sharp, his Saddle and bit strong, and his bridle with an Iron chain to prevent cutting: he is to have a boy to carry his arms, and to forage for him. These are the heavy-armed for the Horse service which are not used amongst us, especially in our settled Militia, nor but few of the next, which are termed. 3. Harnuebuziers, who are very serviceable and are to be armed defensive with a good Buff coat, and to have a back, breast and pot, Pistol proof: and for his offensive arms, he is to have a good Harquebuz, hanging on a Belt, with a swivel, and serviceable Pistols, as is set forth in the Horse service by Act of Parliament for the service of the Militia, but rather somewhat larger, and a good cutting sword; His Horse should be somewhat better than the Militia Horses, as is set forth in the said Statute, with a strong Saddle, and bit; and his bridle to be made with a chain that the cutting thereof may be prevented. 4. Carabiniers are to be armed defensive as the Harquebuziers, their Horses may be somewhat lesser, but for the offensive Arms instead of the Harquebuz, a good Carabine, hanging on a belt with a swivel, by the ring of the Carabine; but for Pistols and Swords, they must be according to the Act of Parliament for the Arming of a Militia Trooper, as in the said Act more at large appeareth. The service of them in execution is not to be disputed; the Experienced Soldier can testify enough of the singular benefit they are of in service; although it is not regarded in some places in the Country, I believe it is not their Judgements, but rather their unwillingness to put themselves (the rich men of the Country) to such a charge, and not to walk one step further than the bare words of the Act of Parliament will empower them. I hope when his Grace the Duke of Somersett shall appear in the head of the Militia of the County of Somersett all defaults of Men, Horses and Arms will then be most regularly amended: And then the Souldrie in general and the Horse in particular, being made complete Carabiniers, the men and horses to be one and the same, kept, preserved, managed, and made fit for service, his Majesty may the better trust to his Militia, who may be also capable of doing him and their Country service. Wounds are never feared by them, who are well horsed, well armed, and well exercised. I crave pardon of the Ingenious Reader if I digressively propound a question or two, and I wish the guilty would answer them by their good examples in better perfomances hereafter. How many of those Gentlemen that should find Horses for his Majesty in the service of the Militia, will send no other, but such as are common for all uses? Instead of keeping them in their stables, well meating, and managing of them fit for service, they'll send them long journeys, set them to plough, or other carriages and draughts, not regarding how suddenly they may be called for service. How many send in their Arms resty and unfixed, not fit for service? some have sent base pads, ordinary hackney saddles; others for covetousness have sent their servants with snafle bridles; How many are there that borrow Horses and Arms one of another? And I am truly sorry to see some sufficient Gentlemen that have taken so much pains to ride for to ease themselves, or to be freed from reasonable assessments upon them. I wish some could clear themselves that command us, whose Horses ought to be the first that should appear, and best equipt, from being the worst and last, nay not at all to some Musters; for this the Country murmurs at: And how can our returns of defaults be executed against the Criminal, when Justice itself is guilty of the same errors? It is the good examples of our Superiors, that should make the Inferior tremble to do amiss, etc. I could wish that all neglects for the completing of His Majesty's Militia might be amended hereafter, according as Authority hath commanded; and for such as must be subject thereunto, they would most willingly be obedient, and to close with their Commanders in any thing that may advance the public service, and not to be stupidly secure, and basely to undervalue the use of Arms: Let such know that I do boldly affirm it for a truth to be a symptom of disobedience and disloyalty. 5. The Dragonier. Dragoones are but Foot, (to be) on horseback and are so mounted for the expedition of their march, who are to have large leather belts, for the more easy carriage of their Pikes and Muskets, in some extraordinary service, for making good of passes, linening of hedges, and other ambushments: But if you raise any Regiments of Dragoons, and so are to march, and to be in a readiness, for the like expedition; their Muskets are to be somewhat wider in the bore than the Field Musket, and about two foot and nine inches in length, and Pikes (if allowed) not to be above thirteen foot in length; his Horse must be of a good mettle and nimble, but of a less price and stature. And in the execution of any service (when commanded) they are to alight, and to every ten soldiers there is one to be allowed to hold their Horses. Some have been of an opinion that he is of such excellent service as that the duty of the Carabinier may be wholly laid aside; whose arguments have been judged frivolous by the judicious in this Art, that I need not trouble you any more with them, but do declare that Musquetiers on horseback to be made Dragooners upon some special service; or that the Dragooner himself may be very useful for expedition and enclosed Countries, etc. I have treated of the Soldier, and of arming of him. I humbly insert; Seeing the whole burden lieth upon the Loyal hearted subject, and the discontented party sit still, grow rich and laugh at it, therefore it hath been the opinion of some Gentlemen, that the discontented party should be armed in the Trained Bands, and made to perform and execute all commands whatever. I am of an other opinion, but shall not presume a determination in this place. CHAP. IU. Of Military Signs. IT is requisite that every Soldier should understand (or learn) all Military signs, and directions; for experience hath taught, that the neglect and error in the right understanding of Signs, hath brought great inconveniences, and quite overthrown enterprises in hand. There are three signs used in War Vocal Semivocal A Mute. 1. A vocal Sign is that when a Captain shall so immediately command, as that every Soldier shall hear him distinctly; or else by some inferior officer to the ear of the Soldier. A Semivocal Sign is that which is distinguished by the Trumpet, or other warlike instruments: In which as to the horse service; the Soldier is to take notice of six points of War, which are Commands to the ear by the sound of the Trumpet; And it ought to be performed with care and diligence. Those Commands that are by the Trumpet sounded out to them are as followeth. The six points of war are Butte Sella Mounte Chavallo A la Standardo Tucquet Charga Anquet. 1. Butte Sella; Or Boutez-selle; when sounded is, Clap on your Saddles. The Soldier must then make himself ready, and horse with all expedition. 2. Mount Chavallo; Or cheval; when sounded is, Mount on Horseback. The Soldier than bridles his Horse, leads him forth, and mounts him. 3. A la Standardo; Or A Standart; when sounded is, Repair to your Colours, or Cornet. Upon this the Soldier must go to his Colours, in order to his march: But when he heareth it sounded in the Field he must retire to them with all Speed. 4. Tucquet; Or, March: When this is sounded he is presently to March; in which he is to observe his right-hand man, and to follow after his Leader. 5. Charga; Or, Charge: When this is sounded, by and with the examples, or directions of his Commander, the Soldier is to give proof of his valour in the speedy charging of his Enemy. 6. Auquet; Or, Watch: When this is sounded at night the Soldier is to repair to the place for mounting of the Guard for Watch; Or at the morning for dismounting of the Guards. I have read of another sound called Attend Ho, for listening unto, A call for summons, A Senate for State; and the like. This when sounded, the Soldier is to hearken unto it, that he may the better be able to perform those Edicts that shall be then commanded. The third and last Military Sign is 3. A Mute; That is by signs to the eye, as by the Cornets Colours; or other motions by the hand of the Commander, etc. You see there are two principal senses of Advertisements, the Ear and the Eye; the true observation and use of these signs availeth much in War: for he that is negligent in either, may not only lose himself, but be the cause of the loss of many others; so that by being careless herein, Victory itself is often lost: How careful ought every Soldier then to be, that by silence he may the hearken to all Commands; that by the Vigilancy of his eye, he may the better observe, Vide Chap. 5. every sign that may by given. For Vegetius saith, that nothing profiteth more to Victory than to obey the Admonitions of signs. CHAP. V For the Marching and drawing up of a Troop of Horse. EVery Troop of Horse must be furnished with a Captain, Lieutenant, Cornet, and a Quartermaster, two Trumpeters, a Clerk, a Saddler, a Chirurgeon and a Farrier. And every Troop is usually divided into three equal parts; each of which is called a Squadron; and are severally known by the Captain's, Lieutenant's and Cornet's Squadron; accordingly there are three Corporals. There are as great diversity of judgements almost as Authors about the placing of some Officers either in their marchings of a single Troop, or being drawn up into a Battalia. Some would have the Captain and one Trumpet in the front; Then the Cornet leading of his Squadron, and the third to be lead by the Eldest Corporal; and the Junior Corporal in the rear, Ward fo. 26. with the Lieutenant who hath the command of a Trumpet with him. Markham varieth something from this and but little, only the two junior Corporals to be extravagant in the March, who are so ordered on purpose to keep the Soldiers in their Ranks and to be orderly in their March: Both Ward and Markham marcheth six in file, but Ward marcheth Five in Rank, and Markham Four only: Others again differ in placing of Officers both in March and Battalia; as, Walhawsen would have the Harquebuzier to March eight in File, and the Cuiraster ten in File. But Markham and Ward being later Discipliners in this Art Military, I shall only insert two platforms accordingly. platform platform These of Markham and of Captain Ward are deciphered six in File; and a File so drawn is distinguished according to their dignity of Place, a Leader, a Follower, two Middlemen, a Follower, and a Bringer up. The Ancient Dignity of a File. 1 Dignity of place. 1 H Leader. 2 5 h Follower. 3 4 H Middle man to the front: 4 3 H Middle man to the rear. 5 6 h Follower. 6 2 H Bringer up. Cruso exerciseth eight deep, and therefore useless to our mode of fight; for our Custom is to make the Horse but three in File. I shall not stand to answer the objections on both sides, but shall leave it to the most expert in this Art; I conceive it enough that our late experience hath taught otherwise; And our present discipline being in practice to the Contrary. Accordingly here shall follow a Troop of threescore Horse marching with each Officer in his respective place, and also the form of a Troop drawn up in a body. And when you march through any City or Town, Observe. your Pistols must be loaded, and so fixed, that you may be in a readiness to fire when ever occasion may be offered and command given; having one of your Pistols drawn forth of your Holster, mounting your muzzel, and resting the butt end thereof upon your Thigh. rank and files A Troop marching to our present mode. A Troop drawn up. In the March some place the Quartermaster to lead up the Lieutenant's Squadron, and the two other Corporals to be extravagant, that is to view and see each Soldier to keep his place. In private exercises it is not denied but the Quartermaster may lead up the Lieutenant's Squadron; But it is conceived best to place the Quartermaster in the Rear; for it is presupposed that he is or may be to take up Quarters, etc. CHAP. VI The Exercising of a Troop, as Armed with a Carabine, and Pistol. THe Horse being in a body to exercise, and to make the Soldier more able to handle his arms, when he shall be called forth to fight; The words of Command shall follow. Notwithstanding there is but little difference between the words of Command for the Pistol with a Snaphans, and the Carabine; I shall however give them severally. Although Mounting to Horse is no Posture of Arms, and but a preparative to exercise and Service, I shall presuppose the Soldiers to be dismounted, and stand ready by their Horses in a body; The word of Command (according to our English mode is) To horse. Now all being ready to Mount must be careful that his Horse be well girt, etc. And as a preparative to Exercise there is another word of Command [Silence] Without there be silence in the body, the Soldier in no wise can distinctly hear, what is commanded by the chief Officer; It is the Soldier's Ear, and care to preserve the body from fractions, and where Silence is not diligently performed, the Soldier doth not only fail in his motions, but the event will be naught, for it is the very footstep to rashness; And it is as Livius saith (Temeritas praeterquam quòd stulta est etiam infoelix) not only foolishness, but infortunate. The words of Command for the Carabine. All the Carabines being dropped (let fall) and hanging by their Swivells; The Postures are as followeth. Silence being commanded. 1. Handle your Carabine. Postures. 2. Mount your Carabine, Some term this Order; and others against that, because it's proper to the Pike. placing your butt end upon your Thigh. 3. Rest your Carabine in your bridle hand. 4. bend your cock, to half bend. 5. Guard (or secure) your cock. 6. Prime your Pan. 7. Shut your pan, (or fix your hammer.) 8. Sink your Carabine on your left side. 9 Gage your flask. 10. Lad your Carabine. 11. Draw forth your scouring stick (or Rammer.) 12. Shorten your Rammer. 13. Lad with Bullet and Ramm home: 14. Withdraw your Rammer, (or scouring stick.) 15. Return your scouring stick. 16. Recover and rest your Carabine in your bridle hand. 17. Fix your Hammer, (or Steel.) 18. Free your Cock. 19 Present your Carabine. In presenting of the Carabine, he must rest it upon his bridle Arm, placing the butt end to the right side near the shoulder; or at length with his right hand. 20. Give fire. Note; That the Carabine is to be fired about twelve foot distance, and to be leveled at the knees of your Enemy's Horse, because that by the strength of the Powder and motion of the Horse your shot may be at Random. 21. Drop (or let fall) your Carabine. These Postures may serve for the Harquebuz; but observe, when at any time you make your Approaches towards an Enemy, your Carabine is to be mounted, with the butt end on your thigh, with your hand above the lock; and so when you march through any Town or City; otherwise to be dropped. Here follow the Commands for the Pistols. Postures. 1. Vncape your Pistols. 2. Draw forth your Pistols. This must be performed with the right hand; the left Pistol first, and then to mount the Muzzel. 3. Order your Pistol. Rest your Pistol a little in your bridle hand, and then immediately take your Pistol near the middle part of it, and place the butt end upon your thigh. 4. Sink or rest your Pistol in your bridle hand. 5. bend your Cock (or draw up your Cock to half bend.) 6. Secure, or Guard your Cock. 7. Open your Pan. 8. Prime your Pan. 9 Shut your Pan, or, order your Hammer or Steel. 10. Cast about your Pistols. Which is to be done against your left thigh, with your muzzel upwards in your bridle hand. 11. Gage your Flasks. 12. Lad your Pistols with Powder. For your more speedy lading of your Pistols, there is lately invented a small powder flask, with a suitable charge; but it is not to be denied but your Cartroaches are very serviceable. 13. Draw forth your Rammer. 14. Shorten your Rammer. 15. Lad with Bullet and ram home. 16. Withdraw your Rammer. 17. Shorten your Rammer. 18. Return your Rammer. 19 Recover your Pistol. 20. Fix, or order your Hammer, (or Steel.) 21. Free your Cock. 22. bend your Cock, at full bent. 23. Present your Pistols. 24. Give fire. In the firing of your Pistols, you are not to fire directly forwards, to your Enemy's horses head, but towards the right hand with the lock of the Pistol upwards. 25. Return your Pistol, etc. The Soldier having fired and returned his Pistol, (if time will permit him so to do) he is to take himself to the use of the sword, (his sword being drawn and placed in his bridle hand, near to the hilt of the sword) and having received it into his weapon hand for service, must place the pummel upon his right thigh, and so to raise his point to his mark, higher or lower, as occasion serveth, and therewith to endeavour to disable his Enemy, either by cutting his Horse's bridle, or other his Arms, that he serveth in, which if discreetly managed will prove perilous to them. And further, it is very requisite that the Harquebuzier and Carabinier be often exercised to shoot bullets at a mark, that in time they may be approved marks-men: In order to which they are to take special care not to over-charge their pieces with powder (as it is too much an error in many, endeavouring more for a report, than for execution;) Wherefore there ought not to be in proportion for any piece, but almost half as much the weight in Powder, of the bullet; or, the Diameter and half of the piece is charge enough: And it ought to be the special care of every Commander to see that his Soldiers be served with good powder and well cast bullets; and that their bullets be directly fit to their Carabines and Pistols. I should now come to show you what is to be learned by a Soldier, for the better demeaning of himself being joined in a body. But shall not in this place show at large what is meant by a File, or Rank; half files or half ranks; front, Read in the exercise of the foot, pag. flanks, or rear; because it will spend too much time, and our late unhappy differences have given some light thereunto: besides there is so much writ of them in several Treatises of the Infantry, that it would be too much trouble here to treat thereupon. CHAP. VII. Of Distance. EVery Troop consisteth of Ranks and Files. Note, That in drawing up of a Troop it must be performed by files (not by Ranks) and by squadrons; as Chap. 5. In Order to distance, I must briefly declare what a File and a Rank is. A File is a sequent Number certain, See Foot, Ch. 3. standing head to crupper in a strait line from the Front to the Rear; and according to our Mode of Discipline consisteth of three Persons. 1 h 2 h 3 h A Rank is a Row of men uncertain in Number; Pouldron to Pouldron; even in breast, be they more or less, according to the quantity of Soldiers, as it falls out, to make a Rank. rank There are to be observed two sorts of distances, or orders in File and Rank. Viz. Close & Open Order. Close Order in Files is three foot, or as occasion serveth, closing knee to knee: Open Order in files is six foot; Close Order in Ranks is three foot, or as occasion serveth closing to the Horse's crupper: Open Order in Ranks is six foot. And herein you must further know, that there is a difference between the manner of taking the distance, of the Cavalry and the Infantry: In the Foot the distance is taken from the Soldier's body; which cannot be understood in this place, but only of space of ground between Horse and Horse. CHAP. VIII. Of Motions. There be four kind of Motions, Face, Doubling, Counter-marches, Wheelings. BUt some of these being not of use to our present mode of Discipline; therefore I shall treat no more of them, but what may be useful. 1. Face are used to make the Company perfect, and to be suddenly prepared for a Charge, on either Flank or Rear. With 10. 8. and 6. in depth. 2. Doubling, There hath been used in the Horse service these following, as 1. As to strengthen the Front. There were used to strengthen the Flanks 1. Doubling of Ranks. 2. Doubling of half Files. 3. Doubling of the Front by bringers up. 4. Doubling of Files. 5. Doubling of half Ranks. The three first as to our Mode of Exercise may be wholly laid aside, in regard they cannot be performed, the Troop being but three in depth. It is conceived the other two may be necessary; either for Exercise sake, or in regard of some sudden Onset, on the Flanks, thereby to strengthen them; but I otherwise think this may be prevented by a speedy wheeling. 3. For Counter-marches, which is but the reducement of File-Leaders into the place of bringers up, or one flank into the place of another; which is more proper for the foot service, than useful in the exercise of the Horse: yet because some have used it in their exercise; therefore I shall demonstrate one Countermarch by Figure in his place. 4. For Wheelings; They are of most excellent use in the service of the Horse, and aught to be very carefully exercised by every Commander; they serve in some respect to execute what is to be performed by Counter-marches; which is to bring the Frontiers, who are always supposed to consist of the ablest men, thereby to be ready to receive the Charge of the Enemy in either Flank or Rear; which by Counter-marches you cannot do. Accordingly the Motions shall follow; that the untutoured Soldier may the better apprehend them; It shall be represented by the Letter h. motion All Motions are to be done entirely, at one and the same time: for in our Military Exercises they are the very life of an Army; and the only means being truly performed that giveth Victory; without which all preparations of Forces are in vain, and avail nothing in the field to the end for which they were levied: And this among experienced Soldiers is of inestimable reputation. 1. To the Right Hand. motion Note, That in all Motions, before a second be commanded (I mean in all single Motions) the body must be reduced to his first proper form. To Reduce them command To the left, or To your Leader, or As you were. 2. To the Left Hand. motion To reduce them command To the Right, or To your Leader, or As you were. 3. To the right hand about. 4. To the left hand about. This is by turning to the left hand until their Faces front the Rear. ranks The proper Front. To reduce them. To the right hand about. 5. Ranks open forward to your double distance. ranks 6. Files to the right double. 7. Files to the left double. files It is most convenient for the Horse to move from the right hand. To reduce them. Ranks to the right double, or Files rank as you were. 8. Files to the right hand Countermarch. 9 Files to the left hand Countermarch. files Foot pa. 60. To perform this Direct, That all the file Leaders move their Horses entirely a little forwards, and so likewise turning off to the left hand, they march even in rank down to the Rear; and none of the rest to turn off until he come to his Leaders ground. To Reduce them. Countermarch to the left. As this is for the maintaining of the same Ground, so there may be a Countermarch for the gaining of Ground; but I conceive them wholly useless but where you have not ground to make your Wheels: Therefore not knowing what necessity may force us unto; it is convenient the Soldier should be sometimes exercised therein. Note, That in your Counter-marches for gaining of ground, the Soldier is to turn off the ground his Horse stands upon, and so passing through each is to follow his Leader. 10. Ranks close forwards. ranks 11. Files close to the left. files 12. Files close to the left to your close Order. files Observe in closing to the left, the left File is to stand fixed, the next are to move to the left. 13. Ranks close forward to your close Order. ranks In performance of this Command the first Rank is to stand; the second moving, and taking its distance, stands likewise; and so the third. It cannot be expected that any Wheeling of the Horse should be so exactly performed in so little a compass as is taken by the foot; therefore every Commander ought discreetly to take larger room for the compass of his motion, so that all his Wheelings may be performed entirely without distraction. Note, That Wheeling to the left for the Horse is the readiest way, except you are prevented by some hindrances, etc. 14. Wheel to the left hand. In this motion the whole body moveth to the left, upon the left hand file-leader as the centre wheeling motion And so you may keep wheeling until you have brought them to their proper front: So if you wheel them to the left about, the Rear then will be their accidental Front. 15. Wheel to the right and left by Division. wheeling motion The Wheelings of the accidental Fronts upon both Wings into the proper Front, and close their Divisions, will reduce them. 16. Trot large and wheel to the left. Wheeling to the right will Reduce them, or by a circular Wheeling of them until they are brought into their proper form. 17. Trot and wheel to the left about. This bringeth the ablest men to be in the Rear for any speedy Onset; and Wheeling to the right about will reduce them, etc. The word Alt doth signify to make a stand, and is derived from the Dutch word Halt; which is as we say, hold, etc. Observe that in all motions you make an Alt, that the Souldery may settle themselves in their places, both in Rank and File, before you put any fresh Command upon them. 18. Gallop and wheel to the left. 19 Gallop and wheel to the left about. To reduce both these is by wheeling to the contrary: All these being performed to reduce them to their first form; Open first your Ranks, and then your Files: and in opening of your Ranks, the best way is to open them forwards. CHAP. IX. Of Firings. I Had thoughts to have treated of Encampments and Embattelings, but that being not my work at present I shall pass them by, because it is my business to treat only of the exercise of a single Troop: In the first place I shall set out one firing of Walhausens; When your Enemy chargeth you in a full career, Cruso fol. ●9. you are suddenly to open to the right and left, facing inwards and charge them in the flanks, and when the Enemy is passed your body, you are to wheel to the right and left inward, and so charge him with a full career in the Rear; but here you must observe their files to be six, and eight in depth; and so his Figure is represented as followeth. firing files This he commends very much, for whilst the Enemy is upon his Career, you are but upon your Trot; and then opening to the right and left, This he speaks of Cuirasiers. either he must run through, and do but little execution, or else Alt in his career, and so disorders himself, which is advantageous to you. But I am of another opinion as to our Mode of fight, being but three in depth; we must rather sink than suffer any Voluntary Breach. The same Author would have our Harquebuziers to give fire by Files, either right or left, advancing before the Body in a full career towards the Enemy; but many do wholly reject it, as being dangerous in Field service. But now for the private exercise of a single Troop, which may be necessary to bring the Soldier to a more ready and complete use of his Arms, I shall demonstrate of Files firing in the Front and Rear, and then of firing by Ranks. And first of Files firing in the Front. firing files 1. Files firing in the Front. The right hand File and the left hand File March some distance before the head of the Troop, and Rank themselves to the right and left inward, and so Present and Give fire; which being performed, let them wheel off to the right and left outwards into the Rear of their first Station, and so set themselves in their respective places even with the remainder of the Body, leaving distance for every Rank to march into his proper place, after they have once fired over. firing files 2. Files firing in the Rear. When they have thus fired they are immediately to fall off to the right and left, and March forth into their places. As you observe in each firing both the Files do rank themselves and then fire: Now a further exercise you may Command for each File to face in opposition, and fire each to the other. firing files Firing in the Front, & firing in the Rear. I shall now demonstrate one platform of firing by Rank. firing ranks But in firing by Rank, observe the first Rank may advance upon a large Trot Gallop, or Carrere, as Command is given between thirty or forty paces from the Body. The first Rank having fired wheels off to the left (if occasion will permit) and falls into the Rear; and immediately upon the wheeling off of the first Rank, the second advanceth according to Command and fireth, and so the third. You may fire also by divisions which is of singular use in the exercise of Horse; either by firing by single divisions both in Front and Rear, or in opposition both in Front and Rear also, as in firing, of the Files before mentioned; so that I need not trouble you with any platforms of them. After that these firings have been performed and the Soldier is grown expert in the handling of his Arms, and well managing of his Horse; there is one thing that ought not to be forgot by any Commander, which is of most excellent use; That is, for the Soldier to be well exercised, both with his Carabine and Pistol to shoot with Bullet at Marks; which if it be not well exercised and taught, it will be to little purpose as to the Executive part of this Art. So it ought to be the care of every Chief Officer to exercise those Troops under his Command, sometimes, as occasion may serve, in a Regimental way; leaving sufficient distances between each Troop, that each other may be relieved orderly; and so to retreat in due order, to avoid Confusion. CHAP. X. The Conclusion. BEfore I conclude these few spent hours about the Exercise of the Horse, and that my demonstrating of them but three in depth; I hear many brave Soldiers (but old ones) to make some objections against me. As first, in meddling with that which is of too high a concern for me. My answer to that is briefly; That those that have writ Books of this Art, although they have been gallant Soldiers if they had been in Command now, and of late years to have seen what have been performed in the Executive part of the Horse service, they would correct their Judgements, and amend their Mode of Exercise, finding in it much error, and serviceable for nought, but to prolong Execution; as if all experienced genus in this Art should be tied up to the Low Country services: And what I have done is but my duty if accepted, else for my own private use, also for my friends and relations that come after me; And because there ought to be a great deal of care had in a work of this nature, I leave the correction hereof to the better Learned and more Experienced in this Military Art. And for the drawing of the Horse but three in File; I say, If the Grecian Writers were alive, and some of our Modern Writers that have Commented upon them and made Collectives out of them, which they have published for authentic Maxims in this Art, would now much admire to see our Mode of Exercise so changed for the better. 64 in a Troop. When as our late Cruso in his Military instructions in his platforms of Exercise demonstrates then Eight in depth, and Eight in rank: And Captain Ward in his Drilling and exercise of Horse is six in File and twenty in Rank, Leo Ch. 7. Sect. 81. Ch. 14. Sect. 78. 108, 109. and allegeth it for the best, and is taken out of Polybius, General of the Achaeans Horse: Leo writeth almost the same; That if there be many horse to be exercised, they are to be ordered ten in File, and if but few no more but five, giving this reason; That if the Body be but shallow, the Body will be so weak, that it is subject itself to fraction: Then Livy verifieth that of Leo, and saith the Soldiers had then Spears of four and twenty foot in Length, which was to match the Pikes of the Infantry: But in some process of time as History makes it appear, the Macedonians found great inconveniency in the length of those Spears, and made some of them to be fifteen foot in length; and being then at that length, determined that five Horse in depth was too many, as to be offensive to their Enemies: but notwithstanding these results endeavoured to make their Battalias seem to be square, and for their better advantage in show, order ten in Rank and five in File to every Troop of Horse; And these depths were only in those days used when the Horse fought only with Spears, and Guns not at all used. Now if they had the use of Guns so much as we, and should fire in Ranks, five, six, eight or ten in depth (and our mode of fight being but three in File) their exercise would be so long in the performance thereof, that it would not only be tedious but hazardous to us; for of late years it hath been experienced, and seldom known any Troops to stand it out, as may be thought that time, in competition for victory: for we know that the ordering of our Horse, in making a large Front, as occasion and ground will give leave, and thereby overwinging our Enemy's Battalia, hath proved Victorious. And whereas they allege when they are six and eight in File, they can make their body to show powerful against their Enemy by commanding them to double their Fronts by their Middle-men (or half-file-leaders) and can if occasion serve take away a party in the rear, and file the Enemy in their Flank, or Flanks, etc. But this I conceive to be dangerous and of ill consequence: for when we are settled in Battalia three deep, we are then fixed for service, and need not be troubled in doubling of the Front, thereby we are free from distraction, and other disturbances which are most incident by sudden motions to the breaking of Ranks and the like, which contrariwise is with us; for our fight is not by wheeling off as formerly, but by charging at Pistols length, and so to charge through; every man betaking himself to his Sword; or otherwise as occasion shall serve: For when we assault our Enemy with our Carabines, and if time will permit it with one Pistol, what need have we of such tedious firing by Files or by Ranks, I shown those firings only for exercise sake. which the experienced Soldier thinks useless; for when our Horse are in a readiness for execution, they must fire entire, which I conceive to be most offensive: except the Enemy retreats, and wheels off, there will be but little use of a second Pistol. Tactics of Aelian. 107. There was also among the Grecians used divers forms of Buttalia's, called Rombes of Horse, and a wedge of Horse. rombes of horse The Rombes were according to these Figures. Some were made of Files and Ranks, some neither filing nor ranking, others ranking but not filing; as Captain Ward hath set it out at large. Likewise in those days they used the Wedge, which they accounted to be of more singular service than the Rombes, and is thus described. But neither of these being used in our Exercise and Mode of fight, I shall give you Euclid's definition of a Rombe. That a Rombe is a square figure that hath the sides equal, but the Angles not right, two of them become sharp and two of them blunt, etc. Thus I have passed over the several forms of the Exercise of the Horse, briefly, both in their face and Battalia's: and I shall conclude these Collectives of the Cavalry, as is needful for the Exercise of a Country Troop; it being but one part as an Introduction to Military Art. I need not plead any thing for this Art; In itself it is commendable. Empiredoms, Kingdoms, Nations, Princes and People can testify enough: no Nation can subsist without experience in it. It being asked the question; What part of the world brought forth the most Valiant men for War? Aelians Tactics. 38. Answer was made they were found to be in all places, where youth was bred up in the shame of Vice, and had audacity to undergo any Peril for Virtue's sake. The Lacedæmonians were accounted the most valiant People of Greece; History will tell you the reason: Therefore to conclude; None are born Soldiers, one may have an Inclination to War more than an other, but experience cometh not without Industry; and pardon me if I boldly affirm, that the English Nation are a Warlike Nation; which if we should neglect our duties herein, the Commander to be industrious, and the Soldier diligent, we shall make ourselves a by word, (or scorn) to other Nations: And our Gracious Sovereign at a loss in his designs, and expectations: The more we engrave this Art in our minds, the more courage we shall have, and the better enabled to fight for, and pray, God save the King. I cannot but give you the saying of M. T. Cicero, in Commendation of this Art, above any other Art whatsoever. Rei Militaris virtus, praestat caeteris virtutibus; and further saith after many other reasons to prove the same; That all other Arts do rest in safety under the Banners of this Art Military. THE ART OF DRILLING Or New Mode of EXERCISING A Foot-Company. BEING Collective Instructions Methodically composed, with their several Figures, for the young Soldier. By Capt. Thomas Venn. LONDON, Printed 1672. TO THE Honourable RALPH STAWEL ESQUIRE, One of the Deputy Lieutenants of the County of SOMERSET, and Colonel of a Regiment of Foot in the same. AS it hath been your Pleasure to accept of the Command of a Regiment of Foot, so it is your design to have it complete, for Officers, Men (and Arms) that they should be well disciplined in Military Art; and being commanded to serve you in the same, I thought it my duty to present to your view some Collections and other Observations in the Art Military, for the Exercise of the Foot: and I am confident of your Honour's care to see what ever is, or may be amiss in your Regiment, to be completed, not only in the certainty of your men, but also for some certain days to be allotted over and above two or three days Musters, (that are only for the Muster-masters due,) for your Commanders to be empowered for to appoint some private Exercising, for the better fitting and preparing of your soldiers for public services: To which end I may presume to say, that what I have presented you with, is none of the least or worst parts of Military Order; which if it passeth my Country's acceptance, by your favourable countenancing of it, I may give it a Supplement to make it completer, not destroying my Title, as he who did supplement Mr Elton's complete Body: Yet I would not have the Eltonist take it amiss, that most of our Worthy Cruso's Works are Verbatim supplemented to his complete Body of Art Military to make it complete, etc. Sir, I have not Embellished this with curiosity of Language, but rendered it for the meanest capacity, that none may be wanting in the Rudiments of Military Discipline; which diligently looked into, will make the younger sons of Mars the better able to perform their Duty when ever his Majesty shall call for it. And now most Noble Sir, True Heir of Honour and Virtue; your Pardon for my boldness, and your favourable construction of my weak endeavours, commands me to subscribe an obligement by the title of SIR, Your faithful and Obedient Captain, T.U. Verses. FOr your experience in this Art of War, With silence hear what your Instructions are. Perform your Postures with a manly grace, Observe your distances, and learn to face To right, and left about, and as you were, By Division, Entire and Anguler; Then to your doublings of your depth and length, When you perceive your Army wanteth strength: Inverting Files, converting of your Ranks, Brings ablest men in Front, or Rear, or Flanks: Your Counter-marches, you must next perform (Of dangerous use in fight in field, or storm) The Chorean and Lacedaemonian, And the feigning Macedonian: Then last of all your motions, learn to wheel, Which doth conclude this Martial Art to Drill. Wherein, were all our Trained Bands well skilled, They'd leave their Ground, to march into the Field; And not be scared and frighted with Alarms, For want of use in Handling of their Arms; Which Bingham, Hexham, Barriff, Elton, Ward, And many others too (as I have heard) Besides myself, who now have written part, That from us all, you may learn all this Art: And were I worthy, humbly should advise Our Lord Lieutenant, and their Deputies, To charge their Muster-master, when they view Defaults of Arms, contempt of Persons too, To see their Arms to be the Persons own, And not then borrowed, only to be shown, And muster in Person, to fight by spell Against our Foes, or Traitors that rebel: Of whom our Church, or State, can't be afraid With fixed Arms, and ready men well paid; Which will Restore to England and its Crown The Subject's Honour, and their King's Renown. Military Observations FOR THE EXERCISE OF THE FOOT. CHAP. I. By way of Introduction. HAving passed some few Collectives to the service of the Horse, I was desired to do the like for the foot; figuring out each Command, or platform after the proportion of Six in File, which is according to our late Mode of discipline. There have been many Books writ of this Military Art, in the Exercise of the Foot, both ancient and Modern; but of our later writers, I refer our new commissioned Gentlemen to the perusal of Bingham, Hexham, Barrife and Ward; I would not have Elton (although a Parliament Officer) wholly to be laid aside; for I have received informations of the great Worth and parts of the Gentleman. To them whose experience have been their masterpiece, I am silent; desiring with all submission rather to learn from such, than presume to direct. Those Gentlemen are to be commended that will bestow time in reading of this Art, but especially such as put in practice what they read; which is the readiest way to make men fit for the service of their King and Country: For what maketh a man more confidently Courageous, than knowledge? There are many Gentlemen that are greater Readers of the Wars, than Practitioners of the same; who have had some cavilling disputes, about the discipline thereof; not considering the great change that time hath made, and experience hath found out in Martial affairs. In the reading of the Roman and Grecian Orders, Discipline, and Government of their Armies, I had thought to have given you a taste thereof, but deserving a better Pen than mine to set forth the Gallantry of them, I shall be silent: And yet if it were possible to renew them, it would never work the like effect, as it did against their Enemies; One great cause thereof is supposed, that they made better pay-men in those days; Vice was severely punished, Virtue most bountifully rewarded: and when the Wars were ended, such as deserved well, were both regarded and rewarded; or else remained enrolled in pensionary pay; so by that means the Exercise of Arms continued. It is to be observed that where Payment and Reward cease, there Discipline and good Order ceaseth also. As for the Exercise of Arms belonging to the Infantry, it is the part of the young Soldier to learn and practise, in the first place, the Postures, and well handling of Arms: Which I may term to be the single Accidence of this Art, before he enters his Syntaxis: and it must be done by endeavouring to set some time apart for the exercise thereof. There have been many that have not only disputed, but have writ against the many Postures now used; but being shamefully confuted by our Modern Writers I shall be silent; and proceed to those Postures belonging to such Arms that are now in use in the Country, which are far short of what is complete in Exercise in the Cities of London and Westminster, and therein of those Honourable Societies of the Artillery and Military Gardens, and also now of late (The Cripple) with out Cripplegate. CHAP. II. Of the postures of the Pike and Musket. BEfore I give you the postures of them both, I shall give you a brief definition of a Posture. A Posture is a mode or Garb that we are fixed unto, in the well handling of our Arms: In which there are motions attendant unto the same for the better grace. Presupposing your company to be in the Field and drawn up in a ready way for Exercise, than the best way, is to Exercise them apart, by drawing of the body of Pikes from their Muskets; that each may be Exercised in their particular Postures by themselves. Only there are some Postures of the Pike and Musket which are answerable to each other by conformity; which ought to be performed in a Body, or upon a March, as occasion serveth: as for Example. In Marching, All are to be shouldered; In Trooping, or in any other Motion, the Pikes are to be advanced, and the Muskets poised: In Porting of the Pike, the Musket to be rested; In Trailing of the Pike, the Musket to be reversed; which is the Funeral Posture: When the Pike is Cheeked, the Musket is to be rested at the Sentinel Posture; when the Musket is presented to fire, the Pike is to be charged; And when the Pike is Ordered, most commonly; (especially in a stand or for Exercise) the butt end of the Musket is to be set to the Ground etc. 〈◊〉 is most proper for the Captain to Exercise the Pikes himself: I do not deny but he may Exercise both; as he ought sometimes to do: and the Ensign and Lieutenant are not to be negligent herein when they are commanded, or in the absence of their superior Officer. The next for the Exercise of the Pike, in point of Antiquity and Honour, the Gentleman of the Pikes craveth the precedency. I have declared in the Exercise of the Horse, what an excellent Virtue, Silence is; which ought in the first place to be commanded; and most diligently observed. The Body of Pikes from their March, and standing all shouldered, Command as followeth. 1. Order your Pikes, to your 1. open 2. close order. This aught to be made use of always upon a stand: And in the daytime it may serve for a Sentinel Posture: And for the abatement of the fury of the Horse, having the butt end of the Pike on the inside of the right foot, Charge then to the Horse, drawing your swords over your left arm, having your Pike in your left hand, you may then receive them by Commanding; either to Charge to the Front, Right, Left, Rear, 1. Order your Pikes. 2. Put up your swords. This is only useful upon a stand of Pikes; and by some able Soldiers it is not thought to be the securest charging against the Horse, or of strength to make the greatest resistance in their full Career. Therefore it hath been thought fit to be most convenient, to close your files to your close Order, and Ranks closing forward, and being thus semented (as it were) will be the better able to ward any resistance. From your Order, Advance Shoulder Port Comport Cheek Trail your Pikes. Order as you were. From your Order charge to the Front, Right, Left, Rear. Order as you were. 2. Advance your Pikes. This is useful upon all occasions when the Drum shall beat a Troop. It is also useful in all motions of Doubling, etc. Only remember when they are reduced they put themselves, or be commanded into the same Posture the standing Party was in. From your Advance, Shoulder Port Comport Cheek Trail your Pikes. Advance as you were: From your Advance, charge to the Front, Right, Left, Reer. Advance as you were. 3. Shoulder your Pike. This is useful and most proper upon a March: It is useful in time of fight, provided the Pikes be upon a stand, for it doth not only preserve the Pikes from shattering, but the Soldier also. From your shoulder, Port Comport Cheek Trail. your Pikes. Shoulder as you were. From your shoulder, charge to the Front, Right, Left, Reer. Shoulder as you were. 4. Port your Pikes. This is useful when the Soldiers are to enter either Gate or Sally-port; and it is an ease for the Rear half Files to Port their Pikes when the Front is at their Charge. From your Port, Comport Cheek Trail your Pikes. Port as you were. From your Port, charge to the Front, Right, Left, Reer. Port as you were. 5. Comport your Pikes. This is necessary for a Soldier upon his March up a Hill, to have his Pike Comported. From your Comport, Cheek Trail your Pike. From your Comport, charge to the Front, Right, Left, Reer. Comport as you were. 6. Cheek your Pikes. This is useful for the Sentinel Posture. From your Cheek, Trail your Pikes. Cheek as you were. From your Cheek, charge to the Front, Right, Left, Reer. Cheek as you were. 7. Trail your Pikes. This is useful in a Trench to move for security of any breach undiscovered; and is seldom used else, but marching through a Wood, etc. From your Trail, charge to the Front, Right, Left, Reer. Trail as you were. From your Trail, Order your Pikes. 8 Lay down your Pikes. Oberve that if your Pikes be laid down when you begin your exercise, than your Command must be— 1. Handle 2. Raise your Pike to your Open order, Order, Close order, etc. You may observe that the Postures of the Pike, some are for conveniency, and ease to the Soldier, as to expedition either in Marching, or other services commanded; and the several charges serve either for defence or offence; none ought to slight any of these Commands, but to put them into practice; for at some one time or other they may be useful. Here followeth the Postures of the Musket, or Calliver. In which, I do affirm, that the word of Command generally used (Make ready) is no Posture, but a word for brevity presupposing the Soldier to be expert in all, and doth include those postures precedent to that (Present your Musket) and so from the Presenting of your Muskets the other postures following unto that (Give fire) which is the completement of all the rest of the Commands given. Therefore for the better handling of Arms no Judicious Practitioner in this Art but will confess, it is better to be Instructed from Posture to Posture for more comely, and swifter execution thereof. The Musquetteer being shouldered Command Snap-haunce. Sloop your Muskets. Let slip your Muskets. 1. unshoulder your Musket, and Poise. 2. Palm or rest your Musket. 3. Set the Butt end of your Musket to the ground. 4. Lay down your Musket. 5. Take off your Bandeliers. 6. Lay down your Bandeliers. 7. Face about to the left & march. 8. Face about to the right and march to your Arms, (or stand to your Arms.) 9 Take up your Bandeliers. 10. Put on your Bandeliers. 11. Take up your Musket. 12. Rest (or Palm) your musket. 13. Secure (or Guard) your cock. 14. Draw back your hammer, (or steel.) 15. Clear your pan. 16. Prime your pan. 17. Put down your steel, (or hammer.) 18. Blow, or cast off your lose corn. 19 Bring or cast your musket about to your left side. Handle your Charger. Open your Charger. 20. Charge with Powder. 21. Draw forth your scouring stick. 22. Shorten your scouring stick. 23. Charge with Bullet. 24. Put your scouring stick into your Musket. 25. Rain home your charge. 26. Withdraw your scouring stick. 27. Shorten your scouring stick. 28. Return your scouring stick. 29. Bring forward your Musket and poise. 30. Palm (or rest) your Musket. 31. Fit your hammer, or steel. 32. Free your cock. 33. bend your cock. 34. Present your Musket. 35. Give fire. 36. Palm (or rest) your Musket. 37. Clear your Pan. 38. Shut your Pan. 39 Poise your Musket. 40. Shoulder your Musket. Match-lock. I need not here insert every Command, but only add such as are used for the Match-lock, wholly laying aside the rest. Take your Match from between the fingers of your left hand. Lay down your Match. Take up your Match with your right hand. Return (or place) your Match into your left hand. Open your Pan. Clear your Pan. Prime your Pan. Shut your Pan. Draw forth your Match. Blow your Coal. Cock your Match. Fit your Match. Guard your Pan. Blow the ash from your Coal. Open your Pan. Uncock, and return your Match. So you are ready for a March; or in the Posture upon the first motion. That which is called the Saluting Posture, is to be performed from the resting (or palming) of the Musket; when he shall have an occasion: as a Soldier to salute his Friend, or to the honouring of any other person deserving. And the Sentinel Posture, is for the Musket to be in the Palm of the left hand, at his Resting posture: But his Musket to be charged with Powder and Bullet, his Cock freed, and to be secured with his Thumb, so to be ready to execute his charge, and commands given, etc. There is indeed a word of Command sometimes used, Reverse your Musket; which is the marching Funeral Posture; That is to put the butt end of your Musket upwards, under your left arm, holding it in your left hand, about the lock of your Musket. Thus I have finished the Postures of the Musket or Caliver with a Snap-hance, and with a Match-lock without a Rest; for your further inquiry, if there need be, I refer you to Lieutenant Barriffe or Captain Ward. If I should forget to say something of the excellency as to the use of the Half-Pike and Musket, that is now of use in the Artillery Garden; Half-Pike. first invented by Lieutenant Barriffe and Mr John Davis of London; whatsoever is performed in the exercise thereof, it is with greater ease than the Rest and Musket is. And knowing how far it hath been the care of many Soldiers, by invention to make the Musquetteers, as well defensive as offensive, but none amongst many of their Projects was received like this, all falling to the ground, and this standing as the best, being of most excellent service; for it serveth as a Rest; as a palisado to defend the Musquetteer from the Horse: When the shot is all spent they may with that Weapon, fall in among the Enemy, and in the pursuit of an Enemy, by reason of the lightness thereof, and their nimbleness in Action, may do great execution; and in Trenches they are good seconds for the Soldier's preservation. Those Soldiers that are thus Armed are the best to be commanded out upon any Party, because they are the best able to defend themselves and offend their Enemies: And when any hedges are to be lined with shot, West Country. that the Musquetteers by their forced service become silent, and the ways deep and narrow; then the Half-Pike will be of singular service. And last of all the Sould●er so marching with his Half-Pike and Musket; It is not only a Grace to the Soldier but a Terror to the Enemy: Besides this hath been apapproved of by some of the ablest Soldiers in this Kingdom. Vic. Wimbaldon, Sir Tho. Genham. If once the Country saw the practice of it, and what a strong preservation it is against the incursion of the Horse, and in all other respects rather an advantage to the Soldier than disadvantageous to him; it would be not only esteemed good but carefully put into practice. As the Musquetteer is secured by the gallant invention of the Half-Pike; Bow and Pike. any strange eye would think it very unjust that such Numbers of the Pike-men should be slain by the shot, and not able to resist and offend again; I could therefore say much for the Long Bow to be joined with the Pike, how their showers of Arrows will gall and terrify the Horse, wound and hurt the Soldiers both on Horse and Foot; So if this should be duly performed all hands would be fight, and all in a readiness for self preservation. History is full of the great slaughters and Achievements in those days, when the Bow was most in use; but because it is laid aside I shall be silent, hoping the practice will never be forgotten. CHAP. III. The Places of Dignities both of Files and Ranks. IN this Military Age, who would have thought that few or any could be so ignorant of the difference between a File and a Rank; but finding in our Annual Exercises many (Farmor like) Soldiers to be much guilty thereof, I shall speak a a little thereunto; showing what is required to the making up of a File, and also of a Rank, with the dignity of each as they stand both in File and Rank. A File. First, Know that a File is a sequent Number of men, standing one behind an other Front to the Rear. Or from the first which is termed a File-Leader, unto the last which is termed a bringer up, which shall be demonstrated according to our mode of Discipline. A Rank. Secondly, A Rank is a Row of men be they more or less, standing or marching, shoulder to shoulder in a direct Line from the right hand to the left, (and from the left to the right) even a breast. And by the way observe that in all preparations to exercise, Files must be made up first, and being then drawn forth, and the Files joined together, Ranks are made. ranks and files Both which are according to Barriffe, Ward, and others; but in giving their Dignities to a file of eight deep there are various opinions, yet all endeavouring after a Geometrical proportion; and it is that which Commanders should chief follow as near as possibly they can. And because the Sages of our Times do differ in their Judgements, more in this particular than in any one thing that I know of; I shall set down what Rules I have know or heard, leaving it to the more experienced that can command better. Here followeth the Rule of Barriffe, Ward, and others in placing the Dignities, for six, eight, and ten, both in File and Rank. ranks and files I shall here insert those various Opinions of the Dignities of Soldiers eight in File, and so for eight Companies in a Regiment; by all which you may dignify each Officer in his due place of Honour; either in March, or in a Body: The consideration that there is, or aught to be an answerableness in the Rear to the Front, in the left flank to the right, by an equitable right in their true Dignity, is that which giveth life and being to orderly Discipline; for the worth of one must be answerable to the other in Skill, Valour, and in Number. ranks and files ranks and files The equality in this opposition is thus; As (1) and (4) makes five in the Colonel's Division, so (3) and (2) in the Lieutenant Colonel's Division makes five also: Then as in the first (5) and (8) makes thirteen; so the second (7) and (6) is thirteen, which is an equal opposition. As informed Mr. Elton's Rule. A Second Opinion for the Dignity of eight Companies, is as followeth. ranks and files These oppose as the first, and somewhat more in the equality of their Number; as one and six is seven in the right Wing of the Colonel's Division, so two and five is equal to that in the right Wing of the Lieutenant Colonel's Division; and six and seven is equally thirteen, in the first, as five and eight in the second. But according to the Rules for the Dignity of a File, the second Captain hath lost his place of Honour. For those of that Opinion who place the second Captain in the Lieutenant Colonel's Division, affirm that there may be a Geometrical equality (in length and breadth) in File and Rank; yet in point of Honour according to first Rule in the Colonel's Division, the second Captain being placed loseth his Dignity; for if the eldest Captain in priority is placed upon the Head or first Division, Body or stand of Pikes, leading the Colonel's Colours, then by the self same Rule of Equity, the second Captain Numb. (5) may and aught to be in the head of the Lieutenant Colonel's Division, Body or stand of Pikes. To which I conclude that the second Captain hath as much Honour to bring up the Rear of the Colonels own Division of Pikes when so marched; but if marched (entire) Regimentally, there to bring up the Rear of the whole Body or stand of Pikes is a greater Honour, and the second Captain's Dignity. A third Opinion for the Dignity of eight Companies. ranks and files This is the most received Opinion of the other two of late years, and the Reasons may be as followeth: First, their opposement is more upon a direct equality than the former, as for example, 1 and 8 stands upon the right Wing of the Colonel's Division which maketh 9; now equally to oppose this there is 3 and 6 on the left Wing of the Lieutenant Colonel's Division, that maketh 9 also; then upon the Right Wing of the Colonel's Division there is 4 and 5 that maketh 9; and to oppose that there is 2 and 7 which is 9 also; all this makes out the justness of this opposement, and in that particular exceeds both the former, for what can be said for the second may be alleged for this third also. The differences in them as to their opposements may hereby be discerned, and how that all three make equal in numbers, as in half Files and half Ranks, 18 is equal to 18, and in Rank and File making (36.) Indeed when the Signior Officers of a Regiment had more Soldiers in their respective Companies, there was then great reason to stand upon an equal opposement; or else one Wing might be too strong for the other. All this being now laid aside and there being of Soldiers an equality of number in each company, why then should our first rule for the dignity of a File be laid aside for the marching of a Regiment either entire or divisional? In the second Opinion the second Captain is placed in the Lt. Colonel's divisions in the third he is placed in the Colonels; although I conceive he ought to be in that Division yet he is there misplaced: for by the same rule in the second and third Opinion, as you place the Colonel in the Dignity of a file leader, the Lieutenant Colonel hath his Dignity in the place of a Bringer up, the Major in the place of the half File leader, the first Captain in the place of the Bringer up to the Front half-files: Thus far all three jointly go together, and because there is no difference in number of men, but equal in both parties, they need not stand so much upon an equal opposement, but that the second Captain Numb. 5. may have his just place of honour immediately next unto his Colonel. If it were not for this mode of Dignity according unto a File in the marching of a Regiment, and so unto a Rank in a Body, I might as well and better require satisfaction (the number of each Company being equal in Soldiers) why there may not be two field officers in the Colonels Division as well as in the Lieutenant Colonels; which I leave to better judgements. For the proof of my assertion, as joining with Barrife, Ward and others in apointing the second Captain, whose is the fift place of Honour next to the File leader, or next to the Colonels own company both in Rank and File. Bar. pa. 17. 1. The File leader ought to be the worthiest because he hath the Command of his File, and marcheth first against the Enemy. 2. The Bringer up aught to be the second place of Honour, because his place of March is in the rear; and is in most danger, should the Enemy charge on that part. 3. The half file leader is the third place of Honour, because when the Front half files are taken off upon any occasion, he is the leader unless he be commanded to face about. 4. The last man (or Bringer up) of the Front half files is the fourth man in dignity, for so he is when the Rear Division is taken of. 5. The next man to the File leader hath the fift place of honour, for one doubling brings him into the Front. 6. The sixth place of Honour is before the Bringer up, for if the Body be faced about, one doubling brings him into that accidental Front, or keeping of his proper Front by once doubling he becomes bringer up to the File leader. 7. The seventh Dignity of place is his who marcheth next after the half file leader, for when the half files double the Front, or march forth, than one doubling ranks him even with the Front. 8. The eight place of Honour (the File being but eight in depth) is the third from the front, for he may be made a File leader also, although it may be with more trouble, for by countermarching of the Front and Rear into the midst, and then facing to the first Front, and after doubling of Ranks makes him a File leader also. I desire to speak nothing here to tie up the Ingenious to any particular fancy, when his own reason shall guide him in this Military Discipline, as may not be irregular and contrary to the rules of Art. Now each Soldier being well exercised in the Postures of the Pike and Musket, and knowing their Dignity both in File and Rank, will not stand still here, but must be labouring to march farther in this field of Military Discipline, that by the knowledge thereof his undaunted courage might conduct him to some higher worth or place of Dignity. CHAP. IU. Of the Drum. I Come in the next place to advise every Soldier to be careful and endeavour to know the several Beates thereof, or else he may often fall short of his Captain's Commands. There are these several Beates to be taken notice of as Military signs, for the Soldier to walk or guide his actions by; and are termed Semivocall signs, as you may see in the Horse service, pa. 9 The several Beates or points of War, are 1. A Call. 2. A Troop. 3. A March. 4. A Preparative. 5. A Battalia. 6. A Retreit. Besides these six there are two other Beats of the Drum. 7. A Ta-to. 8. A Revally. The Ta-to is beaten when the Watch is set at the discretion of the Governor; after which in most places or Garrisons of note, there is a Warning piece discharged, so that none are to be out of their houses, without the word is given them, etc. A Revally is beaten in the morning by day light, at which time the subofficers are to take off their out Sentinels. It is, when by reason of the great noise of Guns, men, arms, and Horses, the Commanders voice for it can neither be heard or obeyed without the beat of the Drum: And the action of the Soldier whether valiant or otherwise is to be guided by it. And For the better performance hereof it is the Captain's duty to teach his Soldiers distinctly the several beats of the Drum, that they may be the better able to perform their respective duties, when ever they shall be so commanded by the Drum. CHAP. V Of Distances. HErein I shall show you what distance is, and the several sorts of distances: Without distance no motion can be performed: Although distance in itself is not motion; yet there is a motion in that action, that produceth our several distances of place, between man and man, or that space or interval of ground, either in File, or Rank. And I may truly assert that the Discipline of a Foot Company, etc. consisteth so much in distance, and motion, that there is great necessity of learning this very principle; for they are not fixed in one station, but are mutually interchanged one with another, as occasion is offered by command, and so are all brought into Order by their distances; for if a perfect form of order be not observed, disorder must necessarily follow; the effect of which produceth confusion▪ In our Modern discipline there are these four distances in use. 1. Close Order. 2. Order. 3. Open Order. 4. & Double distance. 1. Close Order which is both in File & rank one foot and half. 2. Order which is both in File & rank three foot. 3. Open Order which is both in File & rank six foot. 4. Double distance which is both in File & rank twelve foot. There are several distances to be performed in 1. March. 2. Motion. 3. Skirmish. 1. The distance of marching between File and File is three foot. between Rank and Rank is six foot. 2. The distance for motion as for doubling of Files, and Ranks, for face and Countermarches between File and Rank is six foot. 3. Distances for entire doublings and skirmishes between Rank and File is three Foot. 4. Distances for prevention of Cannon shot is 12 Foot, or 24. Foot, the double double distance. Note that the close Order is useful 1. To the Files of Pikes to the charge of Horse. 2. Before you Command any Wheelings. 3. When the Commander is to deliver somewhat to the Soldier that all may hear. Observe. Before you open or close your body by command to Distance to action; let every Captain or chief Officer Command his Soldiers to straighten their Files, and to even their Ranks: In the next place to be silent that thereby they may be attentive to the words of Command, Which for the several distances are as followeth. Commands. 1. Files. to your close Order. 2. Ranks. to your close Order. there might be abreviated into a shorter method but my intents is for plain capacities. 1. Files open to the right. 1. To your Order. 2. To your open Order. 3. To your double distance. 2. Ranks open forward. 1. To your Order. 2. To your open Order. 3. To your close Order. 3. Files open to the Left. 1. To your Order. 2. To your open Order. 3. To your double distance. 4. Ranks open to the rear, (or) backwards. 1. To your Order. 2. To your open Order. 3. To your double distance 5. Files open to the right and left. 1. To your Order. 2. To your open Order. 3. To your double distance. 6. Ranks open to the right and left. 1. To your Order. 2. To your open Order. 3. To your double distance. Reducements. 1. Files close to the right. 1. To your open Order. 2. To your Order. 3. To your close Order. 2. Ranks open forward. 1. To your open Order. 2. To your Order. 3. To your close Order. 3. Files close to the left. 1. To your open Order. 2. To your Order. 3. To your close Order. 4. Ranks close to the rear. etc. 1. To your open Order. 2. To your Order. 3. To your close Order. 5. Files close to the right and left inward, (or) to the midst. 1. To your open Order. 2. To your Order. 3. To your close Order. 6. Ranks close to the right and left inward. 1. To your open Order. 2. To your Order. 3. To your close Order. These are useful and may be used at the discretion of the Commander. And for your better performance in the closing and opening of Files and Ranks, take these following Observations. 1. When Files open to the right, the left, hand File must stand fast; every File taking his distance from the File next his left hand. 2. When they open to the left the right hand File stands fast, etc. 3. When Ranks open forward, the last rank stands; every rank taking his distance from the rank next behind him. 4. When they open backward, (or to the rear) the first rank stands; etc. 5. When Files close to the right, the right hand file stands, the rest close to the right, taking their distance from the right hand file. 6. And if Files close to the left, the left hand file stands; the rest of the Files close to the left, and take their distance, etc. 7. When Files close to the right and left, than they close inward, taking their distance from those Files within them, nearest to the midst of the Body. 8. When files close to the right and left by Division, it must be outwards, according to the fift and sixth observation. 9 When Ranks close to the front and rear, than the first and last Ranks stand; the other taking their distance. 10. If Ranks close to the midst than they close towards their two middlemost Ranks. I have not used the word [Centre] in any of these Commands, because it is conceived that the word is more proper to a circle, and not to a square, (or a broader fronted body.) It is not of absolute necessity that a Commander in the exercise of a private Company shall use all these openings, and closings to those several distances mentioned; but so many of them, as may be thought fit for his present Exercise intended; although it cannot be denied but that they may be useful at some time or other. CHAP. VI Of Marching and Drawing up of a Company. THe Soldier being informed of the Dignity of Place, together with the several Beats of the Drum; and their respective distances: I shall march a Company of Foot, and draw them up: which Company shall consist of twelve Files; four Files of Pikes, and eight Files of Musqueteers. But the Deputy Lieutenants for the County of Somerset have allotted some files more to each Company, and it is a rare thing to have them complete in the Field, so that it hath been too apparent, because there hath not been an equality in Files, their Companies have been wholly unfit for Exercise; but I hope these errors will be better looked into and amended hereafter. ranks and files A Company marching. A Company drawing up. Files are to be at their Order, and Ranks at their open Order. When the Company is drawing up, the Drum is to beat a Troop, the Pikes to be advanced, the Muskets to be poised; and being in a Body are ready for Command. ranks and files A Company drawn up. A number of Men being thus drawn up, and completed (consisting of Pikes and Muskets) there is in them according to the rules of Art; a Front, a Rear, a right and left Flank; Front half files; Rear half files; Right half ranks, and left half ranks; there is the length and depth of the Battle, and these are extended in their number of men. ranks and files The front in this Figure is first of all to be taken notice of: There are in all exercises a proper Front and an accidental Front: the Company being drawn up and standing in a body, with faces to their leader, maketh a proper Front. Vide Chap. of face. And the accidental front is as the Cheifetains shall command the face of the whole body: In short the front is where the faces of the Company are directed one way. The first Rank, or row of men, they are termed File leaders; who have the command of their respective Files, and are to Exercise them severally. Observe, that from, and with the right hand file leader, to and with the left hand file leader, is the extent of the Front, and is termed the length of the Battle. And the Soldiers standing severally from and with their File leaders in a sequence to and with their Bringers up are termed Files, or the depth of the Battle. The Rear of the body is so termed, where ever the back of the Company are turned. Every File leader hath his bringer up, that by death or other absence, next in point of honour is to succeed them, both in Place and power: The extent and length of the Rear (last rank or bringers up) is the same with the Frontiers. The right and left Flanks, are the outmost Files upon either hand of the body from the Front to the bringers up. There is in a body drawn up front half files and Rear half files; the Front half files extend themselves (three in depth) to and with the third Rank; and the Rear half files is the fourth Rank to and with the last, both which have their extents divided in the whole length, and depth of the body. Half Ranks are from the midst of the Files so taking their length, or bounds to the outmost man or file leader, either upon the right or left hand. CHAP. VI Of Face. SOme have thought that Face are but of little use, so that a commander might dispense with the Exercise thereof. There being a mistake in such, I must declare, That face are very necessary, and of such excellent use, as in no wise to be neglected; for in service, their executions are quicker than other motions, and may be performed when other commands cannot be used both for time and place. The Body being faced (or the faces of the Body) is termed an aspect, and being particularly turned by command maketh an accidental front, which is called a facing. So that in short, facing is the turning and altering of the aspect to either hand, Front or Rear, as may appear in the several commands following. In which we must understand that face are either Entire or Divisional. There are Angular face also. 1. Entire Facing is when the aspect of the company is directed one way. There are four entire face, besides Angular. Command. Face to the 1. Right. Each man is to turn upon that foot to which hand the facing is commanded, wheeling the Body to that Aspect. When you face to any hand, you may reduce them to the contrary. 2. Left. 3. Right about. 4. Left about. To reduce them, Command: As you were: or, To your Leader. Angular, face are when directed to make their Aspects to the right or left corner men; (that is, to the right or left Angle.) And so if you command to the four corners, it is to face them to their four Angles, which is Divisional. Command: Face to the Right Left Angle. To reduce them, Command: As you were: or, To your leader. These Angular face are not so much in use as formerly. Divisional face are contrary to the Entire, for they look divers ways. Which are Command: Face to the 1. Right and left. 2. Right and left inward. 3. Four Angles. To reduce them: As you were: or, To your leader. It is necessary that the half files do many of these commands by themselves, that they may the better understand it, when the body shall come to be subdivided. For Angular face, they are out of use, or not so much in use as formerly. By most Authors face are to be performed at open order both in Rank and File: But it is also necessary to exercise the Soldier in these face at close Order: for if a Soldier should be assaulted in a strait or narrow passage that he hath neither time, nor ground to receive it, either by doublings, Counter-marches or wheelings, they stand at their Order, or close Order; may then by their particular face defend themselves against any such assault and with wore ease so charge their Enemy by some of these face, than by any other motion. Face are not to be slighted, but carefully to be observed and practised; they are the groundwork of Military discipline, for all motions have relation in one respect or another to them. There are two face, square as followeth, set down in their platforms, See Barrife & Ward, etc. because they are not only useful but may serve as demonstrations of the former. Command: The two first Ranks stand; the two last Ranks face about; the rest of the body face to the right and left, and march all. ranks and files To reduce them; Command. 1. Face about to the right, march and close your Divisions. 2. Face to your leader, who standeth at his proper front. Figure 2. Command. 1. Musquetteers face to the right and left. 2. Half Files of Pikes face about to the right. 3. March all. ranks and files To reduce them. Command. 1. Face all about to the right, march and close your divisions. 2. Face all to your Leader. By this little you may perceive much of the Nature of Face, and how useful they are towards the making of the Soldier apt and perfect in other motions. I shall proceed to the Nature of doublings with the several branches, or parts of them. CHAP. VII. Of Doubling. IT is allowed by the Judicious that they are most necessary and completely useful for the strengthening any part of the Battle as occasion and discretion shall command. All which consist in these two Generals. 1. Doubling of Length, 2. Doubling of Depth, All times in quantity of Number; sometimes in Number and place. The several sorts of doublings are as followeth, 1. Of ranks. 2. Of half files. 3. Of bringers up. 4. Of the rear. 5. Of files. 6. Of half ranks. 1. The doubling of Ranks is when every Rank double the odd. 2. Half Files are said to be doubled, when they shall double their Ranks into the Front. 3. Bringers up are said to be doubled, when they shall double their Ranks into the Front. 4. The doubling of the Rear is when the Front half file doubles the Rear. 5. The doubling of files is when even files double the odd. 6. The doubling of half ranks is when one rank shall double the other. And that is performed by Passing through. Countermarches. Entire, or divisional doublings. The doubling of Ranks, half files or bringers up into the Front is a doubling of quantity, or number, and not of place. But the doubling of ranks entire, or for to double the front by half files entire, either to the right or left, or by Division; It makes not only a doubling in quantity and of place, but lengthens the battle also. The doubling of files and half files, or half ranks, or doubling to either flank, is a doubling in quantity, and not of place. But the doubling of files, and right half ranks entire, and the depth of the left flank entire, is not only a doubling of number, but of place and depth of the battle. Observe, that all divisional doublings are to be at open Order both in Rank and File. Observe, that in all motions they must be performed in three steps; and first by stepping forth of that foot, which is next to the place named: And for reducement to return by the contrary hand. Observe, that in doubling of Ranks, the doubling of Files reduceth them; so in the doubling of Files to any hand, the doubling of Ranks to the contrary hand reduceth them also. Observe, that in all motions of doublings, that they who are to double, before they move from their places, are to Advance and Poise their Arms; and when they have performed their Commands they are immediately to conform to the same posture that those whom they double are in; whether it be at shoulder or advance. Observe, that all entire doublings are to be performed at Order both in Rank and File: And in all motions observe your right hand man. I shall not only give you the words of command for most particular doublings that may be useful for service with directions for the performance of the same; with their reducements: And as I have been importuned by some of the Deputy Lieutenants to add to them their several platforms (or Figures) it is accordingly performed. But my chief aim is to demonstrate how a Battalia may be strengthened by doublings. And that is either in the 1. Front, 2. Rear, or 3. Both Flanks. The Front may be strengthened by Entire Doubling, Divisional Doubling, Entire Wheelings, & Divisional Wheelings. Of these I shall proceed in their several Orders, showing how entire Doubling do strengthen the Front. And that is by 1. Ranks, 2. Bringers up, 3. Half Files. 1. The Front is strengthened by entire Doubling of Ranks. 1. Command. Ranks to the 1. Right or 2. Left Doubles. Directions for doubling to the Right, from the left, the even Ranks from the Front move forward to the Right into the odd Ranks. ranks and files To reduce them Command Files to the left double, (or) Ranks as you were. The doubling of this Figure to the right doth easily make appear what is meant by doubling to the left, that I need not demonstrate it. 2. Command. Ranks to the right and left double 1. Outward, or 2. Inward. 1. Directions Outward. Even Ranks move outward from the Flanks with three steps forward into the odd Ranks. ranks and files To reduce them: Ranks as you were: Or, Files to the right and left double inward. 2. Directions inward. The even Ranks move inward from the Flanks with three steps forward into the odd Ranks. ranks and files To reduce them: Ranks as you were; Or, Files to the right and left double outward. 3. Command. Double your Ranks to the 1. Right 2. Left Entire. Directions to the right. Even Ranks from the Front, face to the right, and march forth until they be clear of the standing Ranks; then face them to their Leader, and double the odd Ranks that are standing, ranks and files If you command them to close their Ranks forward it will be the same Figure as may be produced by commanding half files to double the front to the right, the difference being only in quality, not in quantity, vide Fig. 3. To reduce them Command. Ranks that doubled, face to the left and march forth into your places. Or, Half Ranks of the right, face to the left and double your left Flank. Or, Ranks as you were. 4. Command: Double your Ranks inward entire. Directions. Every even Rank from the Rear, face to the right and left out wards, and march until they be clear of the standing part; then let every even Rank from the Front (which is the standing part) move forwards into the Front. ranks and files 5. Command Double your Ranks to the 1. Right 2. Left Entire. Every man placing himself on the outside of his right hand man. This doubling, is the same in Figure with the third, they differ only in place, the quantity being the same. Directions. Every even Rank from the Front, face to the right and march, placing yourselves on the outside of your right hand men. ranks and files To reduce them Command. Right half ranks double your left flank each placing yourselves on the inside of his left hand man. 2. Entire doublings for the strengthening of the Front by Bringers-up. 6. Command. Bringers-up double your Front to the 1. Right. 2. Left. Directions for doubling to the right: Bringers up move forwards with your right legs, and pass through ranking themselves even with the Front, the rest following successively and placing themselves even with the standing ranks. ranks and files To reduce them Command. Bringers up, or Rear half files face about to the left, and march into your places. OR, Even files from the left double your depth to the left, each fall behind his accidental bringer-up (or half file-leader.) When they march into their places, the half file-leaders who were the last that took their places, now in this reducement must be the first to take their places. 7. Command. Bringers-up double your Front to the right and left 1. Outward. 2. Inward. This I never saw but once in a private Exercise, but I conceive it more out of curiosity than of necessity. And because it is suitable to the second Command of Ranks, I need not demonstrate them in Figures; as the even ranks move and take their respective places in the second Figure, in this the bringers-up are to be the first movers to the right and left either outwards or inwards. If outwards; than it is to be performed from the midst of the Rear from the right and left into the Front. To reduce them Command. The odd files from the right and left flank double your depth to the right and left inwards, every man falling behind his accidental bringer-up. If inwards; than it ought to be performed from the flanks to the right and left inwards even into the Front. To reduce them Command. The even files from each flank double your depth to the right and left inwards, all falling behind his accidental bringer-up. 3. Entire doublings for the strengthening of the Front by half-files. 8. Command. Half files double your Front to the 1. Right. 2. Left. Directions. If to the right, the half file-leaders must pass through (or move forwards) to the right into the Front, and the succeeding ranks are to follow them. ranks and files To reduce them Command. Even files from the left, double your depth to the left. Or, Half files face about to the left and march forth into your places. Or, Half files as you were. 9 Command. Half files double your Front to the right and left 1. Outwards. 2. Inwards. What I have declared in the seventh Command, I do the same here: However I shall demonstrate the Command by doubling outwards. 1. Directions. It is to be performed from the midst of the half files to the right and left into the Front. ranks and files To reduce this Command. The odd files from the right and left flank double your depth to the right and left inward. OR, Half files face about to the right, and march forth into your places. 2. Directions. If the command be inward, than it is to be performed from the flanks of the half files, marching even into the Front. To reduce them Command. Even files from each flank, double your depth to the right and left outwards. OR, Half files as you were. 10. Command. Half files double your Front to the 1. Right 2. Left Entire. Directions to the right. Half files face to the right and march, until they be clear of the front half files, than face them to their Leader, and march them up even with the Front. ranks and files To reduce this Command. Half files face about to the right and march forth into your places. OR, Half ranks of the right double the depth of your left flank entire. 11. Command. Half files double your Front inward entire. Directions. Front half files face to the right and left outwards, and march until they be clear of the Rear half files; then face them to their Leader and stand. Then let the rear half files march up even into the Front. ranks and files To reduce them. Half files upon the entire motion face about and march; Front half files face to the right and left inward and close your Divisions. OR, Rear half files, double the depth of your Front half files entire, face all to the right and left inward, and close your Divisions. I have showed you how the Front may be strengthened by entire doublings; I shall briefly show how it may be by divisional. The Front is strengthened by divisional Doubling as followeth. 12. Command. Double your Ranks to the right and left by Division. To perform this, Command. Even Ranks from the Front face to the right and left outwards; march forth and double the odd. ranks and files To reduce this; half ranks that doubled, face to the right and left inwards, and march into your places. 13. Command. Half files double your Front by Division. To perform this: Half files face to the right and left outwards, and march until they be clear of the Front half files, than face them to their Leader; then move forward and double the Front. ranks and files To reduce this Command. Half files face about to the Rear, and march until they be clear of the Front half files; then, face to the right and left inward, close your Divisions and face to your Leader. OR, The half files that moved double the depth of the Front half files. 14. Command. Double your Ranks to the right and left by Division, every man placing himself on the outside of his right and left hand man. To perform this Command. Every even Rank from the Front move forth to the right and left outward, each man placing himself according as is commanded. ranks and files To reduce this Command. The half Ranks that moved double your Files to the right and left inward; every man placing himself on the inside of his right and left hand man. I have hitherto shown how the Front may be strengthened by divisional Doubling. Now followeth how The Front may be strengthened by entire and Divisional Wheelings. 15. Command. Wheel off your rear half files to the 1. Right 2. Left Entire into the Front. To perform this to the right, Command. Half files face about to the right, and wheel them to the left about, until they be even with the Front. ranks and files wheeling To reduce this; Wheel off your half ranks, and double your left flank entire to the left. To perform this reducement, let them face to the right; then Command: Right half ranks, wheel about to the right until they be even a breast with the front half files: To your Leader. 16. Command. Wheel your Flanks into the Front. There are diversities of Commands for the production of this Figure, and much according to the opinion of the Commander. I shall insert them, and leave the choice thereof to the judicious in this Art. ranks and files wheeling Wheel your Flanks into the front. Wings into the front. Front into the battle. Front into the midst. Rear into the flanks. To reduce any one of them Command. Wheel your flanks into the Rear. 17. Command. Rear half files wheel and double your Front by Division. To perform this Command. Half files face about to the right, and so wheel off to the right and left about; moving forwards until they be even with the Front. ranks and files wheeling To reduce this Command. Half files that doubled, wheel about to the right and left inward, and march into your places. OR, Half ranks face to the right and left outward; then wheel to the right and left inward, and double the depth of your Front half files, and face them to their Leader. There is some other Wheelings, but I shall not trouble you with them, because they are more for curiosity than for service, etc. CHAP. VIII. I Shall here insert the several preceding Commands for the strengthening of the Front, wherein, in the closing of some of the Ranks, as may be seen by them severally, the Figures are one and the same Battalia, in quantity but not in quality; in number but not in place. Ranks to the right Double. Command 1. Produceth one and the same Figure. 1. Bringers up double your Front to the right. Comm. 6. Half files double your Ranks forward to the right. Comm. 8. Ranks to the right and left double first outward and then inward Comm. 2. Produceth one and the same Figure. Brings up double your Front to the right and left 1. Outward. 2. Inward. Comm. 7. Half Files double your Front to the right and left 1. Outward. 2. Inward. Comm. 9 2. Double your Ranks to the right entire Comm. 3. Produceth one and the same Figure. Double your Ranks to the right entire, every man placing himself on the outside of his right hand man Comm. 5. Half Files double the front to the right entire Com. 10. Wheel off your Rear half files entire into the Front Com. 15. 3. Double your Ranks inward entire Comm. 4. Produceth one and the same Figure. Half files double your Front inward entire Com. 11. Double your Ranks to the right and left by division Com. 12. Half files double your Front by division Com. 13. Double your Ranks to the right and left by division, every man placing himself on the outside of his right hand man Com. 14. Produceth one and the same Figure. Rear half files wheel and double your Front by division Com. 17. Vide Chap. 11. Chap. 14. CHAP. IX. How Battalias may ve strengthened in the Rear. HAving ended with most of those doublings that do strengthen the Front, I proceed to some few that may strengthen the Rear: I might be as large in them as the former; but the labour and pains would be of no great necessity, because all what hath been commanded in the Front may by counterchange of them be performed in the Rear. Therefore I shall only for example sake set down four Commands, and demonstrate them by their respective figures, and they only shall be performed by the doubling of half Files, leaving the rest for the delightful Artist in this pleasing exercise. 1. Command. Front half files double your Rear to the 1. Right. 2. Left. To perform this: (to the right) Command. Front half files face about to the left and march directly forwards to the left of the standing part in opposition even in each rank according to their several places. ranks and files If this be commanded for service then face the Rear half files also about to the left. Then To reduce them. Face them all to their proper Front, and Command: Double your files to the right entire advancing. If it be for a private exercise, Command. Half files face about to the left and march forth into your places. 2 Command. Front half files double your Rear to the 1. Right 2. Left entire. To perform this to the right entire, Command. Front half files face to the right; march until they be clear of the Rear half files; then face them all to the Rear, and march them even in breast with the Rear. ranks and files To reduce this, Command. Front half files, face about to the right and march into your places. OR, Face all to your leader, then right half ranks double your left flank entire advancing. 3. Command. Front half files double your Rear by Division. To perform this, Command. Front half files face to the right and left, and march until they be clear of the Body, than face them to the Rear, and move down to the Rear even in breast with the last Rank. ranks and files If this be for service you may face them all to the Rear. If only for Exercise you may reduce them, as they now stand; by Commanding, Front half files face about to the right and advance forwards, until they are clear of the standing part, than face them to the right and left inwards; and close your Divisions. 4. Command. Front half files double your Rear to the 1. Right 2. Left by Countermarch. To perform this; If the Command given for the left; face the standing half files to the Rear, and the rest Countermarch to the left and lose ground. But if it be only for Exercise you need not face the standing part to the Rear at all. ranks and files To reduce this (as being only for Exercise) Command. Front half files face about to the left and march forth into your places. But if it be upon service that they are all faced to the Rear, than all upon the Reducement, are to face about to the left; and the front half files to march into their places. Object. But Some may object here, and say; that this is a countermarch, and no doubling, and so ought not to be demonstrated in this place. Answ. To which I answer; that what is done by the Front half files, in short is a Lacedaemonian Countermarch, (of losing ground;) but if it were a direct countermarch, they ought not to stand mixed with any other part of the body, by passing through to the Rear, but only to Countermarch into the midst and there remain; so that now passing through into the Rear makes it an absolute doubling. What I have mentioned in the beginning of this Chapter may be sufficient to the ingenious Artist, having concluded what I intended for the strengthening of the Rear. I thought to have inserted here a strengthening of the Front and Rear, but being in the Chapter of Wheelings, Command the tenth, the inquisitive may be better satisfied. CHAP. VI Which is the last in order to show, how a Battalia may be strengthened in both Flanks. THe Flanks are doubled by 1. Files. 2. Half ranks. 3. Division. 4. Wheelings. 1. First by Files. 1. Command. Files to the Right or Left double. If to the left to perform this, Command. Every even ranks from the left, move with three steps into the odd. ranks and files To reduce this, Command. Ranks to the right double. OR, Files as you were. In all motions observe to move that leg first, to which the Command guideth. 2. Command. Files to the 1. Right. or 2. Left. double advancing. To perform this, if to the right, Command. Every even file from the right advance three steps forward and double the odd. ranks and files To reduce this Command. Ranks to the left double. OR, Files as you were. 3. Command. Files to the right and left double outward. In doubling outward, the outmost File of each Flank stands, and the even File each flank doubles the odd. ranks and files To reduce this Command. Double your Ranks to the right and left inwards. OR, Ranks as you were. 4. Command. Files to the right and left double Inward. ranks and files To reduce this Command. Double your Ranks to the right and left outwards. OR, Ranks as you were. 5. Command. Double your Ranks to the 1. Right & 2. Left 1. Outwards advancing. 2. Inwards. This will be performed as in the third and fourth Command, only instead of falling behind their right or left hand men, here they are to advance before them as in the second Command. 6. Command. Double your Files to the 1. Right or 2. Left entire advancing. To perform this, to the right. The even files from the right advance so far until they be clear and double the odd files to the right. ranks and files To reduce this, Command. Files that doubled face about to the left and march forth into your places. OR, Front half Files double your Rear to the left. OR, Half Files double your Front to the right. 7. Command. Double your files to the 1. Right or 2. Left Entire advancing, every man placing himself before his leader. To perfom this, to the right. ranks and files wheeling The reducement. Command. Front half Files face about to the left and march forth into your places. OR, Front half files, turn off by countermarch, and double your Re ex to the right: Face all to your leader. 8. Command. Files double your depth to the right entire. To perform this, Command. Even files from the right face about to the right, and march until they are clear of the Rear, placing themselves after their bringers up; then face them to their leader. ranks and files To reduce this, Command. Half files double your Front to the left. OR, Front half files double your Rear to the right. 9 Command. Files double your depth to the right placing yourselves behind your bringers up. To perform this Command. Every even File from the right, face about to the right and double the remaining files behind their bringers up. ranks and files wheeling To reduce this Command. Bringers up double your Front to the left. OR, Half files double your Front to the left, each placing themselves before their half file Leaders. There is but a small difference between the Figures of some of the precedent Commands, as some may at first sight guess them to be: yet if you would but well observe them the words of Command are several, and in the Battalia there is difference in the Dignity of place; but not in quantity (or number.) Secondly. How the flanks are doubled by half ranks. 10. Command. Half ranks of the left, double your right flank to the 1. Right, or 2. Left. To perform this to the right. Left half ranks face to the right and move to the right forward and double your right flank. ranks and files To reduce this Command. Face to the left and march forth into your places. OR, Double your Ranks to the left entire. You may face them at discretion. I shall demonstrate another Figure to the left, showing how it may be performed without mixture of Arms, etc. 11. Command. Half Ranks of the right, double your left flank to the right. To perform this Command. Half ranks of the right face to the right, turn off to the right and double your left flank. ranks and files To reduce the 11. Command. Ranks double to the right entire, every man placing himself on the outside of his right hand man. 12. Command. Half ranks double your right flank to the right and left 1. Outward. 2. Inward. 1. To perform this Outward. Face all to the right, than the left half ranks move to the right and left outwards, doubling your right flank; face to your Leader. ranks and files To reduce this Command. 1. Front and Rear half files double your ranks entire to the left flank. OR, Half ranks that doubled face about to the right, and march forth into your places. OR, Half ranks face about to the right, and the even ranks from the midst move forth and double your left ranks entire to the left flank; face to your Leader. 2. To perform the 12. Command inward. Face all to the right, than the left half ranks move forwards to the right and left inwards, and double the right flank; face all to your Leader. ranks and files To reduce the 12. Command inward. Front and rear half files, double your Ranks entire to the left. By direction, you may Command. Half files face about, and every even rank from the front and rear move forth, and double your ranks entire to the left flank; then face to your Leader. 13. Command. Half ranks double your right flank to the 1. Right or 2. Left by Countermarch. OR, Half ranks to the right by Countermarch double your left flank. To perform this. Half ranks of the right, 'tis produceth the same Figure as the 11. Command. face to the right and Countermarch into the left flank losing ground. To reduce this. Double your Ranks to the left entire, every man placing himself on the outside of your right hand men, and face to your Leader. OR, Ranks that doubled, face to the right and march forth into your places. In like manner if you would double the right flank by countermarch, the right flank is then to stand, and you are to insert the left into the right flank, as before, the right will be by this Command inserted into the left. And by the reducement of the one by the contrary hand, you may reduce the other also. 14. Command. Left half ranks double your right flank to the right and left 1. Outwards 2. Inwards by countermarch. These insertions I shall not demonstrate by Figure, because the three last being but well observed, will give you a light to the execution of these; only I shall briefly give you the performances and reducements thereof. If Outward, Command. Half ranks of the right face to the right, and left half ranks face to the left, then move forward and double your right and left flank to the right and left outwards; face to your Leader. To reduce this Command. Front and Rear half files double your Ranks entire to the left flank, every man placing himself, on the outside of his right and left hand man. By direction you may Command. The Front half files to face about, and the even ranks from the midst, move forth to the left flank and double the odd, placing yourselves on the outside of your right hand men. And every even rank from the rear half files, move forth and double the odd, placing yourself on the outside of your left hand men; face to your Leader. If Inwards, Command. Ranks face to the right and left outwards, and the left half ranks turn off to the right and left inward, moving forward, until you have doubled the right flank; face to your Leader. To reduce this Command. Front and rear half files double your ranks entire to the left flank, every man placing himself on the outside of his right and left hand man. For direction you may Command. Half files face about, and every even rank from the rear, move forward, and place yourselves on the outside of your right hand men, and every even rank from the front, move forth and double the odd, placing yourselves on the outside of your left hand men; face to your Leader. 15. Command. Left half ranks double your right flank entire advancing. To perform this Command. The left flank (or the left half ranks) march forth until they be clear of the remaining party; then face them to the right and double the right flank, and face them to their Leader. ranks and files To reduce this. The left flank that doubled, face to the left, and march into your places. OR, Front half files double your Rear to the right. 16. Command. Left half Ranks double entire the depth of your right Flank. To perform this Command. The left half ranks to face about to the right, until they are clear of the standing part; then face to the left and double the right flank; face to your Leader. ranks and files To reduce this Command. Half files double your Front to the left entire. OR, Half files that doubled face about to the left and march forth into your places. 3. How the Flanks may be strengthened by divisional Doubling. 17. Command. Double your Files to the right and left by Division. To perform this Command. Half files of the even files from the right, face to the Rear; then, even files march clear of the standing part; then move to the right and left, and double the odd files. ranks and files To reduce them Command. Face to the right and left inward, march forth and take your places, and face to your Leader. 18. Command. Half Ranks of the left double your right flank by Division. To perform this Command. Half files of the left half ranks face about to the right; then, Front and Rear half ranks of the left flank move clear of the standing body, face all to the right flank, and move even in breast with the right flank. ranks and files To reduce them. Front and Rear half files that doubled, face about inwards and march into your places. OR, The half files that doubled may double the depth of their right flank. Obs. You may in the Command, when they are marched clear of the standing party, Countermarch them with this Command. Vide Com. 13. Front and Rear half files of the left flank countermarch to the right and left, losing of ground into the right flank, which will produce the same Figure, Com. 18. only in place. 4. The Flanks are strengthened by Wheelings. 18. Command. Left half ranks wheel off, and double your right flank to the Right or Left Entire. To perform this, Command. Right half ranks face outwards; left half ranks wheel about to the left, and keep wheeling until you have doubled the right flank; face the moveants to their Leader. ranks and files wheeling To reduce them. Face them to their proper Front; then Command, Rear half files double your Front to the left entire. But if you countermarch them, than the reducement of the 13. Command will give you light to it also. 19 Command: Wheel Front and Rear into the 1. Right or 2. Left Flank. OR, Front and rear half files wheel off into the right Flank by Division. To perform this, Command. Face all to the right. Wheel off to the right and jest, and so keep moving until the Bringer up of the right hand file, meet with the right hand file leader. ranks and files To reduce them if faced to the right Flank. Wheel both Flanks into the Rear, and face them to their Leader, But if faced to their proper Front, than Command. Wheel Front and Rear into their left Flank, and face them to their Leader. 20. Command. Left half Ranks wheel off to the right and left, and double your right Flank by Division. To perform this, Command. Half ranks of the right face to the right, than the half files of the left half rank face to the Rear. Front and Rear half files wheel off to the right and left about; and more forwards until you are even a breast, then double your right flank and face them to their accidental Front. ranks and files To reduce them, Command. Files that doubled, double the depth of the standing files entire to the right and left inwards. 2. If you face them to their proper Front, then to reduce them Command. The three first and the three last Ranks double your left flank entire. That is, The three last Ranks face about and wheel to the right, and the three first Ranks wheel about to the left, all moving and meet in opposition in the midst of the left flank; then face them to their Leader. I have ended those Doubling whose Battalia's are strengthened in the Front, Reer, and both Flanks. Although they may not be useful at all times in the field service, yet it is not amiss for every Commander to be well grounded in the knowledge of them, that by his experience therein he may not be silent, when occasion serveth, nor the Soldier seeking what to do, when he may be commanded: They are so necessary, that some are delightful in private Exercises, and most of them profitable in Field (or Garrison.) I am sure the Ingenious if once experienced herein will confess them to be of such absolute necessity as not in the least to be slighted by any. And further, it is adjudged to be most convenient for all the Chief Officers to bend their thoughts before the time of Service, to make their Commands as short as possible may be, in order to which see Chapt. 8. and 11. I do declare that I have heard some of our late young Eltonists to be too tedious in their Commands and Reducements; I shall advise the young Soldier to follow the Rules of Barriffe, Ward, Bingham and Hexham, for there is in them enough to direct for most Services, and then they may peruse Elton at last, whose worth (as I have been informed) is not to be laid in the dust without the due respects belonging to a Soldier, and I hope now a Loyal Subject. CHAP. XI. YOu may perceive in those several Commands for the strengthening of the Flanks, and their Figures being produced, and have closed some of their Files, as occasion may offer itself, they are one and the same in Number but not in Place. As in the 8. Chapter, I have also in this set down the several Commands that produce one and the same Figure, yet the Commands are distinct and several; all which if the Officer please to endeavour the remembering of: How that such and such Commands will produce such a Figure, he may in the hottest disputes take the shortest Commands to expedite his motions, having respect to his Ground for the execution of them. 1. Files to the right double. Command 1. Produceth one and the same Figure. Files to the right double, advancing Comm. 2. Files to the right and left double 1. Outward. 2. Inward. Comm. 3. and 4. Double your Ranks to the right and left 1. Outward advancing 2. Inward advancing Comm. 5. Double your Files to the right entire advancing. Comm. 6. Double your Files to the right entire advancing, every man placing himself before his Leader Comm. 7. Files double your depth to the right entire Comm. 8. Files double your depth to the right, placing yourselves behind your Bringers-up Comm. 9 Double your Files to the right and left by Division. Com. 17. 2. Half Ranks of the left, double your right flank to the right Com. 11. Produceth one and the same Figure. Half Ranks double your right flank to the right and left outwards 3. Half Ranks double your right flank by turning off to the right Com. 11. Produceth one and the same Figure. Pag. Command 16. Half Ranks to the right by countermarch double your left flank Com. 13. Left half flanks double your right flank to the right and left by countermarch 1. Outward. 2. Inward. Com. 14. Left half Ranks wheel and double your right flank to the right entire Com. 18. Left half Ranks wheel off to the right and left, and double your right flank by Division. Com. 20. Left half Ranks double your right flank entire advancing Com. 15. These Figures are much alike, only the change of Ground. Left half Ranks double entire the depth of your right flank Com. 16. A very good Figure is produced by the. Com. 17. Wheeling Front and Rear into the right flank Com. 19 This being an accidental Front is the same Figure with the 5.10. and 15. Command, for the strengthening of the proper Front by the doubling of Ranks. CHAP. XII. I Shall now treat of that which is called in a more particular manner Inversion and Conversion, showing you what is meant by them; And the nature and use of those several Commands, most in practice belonging to each of them. 1. Inversion produceth a File, or Files; That is either by Files filing; or Ranks filing. 2. Conversion produceth a Rank, or Ranks. That is either By increase of File ranking by Even, or uneven Parts. Of Ranks ranking to the Right, or Left. Of Ranks wheeling to the Right, or Left Flank. Observe, That in the performance of most of these Works, there must be either a double or twice double distance of Ground. But it must be the Commanders care so to open his Ranks or Files at such distances as the quantity of Ground will give leave. I shall not demonstrate the Commands in the same method, as I have the Doubling for the strengthening of the Front, but shall insist in that method already set down; because I find the reception hereof to be somewhat of difficulty with some of our Rural Officers. First, Inversion of files, or tiles filing in sequence. Secondly, Files filing by countermarch. 1. Command. Files, file to the 1. Right. 2. Left. ranks and files To perform this, to the right, Command. The right hand file to march away single, clear of the body, than the File leader of the next File is to fall in after the bringer up of the first File, and so all the rest, until the whole Body become one single file. To reduce this, Command. File leaders lead up you Files to to the left. OR, Files, file six to the left. 2. Command. Files file to the Right. or Left. entire advancing. ranks and files To perform this to the right. The right hand file stand, the second from the right advanceth into the Front of the first, the third into the Front of the second, and the rest successively into the Front of each other, until they may be made one direct file. To reduce this, Command. Face all about to the right, Files, file six to the right into the Rear. OR, As they stand without facing, Command. File six to the right gathering towards the Front. 3. Command. Files, file inward into the right Flank. ranks and files To perform this Command. Half files face about, then file leader and bringer up of the left flank advance forward, and each file of the half files from the left, are to fall successively into the Rear of each file until they have made one entire, than face them to their leader. To reduce them Command. Rear half files face about to the left. Front half files, file three to the left: and the Rear half files file three to the right; Face all to your leader, and close your divisions. 4. Command. Files file to the right and left by Division. ranks and files To perform this, Command. The file leaders of each flank march away with your files until they are clear of the Body, than the next file leaders from the right and left are to fall in after the bringers up of the first moveants, until the Body become two files upon each wing. To reduce them, Command: File leaders lead up your files to the right and left. OR, Files file six to the right and left. 5. Command. Files, file inward into the right and left flank by Division. ranks and files Figure. 5. You may the better understand this by the directions for the third Command: But To perform this, Command. Half files face about, then file leaders and bringers up of each file, both from the right and left, and fall successively into the rear of each other, until they have made two entire files on each flank; Face to your leader. To reduce this, Command. Rear half files face about to the right: Front and Rear half files file three to the right and left inwards; Face to your leader and close your Divisions. 6. Command. Files, by countermarch file to the right, every man placing himself in the rear of the right hand file. ranks and files Figure. 6. To perform this, Command. The right hand file stand, the rest of the Body face about to the left, than every particular file march forward to the left, and place themselves behind the bringers up of the right hand file. To reduce this, Command. Files file fix to the left, each placing themselves before their leader. 7. Command. Files by countermarch file to the right by division, each placing himself before his leader and bringer up. ranks and files To perform this; Command. Rear half files face about, the right hand file is to keep his ground, the rest moving forwards to the right, placing themselves before their File leaders and Bringers up. To reduce this, Command. Front half file ●●ce about, and file three to the right, every man placing himself before his bringer up: And the Rear half files, file three to the left, placing yourselves before your leaders. I have with as much brevity, as conveniently I could, set forth by demonstration the first part of Inversion which is of Files filing. I proceed to the second part of Inversion which is of Ranks siling. For the performance of which, observe that in all these motions, your files are to be at their Order, or otherwise as may be thought most convenient, and their Ranks to be opened either forwards or backwards at the discretion of the Commander, but at twice double distance (or more) as may be required to his number of men. The distances being set, let every rank move according to Command. 8. Command. Ranks file to the right, placing yourselves before your right hand man. To perform this, Command. The right hand man of each rank is to stand, the rest are to move forwards with their right leg, and so place themselves before their right hand men. ranks and files 8. Figure. Te reduce them, Command. Files rank twelve to the left: OR, Ranks as you were. Observe, Ranks filing are sooner executed in the commands and reducements, than files filing: For they will sooner be in readiness to receive any opposition with a suitable resistance in the Front: for in files filing it will be some long time before the file leaders will be able to do it. 9 Command. Ranks file to the right, placing yourselves behind your right hand men. ranks and files wheeling To perform this, Direct. If they be upon a stand, they may open backwards to their distance for the work as by example. But if they be upon a march, than the right hand man marcheth first, and all his rank so facing as to march to the right, file-wise after their leader: The right hand man of the second rank is so to do, and fall in the rear of the left hand man of the first Rank. To reduce this, Command. Files rank twelve to the left: OR, Ranks as you were. Aelian Tact. Ch. 30. p. 6. 10. Command. Ranks file to the right and left by Division. ranks and files wheeling The two former are directions enough for this. And may also be performed with the two former, either before their right hand men or otherwise. To reduce this, Command. Files convert into Ranks as you were. OR, Files Rank to the right and left inward as you were. OR, Files rank twelve to the right and left inward. This Figure as by the Notes of Captain Bingham hath been of great use amongst the Grecians, and judged by our ingenious Artists not to be slighted by us for the avoidance of the great Ordinance or showers of small shot: In Cities I have seen it often used for lodging of the Colours: It is also a large Interval for the reception of any Honourable Person. Some may dislike, in this last Inversion of Ranks filing, because there is a promiscuous mixture of Arms: This may be easily prevented by bringing both Divisions of Musquetteers into the Front of Pikes, or otherwise upon a march at the discretion of the Commander. There yet remain divers words of Command of Ranks filing; Vide Conversion. By wheeling your Ranks into the right Flank, or into both Flanks, etc. But the prolixity of them have made me to abbreviate, and being more out of curiosity than of necessity. I have showed what is meant by Inversion both in Files and Ranks, and have demonstrated them by their Figures, so many as I conceive may be sufficient for the knowledge thereof. Many I have heard to use the word Inversion to some of the precedent Commands; but I think it very convenient to be left out in the Exercising of our Rural Militia's; It is a word not suitable to a Rustic capacity, and a word that may be spared. CHAP. XIII. Of Conversion, and the several Parts thereof. COnversion, I have declared to consist of a Rank or Ranks. And that is performed either by 1. Increase of Files ranking by Even, or uneven Parts. 2. Increase or decrease of Files ranking by uneven Parts. 3. Files ranking entire into the Front, and wheeling into the same. 4. Ranks ranking to the right or left. 5. Wheeling into both Flanks. And of these I shall declare unto you, as briefly as I may, that your delight in the true understanding of them may not be neglected, by the least obscurity. Now the reason that I have demonstrated most with Figures, is that the young Soldier may see how many Commands produce one and the same Figure, their difference being only in quality, and not in quantity. 1. I shall begin with Files ranking by even parts, that is when they rank two, three, or four, keeping the same number in Rank, all being in an equal proportion; and if more, what is wanting to make up the Ranks in the Command, must be made good by the next Rank. 1. Command. Files rank three to the right. ranks and files Observe, in this motion, the File leader is first to move unto that hand the Command is given: And if six deep, the half file leader is to advance the same way. To reduce this, Command. Ranks file (or invert) to the right: Then every File-leader, lead up his File, and rank to the right: OR, As you were. 2. The uneven parts of Files ranking, is when there is such an increase either of two, three, or more in each Rank so exceeding the Rank before it: (and these exceed are termed in Arithmetic, A Progressional Increase) Or else by the decrease of each Rank following after. 2. Command. Files rank three first, then by increase to the right two, in each Division of Musquetteers and Pikes. ranks and files These are termed half Rombes, or Wedges. For Exercise sake you may make a Wedge, or half Rombe of all twelve by 3. Command. Files rank first two, and by increase two, from the whole Body. ranks and files You may alter the mixture of Arms at your discretion. 4. Command [is in the nature of a Rombe.] Files rank first two, and by increase, and decrease two in each Rank, Divisionally both of Musquetteers and Pikes. ranks and files The reducement of these three last Commands is, Ranks file as you were. These Rombes, and half Rombes or Wedges were much of use in the Grecian Wars; Read the Tact. of Aelian, pag. 108. But being not now so much in use, I shall not spend much time in them, but leave the desirous to the view of Captain Ward. 5. Command. Files rank to the Right, or Left into the Front. & 6. Command. Files rank to the Right, or Left by wheeling into the Front. I shall demonstrate both in this by Wheeling; only observe there must be so much distance between each file, as will contain each in rank. To perform them Command. Files open to the left to your double distance; Ranks close forward to your close Order, face to the right, wheel all to the left until the whole Body be brought into one entire Rank. ranks and files wheeling 5. & 6. Figure. To reduce this, Command. Face to the Rear; then the first six to the right wheel to the right: (When all have wheeled by six to the right) than face them to their Leader, and close their Files at discretion. 7. Command. Files rank into the Front and Rear by Division. To perform this, Command. Files open to the left to your order; Ranks close forward to your close order; Half files face about to the right, and face to the left, then move all into the Front and Rear, and make two entire Ranks. When the distance is set, Observe that those in motion are to face to the right flank. ranks and files in motion To reduce this, Command. Front half files face about to the left, rear half files face about to the right, then wheel all into their respective Files, than face them to their Leader, and close their files at discretion. Here might be inserted for variety and curiosity some more words of Command of Conversion, of files ranking into the midst; by Countermarches, and by Wheelings. But by what is demonstrated already you'll find enough in them, and I must look to be censured by some for what is done: and conceiving the remainder to be useless, I shall omit them to avoid a further censure, and proceed to the Conversion of Ranks ranking in equal Parts. 1. Conversion of Ranks ranking in equal Parts. Observe, that in Ranks ranking, you may perform it with any number, more or less, as place and occasion may serve; containing in every Rank an equality in Number. And it is to be understood after this manner: When there is twelve more or less marching a breast, and by reason of some narrowness of passage, or some other intent, the Commander causeth his Soldiers to rank either two, three, five or seven, etc. according to the place or occasion. 8. Command. Ranks, rank two to the right. To perform this, Command. The two first in Rank, to the right advance forwards, the next two of the same Rank in the Rear of them, until the first Rank have made six Ranks, and in all 36 Ranks. ranks and files To reduce this, Command. Ranks, rank twelve to the left. Observe, that the first rank stands, the rest are to advance, two and two, until the whole rank of twelve be complete in one rank. 9 Command. Rank two to the right and left 1. Outward, then 2. Inward. ranks and files To perform this outward, Command. The two outmost men, upon the right and left hand, advance forwards, the next in the same Rank are to follow, dividing themselves two to the right hand, and two to the left hand; so when the Work is finished there will be eighteen Ranks in each Division. To reduce this: Ranks as you were. OR, Rank twelve to the right and left inward. 2. To perform it Inward. Ranks rank two to the right and left inwards. Command. The two inmost men of the right and left hand in the midst of the Battle, advance forwards, the next in the same Rank are to follow, two from the right hand, and two from the left, until the Work be finished, making eighteen Ranks. To reduce this, Command. Ranks as you were. OR, Ranks twelve to the right and left outwards. I shall demonstrate one Figure of Ranks ranking in unequal parts which is rather to satisfy the curious than of any absolute necessity. Unequal Parts. 10. Command. Ranks, rank 1, 3, 5, 7, 9, 11. by increase and decrease as they stand in a Body. ranks and files To perform this. The right hand man of the first rank march forth, than the three next of the same rank follow in the rear of him, than five more out of the same rank to make the third, and what is wanting in the first rank of the Body to make good the fourth in Figure, must be taken out of the second in body, and so to proceed in the remainder both for its increase and decrease, until your Command be produced. To reduce this, Command. Right hand men rank, twelve as you were. 11. Command. Ranks rank entire to the Right, or Left into the Front. To perform this, Let the first rank stand, every rank else face to the right, and move away to the right successively placing themselves on the right hand of each rank, until they all stand in one entire rank in the Front. ranks and files Figure 11. To reduce this, Command. Ranks rank as you were. OR, Ranks rank twelve to the left; the second falls into the rear of the first, the third into the rear of the second, and so all successively until they be reduced. 12. Command. Ranks, rank entire into the Front, every man placing himself on the outside of his Right, or Left hand man by Countermarch. ranks and files To perform this, to the right hand man. The first rank stands, the rest moves away to the right on the outside of the right hand man. The precedent reducement will reduce this. OR, Ranks, rank twelve to the left, each placing himself on the outside of his left hand man. 13. Command. Ranks, rank 1. Outward 2. Inward into the Front. 1. To perform it outwards, Command. The first rank to stand, the rest to face to the right and left outwards, the second rank to advance clear of the first, and then to move forth even with the Front in breast, and all the rest successively do the same, until they be all even with the Front in one entire rank. ranks and files To reduce this; Ranks as you were. OR, The first 12, or 12 middlemost stand, the rest face to the right and left inwards; the second to move into the rear of the first rank, the third into the rear of the second, and successively the rest into the rear of the remainder, and being faced to their Leader, and even in their ranks, they are reduced. 2. To perform it Inwards. Command. Ranks, rank inward into the Front. To produce it, the first rank to move to the right and left outwards, and so to keep moving, (or opening) then the second rank is to advance into the ground of the first, and the second is then to move with the first to the right and left outwards; then the third is to advance into the place of the second rank, so all are to do until the last rank is advanced entire into the Front. ranks and files To reduce this; The first six upon the right, and left hand stand; then Command, Ranks, rank six to the right and left outwards; And close your Divisions. Lastly, the Conversion of Ranks by wheeling into the Flanks. 14. Command. Ranks wheel to the Right, or Left into the right Flank. ranks and files To perform this, Command. Every particular rank to be at double Distance in rank; and at close Order in file: Then Wheel them to their right hand, until they have brought their Faces (or Aspects) unto the right Flank. After you may face them to the Front. To reduce this, Command. Files rank twelve to the right. The first man is to stand, the rest is to move forward to the right successively twelve in rank. But if you wheel them to the left hand into the right flank, you must command them to face about and wheel your ranks to the left hand, until their Faces (or Aspects) be brought to the right Flank. 15. Command. Ranks of your Front and Rear half files, wheel outwards to your right Flank. I shall put in execution but two Ranks, one in the Front half files, and the other of the Rear half files, which is sufficient for Demonstration. To perform this, Command. Ranks open all to your twice double distance; then Front half files wheel to the right; and Rear half files wheel to the left. And face to your Leader. ranks and files wheeling To reduce them, Command. Front half files, rank twelve to the right; Rear half files, rank twelve to the left: Face to your Leader; march up and close forwards to your due distance. 16. Command. Ranks of your Front and Rear half Files, wheel inwards into your right Flank. To perform this, Command. Front and Rear half files march clear to your twice double distance; Front and Rear half files face about. Front half files wheel your Ranks to the left, and Rear half files; wheel your Ranks to the right; Face to your Leader. ranks and files wheeling To reduce this, Command. Front half files, rank twelve to the left: Rear half files face about and rank twelve to the right: Face to your Leader, and close your Divisions. 17. Command. Ranks, rank to each Flank, by wheeling to the right and left into the same by Division. OR, Ranks wheel to the right and left by Division into both Flanks; advancing (or placing) themselves before their right and left hand men. Observe, they are to be at double distance in Rank, and at Order in File. ranks and files wheeling Figure 17. To reduce them, Command them to face to the Rear, and wheel into their places. OR, Files, rank twelve to the right and left inward into the Rear, and close them to their order; then face them to their Leader. But if you would avoid mixture of Arms, you may place all your Musquetteers either in Front and Rear. Or else, wheel only the Musquetteers first, and leave the Pikes standing. Or else it may be performed in marching; and then the Reducement is; Ranks as you were. 18. Command. Ranks of your Front and Rear half files, wheel outwards to your right and left Flank by Division. They are to observe the same distance as in the former. To perform this, Command. Half files face about. Ranks open to your double distance, than Front and Rear half files wheel to the right and left outwards into both Flanks. ranks and files wheeling Figure 18. To reduce this, Command. Who being faced to their Leader. Front half files face to the Rear, rank twelve to the right and left inwards. And Rear half files face about and rank twelve to the right and left inward, Files close to the midst to your order: Face to your Leader. CHAP. XIV. Of making File-Leaders successively both of Number and Place in a File, and so for a whole Body. The Sweedish Mode also. AS I have stinted myself to a set Number of Files, so I have also to a set Number in a File, not exceeding six, being according to our present Mode of Discipline; for if I had gone to a various Number in Files, and added two to each File, my Figures had been more delightful to some Spectators; others I hope will find enough in this to qualify, or make them fit to do their King and Country service, etc. And now the Souldery having marched sometimes together, and so loving (being Soldiers indeed) by reason of such experiences as they have attained unto in the exercise of this Military Art, that each Leader is willing his follower should take his place; which is a great encouragement to an ingenious Soldier. This ought not to be slighted, because it is profitable to a Commander to bring what Ranks he pleaseth to lead in the Front, and to exchange them again, and at last to bring the proper File-Leaders into their places; Besides the encouragement it hath in private exercises, it makes men studious, whereby they may be able to Command in their respective Files, when they are become Leaders. In the first place take these short Commands to produce them, as followeth. Command 1. A File-Leader. 2. Rank two to the left, and Files to the left double. 3. Countermarch Front and Rear into the midst, and face to that part which was the Rear. 4. Face about to the right. 5. Countermarch from the Rear into the midst, and face to that which was the Rear. 6. Files rank two to the right, and Files to the right double. This being performed they are reduced. I shall demonstrate by Tables the succession of each man's Leading, and give you some, or several Words of Command according to my own and others, severally, that shall produce such Leader into his place, as they shall stand in sequence, and as they shall also stand in their respective Dignities. The Front and stand of each File as they come to be Leaders according to various Commands. A File 1 2 3 4 5 6. 6 5 4 3 2 1 6 5 4 3 2 1 6 5 4 3 2 1 To make the If upon a single File, Command. 5 6 5 2 1 2 5 6 1 6 1 2 5 6 1 6 1 2 4 3 1 6 4 3 4 3 2 5 4 3 4 3 2 5 4 3 3 4 6 1 3 4 3 4 3 2 3 4 3 4 5 2 3 4 2 1 2 5 6 5 2 1 6 1 6 5 2 1 6 1 6 5 1 2 3 4 5 6 1 2 5 4 5 6 1 2 3 4 5 6 6 5 4 3 2 1 6 5 4 3 2 1 6 5 4 3 2 This I saw July, 1671. Reducement. File Leaders stand, the rest pass through, and place yourselves before your Leaders. Ranks to the right double, and Files to the right double. Ranks to the left double, and Files double your depth to the left. File-Leaders stand, the rest pass through to the right, and place themselves before their Leaders. Half double your Front to the right, and Files to the right double. Ranks to the left double, and Files to the left double. If more Files than one Command. Reducement. File rank to the left into the Front; Rank file fix to the left. File rank two to the right, and Files to the right double. Bringers-up double your Front to the left, and double your Files to the right entire advancing. Bringers-up double your Front to the right, and double your Files to the left entire advancing. Half double your Front to the right; Files double your depth to the left. File rank two to the left; Files to the left double. Reducement. Bringer-up stand, the rest pass through to the left, and place yourselves behind your Bringer-up. Rank two to the left, and Files to the left double. Half file double your Front to the right; and Files double your depth to the right. File rank six to the left, then, Rank file six to the left. Front half file double your depth to the left. File-Leader with the odd men from the Front, face about to the right, and interchange Ground. 6 5 4 3 2 6 5 4 3 2 6 5 4 3 2 The front and standing of each file as they come to be leaders in their respective dignities Dignity. The dignity of a file. 1 6 4 3 5 2 6 5 4 3 2 1 6 5 4 3 2 1 6 5 4 3 2 1 1. a 5. e 4. d 3. c 6. f 2. b 1 2 6 5 5 6 2 4 5 6 6 5 2 4 5 6 6 5 3 4 1 2 3 4 1 3 1 2 3 4 1 3 1 2 3 4 4 3 2 1 1 3 3 1 3 4 1 3 3 1 3 4 1 3 2 1 5 6 6 5 4 2 6 5 5 6 4 2 6 5 5 6 5 6 3 4 4 2 5 6 2 1 4 2 5 6 2 1 4 2 Dignity. I much quastion the dignity of this; how ever I have inserted it, 6 5 4 3 2 1 Dignity 6 5 4 3 2 1 f e d c b a f e d c b a Reducement. Files rank two to the left; files to the left double. Bringer up double your Front to the left. Files double your depth to the left, every man falling behind his bringer up. Half files double your Front to the right. Files double to the left entire advancing. Files rank two to the right. Files to the left double. Bringer up double your Front to the right, and files double your depth to the right, every man placing himself before his leader. Front half files double the Rear to the left. Files double to the left in tire advancing, every man placing himself before his leader. Half files double your Front to the left. Files double to the right entire advancing, every man placing himself before his leader. Reducement. Ranks to the left double, files to the left double: then, half files double your Front to the right, then, Bringers up face about to the right and march forth into your places. File leaders stand, the rest pass through to the left and place yourselves before your leaders. Ranks to the right double; Files to the right double. Front and Rear half files interchange ground. File leaders & half file leaders stand, the rest pass through to the left, & place yourselves before your leaders. Bringers up double your front to the right, and files double your depth to the right. Reducement. Rank two to the left and files to the left double, then Front half files double your Rear to the left entire advancing, every one placing himself behind his leader. Face about into the right and Countermarch your Rear into the Front. Ranks to the right double, and Files to the right double. Front half files double your Rear to the right entire advancing. Bringers up double your Front to the right, & files to the right double advancing, & placing yourselves before your leaders. Countermarch front and Rear into the midst. Front and Rear half files interchange ground. N. 6. N. 5. N. 4. N. 3. N. 2. N. 6. N. 5. N 4. N. 3. N. 2. N. 6. N. 5. N. 4. N. 3. N. 2. CHAP. XV. Of Countermarches. WE read in the Tactics of Aelian of three kinds of Countermarches used amongst the Grecians and Persians; And are termed, the 1. Chorean 2. Lacedaemonian 3. Macedonian Countermarches, There is another Countermarch that is of use in our modern exercises and is termed the Bastard Countermarch, and so called because it participates some times of one, and some times of another, but always, of two, and may in many respects be more useful than the former. Most Authors place this amongst the other Countermarches, therefore I shall not now alter it; although in my opinion, it may be very well ranked amongst the doublings. I thought to have been large in demonstrating the several natures of Countermarches; but being conceived of all motions in this art the least beneficial to our latest mode of discipline, I shall not be tedious to your Patience: But if the skilful Soldier will put them into practice (especially the Bastard Countermarch) he will not only find some of them serviceable but all delightful in private Exercises. Observe the Chorean Lacedaemonian Macedonian is 1. Maintaining 2. Losing 3. Gaining Ground. First, The maintaining of Ground is a Countermarch commanded without any addition to it; and is termed the Chorean, or Cretan. Countermarch. Secondly, The losing ground is a Countermarch commanded when the Soldier is to take his ground from the Rear, and this is termed the Lacedaemonian Countermarch. Thirdly, The gaining of ground, that is a Countermarch taking of ground next before the front, and forsaking the ground it first stood upon, and this is termed a Macedonian Countermarch. In all which there is Countermarching of Files. Ranks The Front. The Rear half files. Half Ranks. And these may all be performed by entire or divisional Countermarches. 1. The Countermarching of Files is when every Soldier followeth his leader. 2. The Countermarching of Ranks is when every Soldier followeth his side man. 3. The Front and Rear half Files Countermarching is when the Soldier shall follow their File leaders or Bringers up. 4. The Countermarching of half Ranks is when the Soldier shall follow their outside men. I shall in the first place show how Entire and Divisional Countermarches are performed by files, and Ranks. 1. Observe, That in the execution hereof your distance is to be at six foot in rank and file. 2. When you are to Countermarch to the right, the file leaders are to step forward with their right legs, and face about to the right, passing down to the Rear with their respective File following them, keeping even a breast with their right handmen, and to be sure not to turn before they be advanced to the ground of their File leaders. 3. All Entire Countermarches of Files or ranks may be reduced by contrary Countermarches: If the Command be to the right, reduce them to the left: And so for Contermarching of the Front, Rear or flanks into the midst, reduce them back from the midst. It shall be my endeavour to demonstrate how all Entire and divisional Countermarches shall lie under these three heads. Of maintaining, Losing, and Gaining of ground. First, of Countermarches maintaining Ground. In the second precedent rule it will not be amiss to cast your eye back, for your better direction, by which you'll be able to pass these Countermarches with greater delight and Order. 1. Command. Files to the 1. Right, or 2. Left hand Countermarch. To perform this, Let the file leaders step forward with their right legs, and march even in Rank to the Rear, and none to turn off until he come to his File leaders Ground. ranks and files To reduce this, Command. Files to the left hand Countermarch. 2. Command. Ranks to the 1. Right or 2. Left hand Countermarch. To perform this, Face them to the Right; and the right hand file is to turn off to the right, and to march even to the Ground of the left hand file. ranks and files You may reduce this, by Ranks Countermarching to the left. 3. Command. Countermarch your Front and Rear into the midst. To perform this, Command. Half files, face about and turn to off the left. Front half files turn off to the right; and face to your leader. ranks and files You may reduce this figure by doing the same over again. Or else, by any other divisional Countermarch. 4. Command. Front and Rear half files countermarch to the 1. Right or 2. Left. ranks and files You may reduce this Figure by doing the same over again, OR, By Countermarching Front and Rear into the midst. 5. Command. Countermarch your Front and Rear half files to right and left from the midst. To perform this, Command. Front half files face about and turn off to the right, and Rear half files turn off to your left: then, face to your leader. ranks and files To reduce this, Command: To Countermarch from the midst into the Front and Rear. The three last figures by command are several, but the figures are still one and the same in quantity, but not in quality, or motion, as you may perceive, etc. 6. Command. Countermarch your flanks into the midst. To perform this, Command, them to face to the right and left outwards, the right flank turn off to the right, and left flank turn off to the left until they meet in the midst. ranks and files To reduce them, Command. Countermarch from the midst to the right and left into both flanks. 7. Command, Right and left half Ranks interchange your ground. To perform this, Face to the right and left inward (and march all) and interchange your ground. ranks and files This is of no great use except it be when the right (or left) flank hath fought, that then the reserved flank may come into service also. You may reduce them by interchanging of them back again. OR, Divisionally to Countermarch their flanks into the midst of the Battle. Secondly, Countermarches lofing ground. 1. Command. Files to the Right, or Left, hand Countermarch placing yourselves before your bringers up. To perform this, Command. The bringers up to face about to the right, than the file leaders with the rest successively to turn off upon the same ground he stands; And on the same hand the Command is given, so to place themselves accordingly. ranks and files You may easily reduce them by any other Countermarch of files. 2. Command. The last Rank stand the rest pass through to the 1. Right or 2. Left placing yourselves behind your bringers up. To perform this: As the last Rank is to stand and keep their first aspect; let all the rest face about to the right, and march all turning successively behind their bringers up. ranks and files To reduce them, you may pass them through, or else Countermarch by file into their places. 3. Command. Front and Rear half files Countermarch to the 1. Right, or 2. Left, From the midst, every man placing himself before his leader and bringer up. To perform this, Command. The first rank of the front half files to stand, the rest to face about and turn off to the right; half file leaders face about and turn off to the left, and both to march clear of the Front and Rear, following their half file leaders, and bringers up of the front half files. ranks and files To reduce this by an other Countermarch. 4. Command. Ranks to the 1. Right or 2. Left hand Countermarch, losing ground. To perform this to the right. As in maintaining ground, upon their turning off, the rest march into the same place (or ground) and turn off also; as in figure 2. Now this of losing ground, altereth only in this, the outmost file is to face to the right about, until he hath directly faced the left flank, and so to gain so much ground upon the left flank as they have lost upon the right; OR, That they have placed themselves on the outside (or before) of their left hand men. ranks and files 5. Command. Ranks to the right hand Countermarch, each following his right hand man; and place himself on the outside of his left hand man. ranks and files To perform this, Command. The left hand file to stand; the out most file to the right turn about to the right as to make his aspect (or face) to the left, then move forward until he be clear of the second file, losing the ground he stood upon, and gain it again on the outside of the left flank. To reduce this figure; may be done by a contrary Countermarch. 6. Command. The right and left hand file upon each flank face to the right and left outwards, the rest pass through, placing yourselves before your outmost files. Observe, files become ranks by their faceing. To perform this, Command. The right hand file to face to the right, and the left hand file to the left, and then the rest of the body to turn their aspects, accordingly, & place themselves before their right & left hand men. ranks and files To reduce them, Command, them to Countermarch to the right and left into the midst of the Battle. OR, Command. If they be faced to the proper Front, The two inmost files to stand, the rest pass through to the right and left inward, and close their divisions. 8. Command. The two outmost files of each flank face to the right and left inward, the rest pass through to the right and left, and place yourselves behind your outside men. To perform this, Command. The right and left hand file of each flank face inward, and the rest of the Body are to face to the right and left outwards, than all are to move forwards, and to place themselves behind their right and left hand men. (Else the motion is the same as the former.) ranks and files To reduce this, Command. The two innermost files face to the right and left outwards, and the rest pass through to the right and left inwards, placing themselves behind their right and left hand men, Then, face them to their leaders. Now if it be the Commanders pleasure to reduce them by any other word of Command, it may be done by the precedent words of Command, or of the next following, or of any other divisional Countermarch (except interchanging of ground.) 8. Command. The outmost file of each flank stand, the rest pass through to the right and left, and place yourselves on the outside of your right and left hand men. The ninth figure is the same as this, if faced to their leader. To perform this. The outmost files of each flank stands; the rest of the body faceth to the right and left outward, and so passing forwards through the intervals into each flank, place themselves on the outside of their right and left hand men. ranks and files To reduce this, may be performed by any of the foregoing Countermarches of ranks: Or else, being faced to any of the flanks, than the Ranks, become files, and by divisional Countermarches of files, you may reduce divisional Countermarches of Ranks. OR, By Ranks files only some face must be observed. For the proper Reducement Command: The two inmost Ranks to stand, the rest to face to the right and left inward, and so march into their places. 9 Command. The right and lelft hand files upon each flank stand, the rest pass through to the right and left, and place yourselves on the outside of your right and left hand men, following your inmost files. Observe in the performance of this the two inmost-files are to be first in motion▪ But first, Command, The two outmost files of each flank to stand, and the rest of the Body to face to their right and left outwards, so moving away first from the midst until they have successively placed themselves on the outside of their right and left hand men: (you may close their files into the midst to open Order. ranks and files The reducement of the eight figure will reduce this also. 10. Command. Front and Rear half files Countermarch to the 1. Right or 2. Left hand interchanging ground. To perform this, Command. Half files to face about and turn off to the right, front half files doing the like move forwards until they be clear one of an other, six foot; then face to their leader if you please and close their divisions. ranks and files A Countermarch interchanging of ground will reduce them and then close etc. 11. Command. Front and Rear half files to the right hand interchange ground. ranks and files You may reduce this, interchanging of ground as they were, or by some other word of Command. Thirdly, Countermarches to gain ground. 1. Command. The file leaders stand, the rest pass through to the 1. Right or 2. Left, and place yourselves before your leaders. ranks and files The Command is so plain that there needeth no directions. Only if your command be to place yourselves behind your leaders, than the file leaders are to face about, and the rest are to execute it as the former, only in placing themselves they are to turn their aspect behind their leaders. And then Commanding them to place themselves before their leaders will reduce them. 2. Command. File leaders face about to the right and stand. Bringers up with the rest following them, pass through to the right, and place yourselves behind your leaders. Face to your leaders. ranks and files To reduce this you may do it by the same Command, or by the first Command. 3. Command. File leaders stand and the rest pass through to the 1. Right, or 2. Left, placing yourselves before your file leaders, following your Bringers up. This is the same with the second figure, only in their work they are to keep their aspect to the Front: And the reducement the same also. 4. Command. File leaders and half file leaders stand, the rest pass through to the right and place yourselves before your file leaders and half file leaders. ranks and files You may reduce this by the same Countermarch, or any other Divisional Countermarch. 5. Command. File-leaders and half file-leaders stand, the rest pass through to the right, and place yourselves behind your Leaders and half file-leaders, following your Bringers-up. The file-leaders and half file-leaders are only to face about to the right and to stand, the motion is the same with the fourth Figure, but in taking their places they are to face to the Rear. The Reducement as the former. 6. Command. File-leaders and half file-leaders stand, the rest pass through to the right and left, and place yourselves behind your Leaders and half file-leaders, etc. I need not demonstrate this, it being the same with the fifth and sixth, only in the motion they are to pass to the right and left outwards. And is reduced as the former. 7. Command. File-leaders to face about, the rest pass through to the right, and place yourselves behind your Leaders and Bringers up. To perform this, Command. The first Rank is to face about and stand; then the two last Ranks from the Rear, (i. e. the fourth and fifth Ranks) are to face to the Rear and move all, etc. ranks and files The former Directions upon any Divisional Countermarch will reduce this. 8. Command. The outmost File of the right face to the right, the rest pass through to the Right, or Left, and place yourselves Before, or Behind your right hand men. ranks and files If your Command be behind your right hand men, than the right hand file is but to face to the left. I shall not trouble you with them, conceiving them of no great use. You may reduce these by a contrary Countermarch. 9 Command. The outmost File of the right hand stand, and the right hand File of the left half Rank stand, and the rest pass through, and place yourselves on the outside of your right hand men. Face to your Leader. The same is done on the left hand. And if you place them before their left hand men, than face them all to the right, and so let them pass through observing the motion: And if you place them behind their right hand men; then let the right hand men face about to the left, and the rest pass through and fall behind them. ranks and files Figure 9 A Counter word of Command will reduce them, etc. There are many Countermarches that produce one and the same Figure: provided you close your Divisions, and face them to their proper Front; only they differ in place. First, therefore you may briefly observe that in those Countermarches that Maintain their Ground, the first, second, third, fourth, and fifth Commands; then in losing of ground, the first, second, third, fourth, fifth, tenth, and eleventh Commands; and in gaining of Ground, the first, second, third, fourth, fifth, sixth, and seventh do and will produce one and the same Figure. Secondly, Also for maintaining of Ground, the sixth and seventh; and in losing of Ground the sixth, seventh and eighth; and also in gaining of Ground the ninth Commands produce one and the same Figures. Oserve, For the Countermarching of half Ranks, see in the doublings of the Flanks, thirteenth and fourteenth Commands, they producing the same Figures as the eleventh and twelfth Figures; by all which you will the better understand the one for the other. Although Countermarches are of great Antiquity, and used amongst the Grecians; yet it is not much of use in our present Mode of Discipline: Therefore to conclude, though knowledge of them be no burden, yet to be exercised in the face of an Enemy may prove prejudicial; and the best expert in this Art, allow that they may be best spared of any motions whatever. CHAP. XVI. Of Wheelings. I Am to treat of Wheelings, and the several uses of them, as to the strengthening of the Front, Reer, and both Flanks. Before you enter upon them, take these four Observations. 1. That you close your Ranks and Files to your Order. 3. Foot. 2. That in all your Wheelings, you keep a due distance to your Leader. 3. That in all Commands for Wheelings, such moderation is to be used in their motions, that they on the contrary flank be not forced by running to disorder themselves. 4. That your Arms be at such Postures as may be equivalent to each other; (This is) If the Muskets be poised, the Pikes are to be advanced (which are the Postures best to be used in these Motions.) There are two sorts of Wheelings. First, Angular Wheelings. Secondly, Wheelings on the midst (or Centre:) I shall not use the word Centre, for it is more proper to a Circular body than to a square. These in their Motions (or Actions) are termed either Entire or Divisional. 1. Entire Wheelings, are for the gaining of ground upon the Enemy, or to fight him with your best men, as occasion serveth, turning the first Aspect wholly to the Command given. 2. Divisional Wheelings, being performed, extend the Battle either in length or depth: And may for the most part of them be called Doubling. I have in the exercise of Doubling demonstrated some of them by Figures, and shall not recite them here again, but quote them by their several numbers of Commands. First, I shall begin with Angular Wheelings. And they so called, because the corner man to which the Aspect is commanded, is the main hinge of the motion. Observe, the Wheelings to the right and to the left; To the right and left about are termed Angular. And for the Wheelings to the right and left, and to the right and left about on the same Ground are Wheelings on the midst of the Front, all which are Entire, the other Divisional. Centre. 1. Command. Wheel your Body— all, or your Battle to the 1. Right, Entire Angular Wheelings. or 2. Left. This Wheeling moves the main Body from the Ground whereon it first stood, and placeth it on the right Flank, causing the Aspects of the proper Front to be upon the same. Observe, that the right hand man is to move to the right hand with a very small Motion, and every man else to remember that the farther off he is from the Right Angle, the swifter must his motion be. ranks and files wheeling To reduce them. Wheel to the left. But this will not transfer them to the same Ground: But to reduce them to their first Aspect on the same Ground; you must face them all to the right, then wheel them to the left, and facing them to the left, it is complected. 2. Command. Wheel your Body— all, or your Battle to the 1. Right, or 2. Left about. This turneth the Aspect towards the Rear: Now by reason the motion is twice as much as the former, there ought to be the greater care had in the performance of it; observing so much the motion of the right hand man, that they fail not of being even in Rank with him. ranks and files wheeling To reduce them to their first Ground, face to the right, wheel to the left about, than face them to the left: Although to the left about may reduce them, but not on the same Ground. You may observe that Wheelings are the most facile for their Reducements; as for Example, Wheel your Flanks into the Front, is reduced by wheeling your Flanks into the Rear. OR, To wheel your Front and Rear into both Flanks, is reduced by Wheeling both Flanks into your Front and Rear, etc. Secondly, I proceed to Wheelings on the midst (or Centre) of the Front, which are Entire and Divisional, and are quicker in their motions, and performed on less Ground. 1. Command. Wheel your battle to the 1. Right 2. Left on the same ground. Entire. This is termed Grove Van Nawsaw's Wheeling. But it is a wonder to me why our Ancient and Modern Writers call these Commands Wheelings on the same Ground, when I am sure there will be ground lost (in the motion) from the first they stood upon: In a direct square this may be better performed and less loss of Ground. To perform this, Command. ranks and files wheeling The left Flank advance forward still wheeling to the right, and the right flank contrariwise facing to the left, and keep falling backwards even in Rear with the left half ranks, and so still moving unto the place commanded, face all to the right flank. You may wheel to the left also. To reduce this, Wheel your Battle to the left on the same Ground. 2. Command. Wheel your Body to the 1. Right, or 2. Left about on the same Ground. The direction to the former will serve for the performance of this, only the motion is double as much, and their faces are turned from the first Front toward the Rear. ranks and files in motion To reduce this, wheel your Battle to the left about on the same Ground. Divisional Wheelings. Bingham 2. part Tactic. pag. 92. 3. Command. Wheel to the right and left from the Front, OR, Wheel off your Front by Division. Or if you will not go so far, then wheel your Front into the Flanks by Division. This wheeling your Front into the Flanks by Division produceth the same Figure with Figure ●. If upon occasion Musquetteers be on the Front of the Pikes, by this motion they will flank their Pikes: But otherwise being to be performed in a standing Body, the Pikes will flank the Musquetteers, and may easily he performed. The File-leaders of the right flank with their respective Files are to wheel about to the right, and the File-leaders of the left flank are to wheel about to the left and close their Divisions. ranks and files in motion ranks and files in motion Figure performed. To reduce them, wheel them off by Division again from the Rear, of by the fourth Command. 4. Command. Wheel your Body inward to the Rear. If this be to reduce the former, it is presupposed the Commander is in the head of the first proper Front, than the Pikes will be in the midst of the Battle, as at first again: But if reduced without this Command, the Pikes will be in the Flanks ready to defend the Musquetteers from the fury of the Horse. To perform this, Command, the Body to open from the midst to the right and left, to such a distance, as they may turn off to the right and left. This I shall not demonstrate to you in Figure, because the precedent Figure performed will give light to the execution of this, and so for the next Command. 5. Command. Wheel off your Body from the Rear into the Front. To perform this, face them to the Rear, then to the right and left, and wheel them inward to the Front. To reduce the fourth Command, and this also: Wheel them off again to the right and left by Division. 6. Command. Wheel off your Front and Rear into the right Flank. These Commands following will produce the same Figure. Wheel of your Body by Division from the left Flank. OR, Wheel your left Flank into the Front and Rear. OR, Wheel your right Flank into the midst. To perform this sixth Command. Command them to face to the right; this done they must wheel together about the third and fourth men in the right hand File, the Front Division wheeling to the right, and the Rear Division to the left, until the Bringers-up meet with the File-leader. ranks and files Figure 6. To reduce this, it may be performed several ways, as the Body may be faced. If they stand faced to the right, then wheel your Flanks into the Rear; and being faced to their proper Front they are reduced. But if faced to the Front, then wheel the Front and Rear into the left Flank. But for the performance of the same Command into another Figure; It is but to pass through your Musquetteers from the left Flank to the right, than the same Command will bring all the Pikes into the Front. 7. Command. Wheel your Body inward to the right Flank from the left. To perform this, Command, To face to the right; then open to the right and left to a convenient distance, etc. ranks and files wheeling Figure 7. To reduce this, it may be done several ways as the former at the discretion of the Commander. This produceth the same Figure as the sixth, only it is altered in motion, therefore I thought good to demonstrate it; although Wheelings in this nature is difficult. 8. Command. Wheel off to the right and left inward to the Front: ranks and files wheeling To perform this, let them open to the right and left from the midst, and then wheel, etc. ranks and files This Figure when performed is serviceable against the Horse, because all the Pikes are in the Front, and stand according to this Figure. To reduce them, is by wheeling them off to the Rear. 9 Command. Wheel your Flanks into the Front. This is performed folio 62. Command 16. where you may see the diversity of words of Command for the producement of it. 10. Command. Wheel your Flanks into the Rear. The former Command folio 60. being reversed will serve for your better intelligence herein. 11. Command. Wheel Front and Rear into the right Flank. This is performed folio 78. Command 19 12. Command. Wheel both Flanks into the Front and Rear. OR, Front and Rear half files wheel off by Division inwards into the midst of Ranks. To reduce it, by another word of Command. Right and left half Ranks wheel from the midst inward to the Front and Rear. ranks and files wheeling To perform this Command. Half files face to the Rear. Front half files and Rear half files move all together, and wheel off your Divisions to the right and left. Then face them to their proper Front and close their Divisions. To reduce them. The reducement of the next Figure will serve for both. 13. Command. Wheel Front and Rear into both Flanks. To perform this from the precedent Figure, Face to the right and left outward, observing the former direction, and giving due distance for the motion. ranks and files wheeling There are several Commands that will produce this Figure. Wheel off your Body by Division from the midst of the Battle into the right and left Flank. OR, Wheel the midst of your Body by Division into the Front and Rear. OR, Wheel your right and left Flank into the midst. OR, Right and left Ranks wheel off by Division to the midst of Files. To reduce this, Wheel Front and Rear into the midst of the Battle. OR, By Wheeling the Flanks into the midst of the Battle, if faced. OR, If you please to face the Body to one of the Flanks; then wheel Front and Rear into both flanks, and face them to their proper Front, and close their Divisions. 14. Command. Left half Ranks, wheel off to the right and left, and double your right Flank by Division. Folio 79. Command 20. 15. Command. Front and Rear half Files, wheel off by Division. Folio 78. and Command 19 16. Command. Right and left half Ranks, wheel off by Division from the midst of Files. ranks and files To perform this, Command them to face to the right and left inwards, and then let them move backwards to such a convenient distance as to wheel off from the midst of Files. To reduce them, wheel off to the right and left inwards. I need not trouble you with more Angular Wheelings, either wheeling them outwards to the right and left about from the midst of the Battle; Part of Aelian's Tactics: chap. 36. 34. 46. or inwards to the midst, because the demonstration of the former may give light unto all such, etc. and I conceive them not of such absolute necessity. But I must advise that those Entire and Divisional Wheelings may be diligently learned and practised, as being of great use in this Military Art. I have in all my method demonstrated the Commands by their Figures to the right hand, you may easily command the same to the left hand, and the Reducements accordingly. You will find to several Countermarches and Wheelings no Reducements directed for them, because they may be reduced the same way back as was commanded, or by some other Command as directed. I know but little more to be invented for the secure Exercise of a Foot Company, (and because I would not be singular) I have demonstrated some that may be better spared than practised in service; however here is for all: Some may make use of what is necessary to the fitting of the Soldier for field services; and others at their pleasure what their fancy may guide them unto. And thus I have passed over the Grounds of Discipline for the Foot, I expect Censures; by the Ingenuous I submit to a correction; but for the Carper, let him remain in his own mud, he shall never be complemented to a cleared fountain by me. CHAP. XVII. Of making file leaders successively both in number and place in a file, six in depth, and so for a whole body. THe Soldiers having passed thus many day's exercise in these principles of Art Military; and now each Soldier is loving to his Comrade; every file leader to the rest of his file; being willing that their files should successively demonstrate some experiences as they have attained unto, in the exercise thereof: which will prove a great encouragement to the Ingenious: Also it is profitable to a Commander to bring what Ranks he pleaseth into the Front, and to exchange them, and to reduce them to their proper file leaders. A File to be made file leaders successively according to Number; or by commanding as followeth. Commanding by the file leader. 1 File leaders. — Rank two to the left, and file to the left double. 2 2 Ranks to the left double, and Files to the left double. — Countermarch Front and rear into the midst, and face to that part which was the Rear. 3 1 3 Half files double your front to the right, and files to the right double. — Face about to the right. 4 4 2 4 File leaders stand, the rest pass through to the right, and place themselves before their leaders. — Countermarch from the Rear into the midst, and and face to that which was the Rear. 5 3 6 5 5 Ranks to the left double, and Files double your depth to the left. — Files Rank two to the right, and file to the right double: face them about and it will reduce them. 6 6 1 1 6 6 Ranks to the right double and Files to the right double. To Reduce — 5 5 6 3 5 1. File leaders stand, the rest pass through and place yourselves before your Leader. 4 2 4 4 3 1 3 2 2 1 A File to be made file leaders successively according to their Dignity. 1. File leader. 1 The second man from the Front. 5 2 Bringers up double your Front to the right, and files double your depth to the right. Bringer up to the Front half file. 4 6 3 File leaders and half file leaders stand, the rest pass through to the left and place yourselves before your leaders. 3. Half file leader. 3 3 6 4 Front and Rear half files interchange your ground. The second man from the Rear. 6 1 2 5 5 Ranks to the right double, files to the right double. 2. Bringer up. 2 5 4 1 4 6 File leaders stand, the rest pass through to the left and place yourselves before your leader. 4 5 3 3 2 To reduce them. 1 6 1 1 1. Ranks to the left double and files to the left double. 2 2 3 2. Half files double your front to the right. 6 4 3. Bringers up face about to the right and march forth into your places. 5 CHAP. XVIII. Of certain firings in the Front. HAving passed over the grounds of this Art Military, I am now come to the executive part of the Tactics; and shall not here exceed the exercise of a single Company, showing the Soldier the use of some few Firings, that they may the better perform their respective duties when they shall be commanded thereunto. None can positively say, this or that figure shall be, or serve this day, time or place etc. because of the diversity of forms occasioned by situation of ground, he number of men, the order of the Enemy; with many other observable Stratagems, for the obtaining both of Wind and Sun. I shall therefore according to my allotment of twelve files demonstrate by figure some Firings, which being well understood may enable such for higher preferment as time and place may fortune them unto. By way of digression; I am sure it is a trouble to most ingenious spirits to see some Gentlemen chosen Captains in the Militia, that are but prisoners to their own reasons; and instead of being experienced in this Art have been wholly Ignorant of the least part thereof. It is no wonder then if his Majesty may lose his expectation of a well disciplined Militia; and the Soldier in hazard of his life and Country too. How easily might this be remedied, if our Commanding power would but authorise the Commission officers to meet once in a month to exercise each other, by their respective turns, etc. where they may also discourse and consult about Military affairs; and then for these private Commanders by their affable and heroic persuasions to get some of their soldiers as may be for their conveniency to meet with their arms, and to exercise them; this would not only be delightful but profitable both for King and Country. And on the contrary, the neglect hereof, and also of the full number of men and Arms in the Militia, hath made it to be ill spoken of, and so little feared; especially by those of our own inbred Enemies to the Royal Government. these things will be better looked into hereafter. If they will not be drawn to love and to be obedient to Royal Prerogatives, they must be made to dread it; And I humbly conceive there is no better way to effect the former than by having a choice Militia, of such whose spirits should account it a baseness to abuse the Country; and make not their Musters, pass times for debauchery; and that their Companies be not only well disciplined, but well Armed also. I proceed to the drawing up of files again into a body, and preparing them for skirmish. ranks and files A Company of Foot being thus drawn up for service and the Colours flying in the head of the Company, and there they are to remain, until all forlorn firings are ended: But so soon as the Drum shall beat his further preparatives for a close skirmish, the Ensign is to furl his Colours and retreat to the half files of Pikes. Observe, That all firings are either direct, or obliqne; and the manner how they are to be performed, are either Advancing, Receiving, or Retreiting: otherwhiles there may be firing in the Rear, marching from the Enemy; or in the flank marching by an Enemy: and also at several places, for an Enemy may at one and the same time charge, either in the Front or Rear, in Front and Rear, also in Front, Rear and Flank: and of these I shall demonstrate some that I at first learned, and some amongst others that are most convenient to be learned. Now that the Soldier might be expert in his firings against the Enemy, let him be often exercised with firings only, in the pan, falling off and on as shall be Commanded. All which being well performed by the Musquetteers is a full accomplishment of what hath been before taught him, by which the Commander shall be credited, and the Soldier preferred to his merit. Of firing by forlorn files. 1. That which is to be used in our modern exercise is two manner of ways; the two outmost files of each flank of Musquetteers to march with two Sergeants so far as shall be commanded, and there to stand: and the foremost ranks are to give fire and to fall into the Rear of themselves, either by wheeling off to the right, or to the right and left: Then let the remaining do the like and fall into their places. ranks and files Those that have fired are to fall off on the inside of the Musquetteers between them and the Pikes; and as they are thus trooping back (after firing) to their places, the rest are in like manner to move away, and fire, and fall in next the Pikes. 2. Accordingly as you draw out two files, so you may draw out more files to the number of Musquetteers; and so to fire and fall into the Rear of themselves, and places etc. 3. You may move them all clear of the Pikes, and let them open from the midst, leaving sufficient Intervals for their wheelings in the Rear of themselves, and then to place themselves even with their Pikes, the second having fired as before place themselves in the Rear of the first division etc. ranks and files 4. Advance the two outmost files by the Sergeants, who are to lead them to the place for execution as by order received; Commanding 1. Files to rank inward; to present and give fire all together. 2. You may rank inward two Files, or more, and fire as before. And having fired are to wheel off to the right and left by their respective file leaders, placing themselves next the Pikes. I proceed to a second way of firing and that is by Ranks. First, By advancing before the Front. Secondly, firing even with the Front. Thirdly, firing even with the half files. Advancing before the Front may be performed by advancing of single ranks, and so firing in the Front; or by advancing of both flanks into the Front before the Pikes, and so to fire by single ranks. Which is performed by Commanding Demyhearse. ranks and files 5. Pikes stand, Musquetteers move forward and place yourselves before in the Front of your Pikes, and close your Divisions. I mention nothing to tie up the hand of the ingenious to any stinted form, whose ablities may command his figures at pleasure. Observe, that when the forlorn files or Ranks march out, they are to give fire as upon a retreat (that is) to stand and fire, and wheel off that their followers may do the like, unless the Enemy give ground. And when the two last ranks were presented, the next two ranks must be ready to march forward being fixed to present and give fire also: Thus having fired in the Front by one single Rank, or more, they are by wheeling off to place themselves in the Rear of their own divisions before the Pikes; the rest doing the like until they have all fired round. A second way of firing by this figure shall be a reducement to it. First, The Frontiers having performed their firing are to wheel off by division until they come down so low as to be even to the first ranks of Pikes, and so to rank even a breast: All the Musquetteers are so to do successively and flank themselves even with the Pikes. ranks and files 6. Ranks advancing from the Front of a standing Battalia. A Sergeant from each Flank leading up the two foremost Ranks (according to order) the first Rank is to give fire, wheel off, and place themselves in the Rear of their own divisions: the second in order is to execute the same with speed, being not above three foot distance from the first, being ready with his Musquett palm'd, his Cock bend, and Muzzel mounted; so to Present and give fire; and so to wheel off and place themselves as their Leaders had done before them. ranks and files 7. Ranks firing even with the Front. The first Rank having fired and wheeled off placing themselves in the Rear of their Divisions, the next ranks are to move forwards at three motions into their places (making good their leaders ground) and there to present and give fire; wheeling off and placing themselves as by the former directions. By the way you must observe, if the body be upon a march the Pikes must be shouldered; and when they come to charge, they are to close forward at their close order. ranks and files It is presupposed ere one firing or two be performed (or past) over, the bodies are almost close; Then the Pikes are to be at their Port; and at length to be at their absolute Charge and push home: and being so near they may do great execution with their Muskets, firing upon the half files of Pikes as if they were even with the Front. Which brings me to 8. Ranks firing even with the half files. When the Pikes are charging then the musquetteers may perform this who are to advance no further than the half files of Pikes, and there you may either fire one Rank or more at the discretion of the Commander; and as soon as every Rank hath fired successively they are to wheel off and place themselves in the Rear of their own leaders. ranks and files When the firing is ended, and each Soldier in his proper place, the Musquetteers marching up even in breast with the Front of Pikes they are reduced. But in this firing the Musquetteers are to make good their leaders ground, except it be upon a retreat, than they are to fire upon the same ground and to wheel off, that their followers may do the like, unless the Enemy give ground. Horn. Bat. 9 Command. Pikes stand; Musquetteers march until the bringers up rank even with the Front. ranks and files You may in this as with some of the former fire two Ranks ten paces advanced before the Front, and so whel off and place themselves in the Rear of their own files. OR, Secondly, let the first Rank of Musquetteers present and give fire and wheel off to the right and left, placing themselves in the Rear of their own files: then the second Rank firing are to advance into their leaders place, firing and wheeling off in the same manner, and so they are all successively to do the like. Then Thirdly, when they have all given fire, let them begin again, and the file leaders having fired they are to wheel off to the right and left & flank themselves even with the Pikes; the second Rank now is to fire upon the same ground he stands and must not at all advance into his leaders ground as before, and having once fired all over they are reduced. OR, You may reduce themby Commanding the Musquetteers to face about to the right and march down into their respective places, OR, Command the Pikes to march up and even the Front with the file leaders of Musquetteers. A triple firing. 10. Front half files of Musquetteers double your Front of Pikes by division: 2. Rear half files of Musquetteers open to the right and left and Rank even with the Pikes. To perform this, direct the Front half files to advance clear of the body of Pikes, than face them to the right and left inwards, and so close their divisions before the Pikes. ranks and files You are to observe in this firing that the Musquetteers of the Front and both flanks are to present and give fire together; the Musquetteers of the Front division after firing are to wheel off to the right and left between their intervals, and place themselves even in Rank in the Rear of the Rear divisions of Musquetteers. Then the Musquetteers that fired in the flanks march directly down and place themselves even in breast with the Rear of Pikes. Thus they are reduced: Or else you may continue firing at your pleasure; and arging of your Pikes. 11. Wheel your flanks by division into the Front. When they have fired let them march (or pass) down through the intervals, and place them in the Rear of their own divisions; And then upon an other firing they may place themselves in the Rear of the Pikes. The Pikes here may charge either at hand or foot, the Musquetteers may also fire over them. ranks and files To reduce them: if it be upon the first Command firing and falling off in the Rear of their own divisions, let the Body close their Divisions, and wheel their flanks into the Rear, and face to their Leader. But if you fire a second time, and wheel off your Musquetteers into the Rear of the Pikes, Command the masquetteers by division to double their Front entire, and then wheel both flanks into the Rear, and face them to their Leader as before. 12. Command. Musquetteers, Poise your Musquetts, and march until till they be clear of the Body of Pikes: Then, Front half files face to the right and left inward, close your divisions, and face to your leader; Rear half files open to the right and: left; Front half files of Pikes face to the right and left outwards, and march even to flank the Having fired let them wheel off to the right and left, the Front Divisions falling in the Rear of themselves; and the flanks either in the Rear of themselves, or else in the Rear of their Pikes, the Pikes moving forward and maintaining the Musquetteers ground. ranks and files To reduce this, Command. Front half files of Musquetteers face to the right and left outwards, and march even in flank with the Rear half files of Pikes: Then wheel your flanks into the Rear. Front half files of Pikes face in opposiition, and march into your places. Musquetteers face about to the right and march closing of your divisions: face all to your leader. 13. Command. Musquetteers march all until your half files be even with the Front of Pikes; Front half files march three paces forward and stand: Rear half files of Musquetteers face to the right and left outward and march clear of the Front half files. Rear half files of Pikes open to the right and left outward, and march clear of the Front Division of Pikes. ranks and files The first Ranks of all divisions having fired they may in the first place fall in the Rear of their own divisions. And for a second firing so soon as the first ranks have fired in the Front, they are to wheel off to the right and left, and flank the Pikes as they were: then the Rear division of Musquetteers after firing fall off to the right and left, and place themselves even abreast with the Rear division of Pikes: Then Rear half files of Pikes face to the right and left inwards and march into your places: By this they are Reduced. 14. Command. Musquetteers march until your two last Ranks are equal with the two first Ranks of Pikes. The two second Ranks of Pikes, face to the right and march into the Rear of the right flank of Musquetteers. The two last Ranks of Pikes face to the left and march into the Rear of the left flank of Musquetteers. Having fired let them whel off to the right and left falling in the Rear of themselves; and so having fired once or twice over, they may fall in the Rear of their own Pikes, every Musqueteer as he fireth to advance unto his leaders place, and the Pikes to advance also, who are to be ported, and when the two last Ranks are firing they are to charge at the discretion of the Commander; which Figure I have here set down, because from it the fourteenth shall be reduced. ranks and files The Reducement. The two ranks of Pikes upon the right flank face to the left and march etc. then march the four ranks direct; The two Ranks on the left flank face to the right, and place yourselves as you were facing them to their Leader, the Musquetteers to advance and flank the Pikes; they are reduced. 15 Command. Front half files of Musquetteers, and the two first Ranks of Pikes march three foot: The four Ranks of Pikes wheel your flanks into the front by division, and face to the right and left, and march even in the Rear of the Front Division of Musquetteers; Then the Rear half files of Musquetteers face to the right and left, and march them clear of the division of Pikes, facing them to their Leader, and march up even with the flanks of Pikes. ranks and files Having fired and wheeled off in the Rear of their own divisions of Musquetteers, then for a second firing let the Front divisions of Musquetteers fire and wheel into the Rear of Pikes, the pikes porting, and charge as in the figure and retreat; and upon the retreit the Pikes to fall all even in breast; And the front division of Musquetteers to sleeve up even in breast with the Rear division of Musquetteers; Then the Pikes to charge on again, and the rear division of Musquetteers to fire, wheeling off to the right and left, and fall into the Rear of the front division of Musquetteers: who will then stand after this form. To reduce them, Command. The Pikes to advance and march all to a convenient distance, then march the middle division of Pikes six foot; then the two divisions of pikes upon the flanks to face in opposition and close their divisions; Then Wheel their flanks into the Rear and face them to their leader, which being done the Pikes are reduced. The Musquetteers are to march up and flank the Pikes. ranks and files Many firings the ingenious might invent to the Front more than what I have demonstrated: I shall only mention the Introductive, and Extraductive firings. I must give my judgement with those who do not allow the firings by way of Introduction to be useful in our modern Wars; nor are they secure to the Soldier unless when the Commander shall find his Soldiers to be well exercised, then amongst other various curiosities these may be performed. By the word Introduction is meant a passing through, or between, and by its motion doth advance and gain ground upon an Enemy. 16. Command. Make ready to give fire by Introduction: Then Command the files of Musquetteers to open by division to their open order, and to pass through to the right, etc. ranks and files The first rank of each flank presents and gives fire, so done they stand and make ready again. The second rank so soon as the first have fired, passeth through, and placeth itself before the first, and do their fire, and stand also and make ready again. The third is to pass forward and stand in rank even with the first, and when the second rank hath fired, they must step before the second, and having fired are to stand and make ready again; and thus every rank is to follow his Leader successively, until the Bringers up of each Division are to give fire, and stand in the Front of all. Observe, in this firing you may keep your Pikes shouldered, still moving slowly forwards (if there be no danger of Horse) and so keep even with the Front of Musquetteers: This done twice over will reduce them. A Second way of Introductive firing. The first Rank is to fire and stand, as in the forementioned Figure; then the Bringers-up (or last Rank) whilst the File-leaders are firing shall, march up and place themselves even with the second Rank, and when they have fired, the Bringers-up are to step before them, and immediately to present and give fire; and when the rest have followed their Bringers-up, and fired once over, be sure that the File-leaders fire twice; Both produce the horn battle. who ought to be the first and the last, and so stand: the Pikes are to march up even with the Front of Musquetteers as in the former direction and they are reduced. Extraductive. 17. Firing. There have been in use two Extraductive firings, I shall speak but of one which is allowed somewhat useful, especially in narrow passages, and in case your Enemy be too powerful, either in Horse or Foot; that then the passage might be filled up with the Pikes: but if your Pikes be not sufficient to do it (as you will perceive by my Figure) then double your Ranks, let your Pikes be in such posture and motion accordingly as occasion shall offer itself. Command. Musquetteers face about to the right, and march until you are clear of the Body of Pikes; then face inward and close your Divisions: for the Pikes command them to double their Ranks to the right; Or, half Files double their Front to the right. To perform this Command. The first rank of Musquetteers next after the Pikes, face to the right; then to march forth file-wise, close up by the right flank of Pikes; and when the Leader is advanced into the Front of Pikes, he is to lead them athwart the whole Front of Pikes; after which they are all to stand, present and give fire, and having fired they are to wheel off to the left, and fall into the Rear of Musquetteers; and whilst the first Rank is firing, the second is to be marching so as to be ready to fall into their Places. ranks and files To reduce them, Command the Pikes to advance six foot (if they be doubled their Ranks to the right) let them now double their Files to the left; then Command: I could have mentioned a great many more firings to the Front: but through my confinement to such a small number of men, and not an equality in arms, Art completed cannot be expected from me. Must of these firings are solid and serviceable; yet it cannot be conceived that three Ranks can make any abidement of Battle for continuance against any Enemy: although sometimes they may be forced to be reduced into less Numbers, yet by showing the nature hereof you will be the better able to manage a greater, etc. CHAP. XIX. Of firing in the Front and Rear; And Rear alone. BEfore I demonstrate the firings in the Rear, I thought it fit to give one Figure of firing to the Front and Rear, which may serve also for a firing to each Flank, when the Commander pleaseth. 1. Command. Front half Files of Musquetteers march until your Bringers-up be even in breast with the Front of Pikes: Rear half Files of Pikes face about to the right. Rear half Files of Musquetteers face about to the right, and march, until the half File-leaders are even in breast with the Bringers up of Pikes. ranks and files For the first firing by this Figure, so soon as the Ranks upon each Division have fired, they are to wheel off to the right and left, and fall into the Rear of their own Divisions: And having so fired all over they are to wheel off and place themselves even in breast with the Pikes, as now they stand faced; then being faced to their Leader they are reduced. This is not our drift of firing in the Rear; but if in a March an Enemy eagerly pursues and assaults, then by facing about and firing in the Rear, or by Countermarching, or Wheeling about, and so firing; these repulses orderly performed may cause a disorder in the pursuants: And it is good sometimes as occasion may offer to keep an Enemy in play, whilst he may advantage himself in his Ground, either for his Embattlement, or Ambushes, or for the conveyances of Gunns or other Carriages, etc. 2. Firing. Upon a March the last Rank is to face about, and so to give fire, wheeling off in File by Division, and marching up towards the Front, and placing themselves before their File-leaders. ranks and files 1. Observing, that they rank even with the second rank of Pikes. 2. In the performance of this, you will lose one rank in the Front. 3. Observe, that whilst the rank of Musquetteers are firing in the Rear, the next rank although he be marching, he ought to be preparing with his cock bend and guarded, that with his three motions, he may next fire so soon as his precedent rank is wheeled off. 4. Although you are upon a march, yet you are to fall one rank nearer to the Rear, that the Body may be preserved entire. 5. Observe further in the performance of all this, your preparations and firings ought to be at three motions: Cock your match, Blow your coal, Present, etc. Let the first be with the right leg advancing, the second with the left leg advancing, bending your cock; then a little advancing forward with the right foot, to present and give fire. Now I give these Reasons for the Observations of some motions in these firings to the Rear; because so soon as the Soldier hath fired, if the last rank should immediately face about and present, etc. there would be a present encumbrance; This experience hath discovered, and that firing upon motion to be the most speediest and safest way for firing in the Rear. Now for a Public Exercise, when you have fired over once, you may then face them to their Leader, and fire in the Front. But if you be upon a march, and should be pursued by an Enemy's Horse, then Wheel your Flanks into the Front, and face to the Rear; your Pikes will defend your Body, so your Musquetteers may fire over them as in the 17. Figure by extraduction, and reduced accordingly. Secondly, In firing to the Rear, the Musquetteers may be in the Rear of the Pikes. And first having fired they are to wheel off and place themselves between the Front of Musquetteers and Rear of Pikes. And secondly, having fired in the Rear they may wheel off by Division and march into the Front of Pikes, the Body still marching. Or, if both flanks be in the Rear, they may fire & wheel off by Division, and double both flanks. This last hath reduced itself; and for the second you may for exercise, fire them in the Front, and in their wheeling off to flank their Pikes; or for expedition, for the Musquetteers to open to the right and left, and march the Pikes up in the interval, and they are reduced as at first. You may perceive the use of firings in the Rear, and that the Soldier ought to be very well exercised in them: For a true experience herein doth not only add to the perfection of the Soldier, but his safety also. Before I conclude this Chapter, I shall add two Figures of firing in Front and Rear marching. 3. Command. Front half Files of Musquetteers, march until you be clear of the Front of Pikes; Face in opposition and close your Divisions. So for the rear half files, face about to the right, and march until you be clear of the Rear of Pikes; face them in opposition, and close their Divisions. ranks and files Having fired their first and last Ranks, they wheel off to the right and left by Division, the Front Division are to place themselves even in Rank with the Front of Pikes, and the Rear Division of Musquetteers are to place themselves even in Rank with the Bringers-up, and so each Rank successively after each other, will reduce this Figure. 4. Command. Half Files of Musquetteers, fire to your Front and Rear placing yourselves between your Divisions. ranks and files This firing is plain without direction, and the firing being ended they are reduced. CHAP. XX. Of Firings in the Flanks. THere are reasons to be given, and Experience hath found it necessary, for firing in the Flanks: When you are upon a March, an Enemy may endeavour an assault to molest you in your passages, that your disadvantages may be the greater, either by ambushments laid against you, or to frustrate your designs. Now in the performance hereof there are several circumstances that are to be taken notice of, as the strength of your Enemy, the time, number and place; all for your own security, or advantages against him. I shall begin with some Exercises upon the right flank, and what is performed there by Figure, may also be performed upon the left hand. In order hereunto pass all your Musquetteers into your right flank by Commanding: Musquetteers of the right Flank open to the right, and being opened to a convenient distance, stand; then Musquetteers of the left Flank, pass through your Ranks of Pikes to the interval of the right Flank, then stand, and face to your Leader. Your face to the right or left, is that, by which the flanks become accidental fronts, and then for the firings thereupon, you may to your discretion use such as are most convenient; being already shown Chapter 18. I shall not here take up any room with the demonstrations thereof, and shall show but some few firings in the right flank, as the Body shall be marching, in all which you are to observe the Pikes are to be shouldered. 1. Command. Musquetteers give fire to the right, and wheel after your Bringers-up, between your Divisions. ranks and files And this at the discretion of the Commander is done two ways, either by commanding to be lead into their places by their File-leader, or by their Bringers-up, and to place themselves before them, etc. Here by this Figure, they in the first place, as the Body is marching, face to the right (the outmost File) presents and gives fire: after their firing, they face to the right, and after their Bringer-up, who leads them off in the Rear of the Musquetteers, and up into the Interval between the Pikes and Muskets, until the Bringer-up of the File hath placed himself even in breast with the Frontiers; and so the marching Party, as Command shall be given, are to open, that the Files of Musquetteers after they have fired may march up between the Divisions, and so every File is successively to fire, and wheel off and place itself. This firing being performed twice over they are Reduced: If but once, you must countermarch your files of Musquetteers to reduce them. 2. You may secondly after they have fired, Command them to face to the right, and to wheel off, every man placing himself before his Bringer up (or present Leader) hereby the Bringer up will be in his due place and the file-leader in his proper place, also. 3. A Third way of firing upon this Figure, is to fire in the right flank, and to be lead off into their places by their respective File-leaders. The Body marching, the outmost File faceth to the right and fires, and when the body is marched clear of the standing file, than the next file presents to the right and fires, and whilst he is firing, the first file that is fired faceth to the left, and marcheth up between the Musquetteers and Pikes. Observing the former directions in their march, that there may be space enough in the Interval for the several Files successively to march into these places. ranks and files 4. There is a fourth way of firing, that is, to give fire to the right and gather up your Files. The Body marching the outmost file faceth to the right, fires, then stands, and faceth to their Leader: Then when the Body is clear of the standing file, the second file faceth to the right, and fires and stands also, facing to their Leader; then the first file is to advance up to the second, and so when the first and second have fired they are to be lead up to the third. Thus having fired, they are to be lead up even in breast to the file that last fired, and having all fired, they are to be marched up even with the Front Pikes. ranks and files To reduce this, Command: Left half Ranks of Musquetteers, face to the left; Pikes face to the right, pass through interchanging of Ground; Face to your Leader. How beneficial this may be to the security of the Soldier, they that will make use of it that are ingenious will better judge: but I am of opinion it is more fit for a private Exercise, than for public Service. 5. Command. Give fire to the right, and place yourselves even in Front with the Pikes, marching up between the midst of the Pikes. Observe, in the performance hereof, the Pikes as they march are to open to the right and left, and the fired Musquetteers are to be lead up according to Command. ranks and files To reduce this, Command. 1. Pikes to face inwards. 2. Musquetteers face to the right and left outwards. 3. Pass all through and interchange Ground. 4. Face to your Leader. 6. Command. Musquetteers give fire to the right, placing yourselves on the outside of the left Flank of Pikes. ranks and files If you will reduce this without any firing, you may Command the right half Ranks to pass through your Ranks of Pikes. (The Ingenious may find many ways for the Reducement.) Or, when all the Musquetteers are on the left flank, you may fire them over again, and they are reduced. 7. Command. Musquetteers give fire to the right and to the Rear; placing yourselves between the Pikes and your own Divisions. Having placed your left flank of Musquetteers in the Rear, A useful firing. then Command, ranks and files The outmost file upon the right flank, are to face to the right, and the last rank of Musquetteers in the Rear are to face about, and both are to present and give fire together; and having fired the outermost file upon the right hand faceth to the left, and marcheth after their Leader in the interval between the Muskets and the Pikes; They are to march a reasonable pace. and the rank fired in the Rear is to wheel to the right, placing itself in the Rear of Pikes, etc. This is easily reduced, by commanding the Musquetteers to draw off into the left flank again. Observe, that flank that is farthest from the Enemy ought to be drawn into the Rear. 8. Command. Musquetteers give fire to both Flanks (marching) and place yourselves between the Pikes and your own Divisions. ranks and files To perform this, the outermost file of each flank presents outward. 9 Command. The Body standing, Advance your Pikes; Musquetteers and Pikes face to the right and left; Musquetteers present and give fire to both flanks, and flank your Pikes. The outermost file upon the right and left flank presents and fires, wheeling off by Division, ranking or flanking the Pikes, as they stand faced, leaving such a distance as the rest may securely follow them, every rank is to fire upon the same Ground, and wheel off by Division after the same manner. ranks and files From this Figure as they will stand after firing, there may be produced a great many brave Figures; but now I must leave them to the skilful Artist. To reduce this Command. The Musquetteers to march all until they are clear of the Pikes; then face them to the right and left inwards, and close their Divisions, and face them to their Leader. 10. Command. Because it may easily be produced from the precedent Figure; it shall be from the first Figure of firing in the Front and Rear, Chap. 19 the Body being faced to the right and left will be a firing to both Flanks. 11. Command. Shall be a firing to right Flank and to the Front and Rear. Left half Ranks double your right Flank by Division. ranks and files You may face the Divisions any way, which you intent for their firing. After firing they are to wheel off into their own Divisions, every Rank moving into his Leaders Ground. To reduce them, face them to their proper Front, then Command half Ranks that doubled face to the left, and so march into your places. See the doubling of Flanks Figure 17. CHAP. XXI. Of several Divisional Firings. I Might here make mention of a great many Figures for firings, some serviceable, and others not, but all left to the judicious for censure, and to make use of the best; yet none useless for delight or Garden Exercises: The Figures cannot be perfect because I am tied to the exercise but of twelve Files, four of them Pikes and eight Musquetteers; it being a Number that our Western Commanders can make use of, and no more; yet any who may be capable to perform them, will be able to invent others; and command the production of such like in geater Numbers, and with better delight. 1. Command. The two outmost Files upon each Flank stand; the two inmost half Ranks of the Rear face about to the right: the two inmost half Ranks both of Front and Rear, march until you are clear of the Body of Pikes; then half Files rank to the right and left inwards by wheeling into the Front. For the Pikes, open them to the right and left from the midst; then Command the right and left hand File of Pikes to stand; the Rear half Files of the remainder face about to the right, than both half Files rank to the right and left inward into the Front and Rear. This Figure in great Bodies must be performed otherways, and may be very serviceable against the Horse; the Pikes may advance into the Front of Musquetteers to secure them against the Horse's fury if occasion shall serve. ranks and files After their first firing and wheeling off to the right and left in the Rear of their own Divisions, then when the Pikes are defending them from the Horse, let them fire over the Pikes. This being done pass through the Musquetteers before the several Fronts of Pikes, as they were before any firing. To reduce them, Command. Face the Front and Rear to the right and left inwards: The Front and Rear Ranks of Pikes file to the right and left inwards; the right and left hand files of Pikes close to the right and left inwards; and close all to the midst: Then Command the Front and Rear Ranks of Musquetteers, file to the right and left inward, face in opposition and march into your places; closing the whole Body to their close Order; and open them again to their Order: Evening of their Ranks and straightening of their Files they are reduced. 2. Command and Direction. Musquetteers open six foot to the right and left: Front half Files of the right Flank of Musquetteers, Advance entire into the Front of Pikes: The Rear Division of the left Flank of Musquetteers face about to the right, and double entire the Rear of the Pikes: The Front Division of Musquetteers of the left, face about to the right, and march even in breast with the Rear half Files of Pikes: The Front half Files of Pikes face to the right and left outwards, and march until you are clear, etc. Face them to their Leader. ranks and files To reduce them. The Front Division of Musquetteers face to the right, and march into your places: Rear Division of Musquetteers face to the left, and march forth into your places: Front half Files of Pikes face in opposition and close your Divisions: The left flank of Musquetteers advance even with the Front of Pikes: Musquetteers close to the right and left inward, and face them to their Leader. And they are reduced. 3. Command. Front half Files face to the right and left, and march clear of your Rear half Files: Face them to their Leader, and march them until their Rear be even in Front with their Pikes: The two first Ranks of each Division face to the right and left and march them clear of their own Divisions; face them to their Leader: The four first Ranks of Pikes open to your open Order, and double your Ranks to the right, the two last Ranks of Pikes face about to the right and march clear of the Rear of Musquetteers: Face to your Leader. ranks and files To reduce them, Command. The first Body of Pikes to double their Files to the left, the two last Ranks of Pikes march and close your Divisions. The two first Ranks of Musquetteers face in opposition, and close your Divisions. Then the Front Divisions of Musquetteers face to the right and left inwards, and march even to the Front of Pikes, than face them to their right and left, and close their Divisions: Face them to their Leader: evening their Ranks and straightening of their Files, they are reduced. 4. Command. Front half files march clear from your Musquetteers: The Rear half files of Musquetteers face about to the right and march clear of your Pikes; and face to your leader. ranks and files The Reducement. The Front Division of Pikes, face about to the right, and march into your places; the Rear Division of Musquetteers march up into your places. 5. Command. Wheel both your Flanks of Musquetteers into the Front, both flanks of Musquetteers open to the right and left: Front division of Pikes march clear of the Front of Musquetteers, and open to the right and left, until you are clear of the Angles of the Rear half files: The two inmost files of Musquetteers march until you are clear of the Front of Pikes: The next two inmost files of Musquetteers face in opposition, march and close your divisions in the Front of the Rear division of Pikes; face all to your leader. ranks and files To reduce this; The four middle files of Musquetteers face to the right and left and march into your places. The files of Musquetteers in the Front face about to the right & march into your places. Face them to their leader. The Front half files of Pikes face in opposition, and close your divisions facing them to the Rear and march them into their places; then close the Front of Musquetteers as at first, and wheel the Front into your flanks etc. they are reduced. The two next figures are almost one and the same, and with but a little alteration in their Commands they may be either produced, or reduced. 6. Command. Pikes stand; The Rear half files of Musquetteers face about to the right: Musquetteers march all until you are clear both of your Front and Rear of Pikes, face in opposition and close your divisions: The four inmost Ranks of Musquetteers march clear of the remainder both in Front and Rear. The two last Ranks of Pikes stand, the rest to the right and left by division march clear of the Musquetteers, and wheel to the right and left outwards. ranks and files Directions for firing upon this or others I must leave to the ingenious; wishing the unskilful to fire only as the Figure lieth, lest it may prove trouble to them to reduce. The Reducement. The two ranks upon the flanks wheel to the right and left inwards and march into your places: Front and Rear Musquetteers face about to the right and march forth into your places (provided they are faced to the Rear) only than the Front Musquetteers are to face about. Then Musquetteers face to the right and left outwards, and march clear of the Pikes; face in opposition and close your divisions, and face all to their leader they are reduced. It is but marching up of the two last ranks of Pikes into the Rear of the Front division of Musquetteers, and the Musquetteers even to the Rear of the Pikes, which produceth this next figure. ranks and files 7. Command. Half files double your Front to the right, the two outmost files of Musquetteers of each flank march ten paces direct and stand. The two next files of Musquetteers of each flank march to the Rear of the first, and the two next Ranks in the Rear of the second, until they are clear of the Front of the battle: And thus is this figure produced. Or by Commanding. The two outmost in each flank to stand, the rest of the Body face about to the right and march, and so leaving the two outmost files in the Rear of the first, and the third in the Rear of the second, and the remainder of the Body in the Rear of the third; facing all to their proper Front. ranks and files To reduce them, Command. Musquetteers face about to the right and march into your places; Then half files that doubled face about to the right and march forth into your places. Or, Even files from the left, double your files to the left. 8. Command. Half files double your Front to the right entire, then command the two outmost files of Musquetteers of each Flank to march until they are clear of the Front and stand; the four inmost files march until they are clear of the Battles also and stand. ranks and files To reduce them. Musquetteers face about to the right, and march forth into your places. Then half ranks of the right double the depth of your left flank entire. 9 Command. Pikes march clear of your body; Pikes wheel your flanks into the Rear; Musquetteers close to the right and left inward: Half files of Musquetteers double your Front to the right: The four innermost files of Musquetteers face about to the right & march clear of the Rear: even your Ranks and straighten your files both of Pikes and Musquetts: Then the four innermost files both of Pikes and Musquetteers march ten paces direct. Then Pikes and Musquetteers of each Flank face to the right and left, and march ten paces; facing them to their leader. ranks and files To reduce this, Command. The front division of Pikes and Musquetteers face about to the right and march even in breast with the Rear of Musquetteers of each flank. Then face the division to the right and left inwards, and close your divisions, then Command the Musquetteers to open to the right and left from the midst, and the Rear divisions of Musquetteers march into the intervails (or into your places as you were. Then Command the Pikes to wheel their flanks into the Front, then open the divisions of Musquetteers to the right and left, facing the Pikes about to the right, and march into their places: so facing of them to their Leader they are reduced. I might have added more, as the Plinthium Battle. For which and more read Captain Bingham Chap. 42. pa. 55. as also Barrif, Ward. And Elton as I am informed has written at large, but I never saw his works. CHAP. XXII. IT may be expected I should treat also of large Battalias, or great numbers of men; demonstrating of them likewise by their several Plat-forms: But having my Number proportioned, as you see by my several exercises, I have stretched them as far as is convenient, that by their figures they may be so well understood, that when larger numbers are before you, your Commands may be performed with more delight and security. But before the Drum beats a march to departed the field, I shall briefly declare, That in grand Battalias (or field services) the Soldier fires by volleys, or (as termed by some) Salves of shot; that is, when they are to fire entirely by two or three Ranks, or more, as your number will permit, and occasion require; thereby pouring showers of lead upon your Enemy: Now this way of firing, and those also of gaining ground I could wish the Soldier should be often experienced in: The Commander in taking pains with his Soldier cannot be the worse for it, and I am sure the Soldier much the better; being fitted thereby to meet his Enemy in any field service, when his Majesty shall have occasion to Command him. For that Commander that is experienced in this Art Military finds that those who know but little more than the Theory part, are oftimes puzzled (or at a stand.) What can such who are but mere Bookleidgers do? when their Number of men is wanting; or nature in place sparing to their advantage or intentions; such when they are forced to action, they will fail of their expectation, and at last must be beholding to others that are better Artists, or else it may prove a fatal ruin to both. Some of my friends might think that I should treat also somewhat concerning the dignities of Officers in marching & in placing of them in field services: but that belonging to Commanders of an higher degree, it would be presumption in me to lay down rules for them to follow; for any Minor Officer that for his satisfaction will be pleased to view the third Chapter of these Obsevations, he may understand the method and mode thereof; and I hold it in my judgement, that all dignity in marching of a Regiment is from a file; and the drawing up of Companies for a Battalia, is from a Rank. In the next place I come to show the necessity of the exercise of Arms, etc. CHAP. XXIII. Showing the necessity of the Exercise of Arms with their Antiquity. BEcause I have heard it sounding in my ears; what needeth all this trouble and expenses, in the exercise of Arms? We are now in times of Peace what need we to make provision, & c? I shall lay down some examples showing. First, How Ancient the use of Arms have been. Secondly, A complaint for want of Arms. And Thirdly, The end and use of them. For the first, Abraham had three hundred and eighteen men in his House fitted for War, upon short warning. Moses shown the people how to encamp by their Standards, under the Ensigns of their father's Houses. Joshua and the Judges, under whom of Reuben and Gad and the half Tribe of Manasseh were four hundred and forty thousand, seven hundred and sixty men exercised in Wars. You may read of David, of Solomon, of Jehosaphat, of Asa, of Vzziah, whose care in this particular is most plentifully declared. Secondly, Of the complaint for want of Arms. We read in the History of the Judges, Was there a shield or a Spear seen among forty thousand in Israel? This question is a plain negative, there was not; here is that Defectus Remedii, the want of help: Great was their misery, but no remedy; not a Spear to offend, nor not so much as a Shield to defend; War was at their Gates, yet neither offensive nor defensive weapon to assist: Such an extremity as this was will cause all to be lost; either present possessions, or in future possibilities, so that hope and help in such extremities must be laid aside. There was likewise a great distress in the time of Saul; when the spoilers were come out from the Philistines, there was neither Sword nor Spear found in any of the hands of the people that were with Saul and Jonathan (but with Saul and Jonathan only) yet although here was a great want they had victory. It is well known that God can give victory by small means, (and as the Apostle said to Christ, Master, here are two Swords; he answered it is enough. He can give your Enemies into your hands with two Swords, with one Sword, with no Sword.) All this was to convince the Children of Israel, that God fought for them, to move them to bless the Lord, Fifth monarchy men. Although some have been such audacious Rebels to think their zeal should even beck God Almighty, or to command power and aid from him to fight for them; therefore boldly attempted of late, saying that ten should chase an hundred and an hundred a thousand: But through the unjustness of their undertake (and fewness in Number) they must sink; to convince them and all others upon any pretence of Religion that will be such Rebellious dissenters, God Almighty will not only fight against them, but will deliver them into the hands of Justice, to magnify his own power in bringing such to condign punishment. Thirdly, For the end and use of Arms; It is for the recovery of our just rights which wrongfully have been detained; or for the preservation of them, against any opposer either foreign or domestic: For these ends Arms may be used, and War proclaimed; yet not by any other way or pretence, but by and with his Majesty's consideration thereof whether just or unjust; by which we are to be either encouraged or discouraged. A just cause may be farther considered in the Peace of the People, the safety of the Country, and the Glory of the Kingdom: As to the first, there was never any War intended but to make way for Peace, (it is a base end to desire Peace, by which to levy a force against an unjust War) but so to desire a just War that thereby may be settled a well grounded peace. A second thing that may be considered is the health and safety of the Country: some must be endangered that all may not be destroyed: I could wish that our Chiefetains and Gentlemen with those dull, leaded spirits of our rotten Country— and miserable worldlings would consider for whose sakes the worthy Soldier spares neither time nor purse in this Noble Exercise; but even for them and theirs, theirs and their Children; yet they must be judged most contemptible; rather than to countenance them, some will burden them in their rates and taxes, and keep their just deuce and pays from them: yet consider who it is that must preserve your Cities and Countries, Temples and Palaces, Trafficks and Marketts, Ships and Shops, from ruin, desolation and destruction; but the Soldier under God. Thirdly, The Glory of a Kingdom lieth much in a people well disciplined in the Art of War. That Prince that maketh it his designs to have his people instructed and trained up in Military exercises, will make his Enemies to fear him both at home and abroad: And that people that shall justly be called forth upon these principles, need not fear of being conquerors. A just cause may be spoiled through the ill management thereof, or through perfidious deal. A Rebellious Conqueror may make laws even to death itself, to maintain his Victory; as our late Usurpation hath experienced: But at last the whole world beheld with an eye of admiration, to see how miraculously God restored his Majesty to his Crown and Dignities; the Church and People to their just rights and liberties. I do affirm and truly say of Sovereign Power, Kingdoms, Laws and Armies, as was said of Hippocrates' Twins, they laugh and weep together, they live and die together; for as without Laws the Sovereign power and the Commonwealth cannot subsist by reason of disorders within; so without Arms, and the exercise of them th● cannot be safe by reason of dangers without. I shall further and briefly prove that the safety both of King and people is much advanced by the exercise of Arms: although Solomon saith In the multitude of people is the honour of a King, and for want of people cometh destruction. Notwithstanding I may affirm that safety is not in a multitude of men without weapons, and skill to manage them. It is asserted That Counsel and strength are for War; Then, how shall Counsel and strength be established, Isa. 36. without education and instruction to service? and how shall a man be instructed without Military Exercises? There are some disadvantages that happen in Wars, partly by reason of the suddainness of the War, and partly in respect of the inequality and odds betwixt party and party; Now Soldiers without dexterity and skill, can never be able to extricate themselves out of such difficulties as may befall them: All which proves that the exercise of Arms is to be allowed and Commanded. And as I told you at first I have heard some say, that we live in Gospel times, which are to be times of Peace, and not of war, therefore there needeth not those Exercises of Arms as you reason for etc. This is argued by some out of covetousness to save their expenses; but are ready to declare when there is occasion, than they will be in a readiness to do their best: There are others of a Fanatic humour, He speaketh not against the use of weapons or lawful War. Whereas before Christ they were enemies, but now there shall be love etc. unwilling to set forward any thing that may be commanded them, & argue from that in Isaiah, They shall heat their swords into plough shares and their Spears into pruning hooks. Nation shall not lift up a Sword against Nation, neither shall they learn War any more. Now in answer hereunto we must oppose it by another saying in Joel, where the people were called upon to beat their plough shares into swords, and their pruning hooks into Spears. For the reconciling hereof the learned say that Isaiah was to distinguish between the purpose and intent of Christ's coming into the world, and the other showeth the success and event which was accidental in respect of man's malice: Again to the first of these they argue what Christ said to Saint Peter, Put up thy Sword, for he that strikes with the Sword, shall perish by the Sword. But I pray you observe what he saith to his Disciples, That he that hath no Sword, let him sell his coat and buy a Sword. Although the end of Christ's coming was to reconcile things in Heaven and things on earth; I have been further taught by the Learned that this is attained unto between God and us in our Justification; and will be accomplished between man and man in the day of Redemption: Yet as long as there is a Sathanical Spirit in the children of disobedience, and so long as there is a remnant of sin in the heart of any, there will be Divisions, Familists, Quakers, Anabaptists, Independents, and Presbyterians; All being refractory to the present commands etc. Which showeth a necessity to have a care and prepare for the exercise of Arms; That none of these by their Usurpation may for ever hereafter snatch the Trumpets out of Moses' hands; nor the Trumpet only, but the Sword also, nor the Sword alone but the Crown and Sceptre also: Now by this mutual exercise of Arms I doubt not but in a little time God Almighty will unite the affections of most against such as shall exalt themselves above all that is called God. Let me excite all to be diligent, in the use of the means, to make themselves able and fit Soldiers and Commanders, by often Exercising, and willing to get complete Arms, to be exercised in Martial dispipline; considering how ill it was with Israel when there was not a shield to be found amongst 40000 men; And consider again how worthy of praise it was to Martial Discipline in Israel, when they had 170000 every one able to lead an Army, etc. I must tell you we have not our peace by Patent, we know not how long it may continue, Let war therefore be provided for, as to train up some to military practices: If War should come, it is labour well spent; If not, it is a labour well lost. Long preparations make a short and quick victory. Some are apt to say we have Soldiers enough, we will all fight when occasion shall serve; Let me tell such that they that never tried it, think it a pleasure to fight, and they will fight strangely, if they have no weapons, and use their weapons more strangely if they have no skill: Re Milita. lib. 1. c. 20. It is a saying of Vegetius, Non de pugna, sed de fuga cogitant, qui nudi in acie exponuntur ad Vulnera. Their minds are not so much on fight as fleeing, that are exposed to War without weapons; and a Soldier may be almost as well without them as not to know how to use them. Now that the Soldier may not be failing herein, and that his Majesty may never want able Soldiers in the Country as well as in the City; I most humbly beg, and crave pardon in presuming to present it, That the Muster master in every Country should be a careful person, an able Soldier, and one whom the Commanders and Gentlemen love and affect, who should be always by authority to attend at such times and places, as shall be thought convenient to exercise and teach the Art of Military discipline to all that shall willingly embrace it; And if his pay be too little for him, to make it his business and to attend upon it: It may be then augmented without any trouble; and the Soldier will be found much more capable for service when commanded. There must be exercise or else men's spirits will grow resty: what turns to putrefaction sooner than standing water? what is Virtue without Action? Idleness doth neither get, nor save; but lose: If exercise be good than those are best that tend to the most good: The exercises of War step in to challenge their deserved praise, which I leave to the most Judicious to give them their due in time and place. The ancient Gauls were said to be the most Warlike and Valiant men of all Nations: But how became they such? It was by the continual exercise and use of Arms; Caesar's Com. l. 5. & 7. for it was their Custom, to come Armed to their Councils. Their applause of any Oration was signified by clattering of their Arms, and their Oaths taken were upon their Arms. The Germans were wont to go Armed about their negotiations, and to their Banquets. The most Warlike Nations in the world have accounted it a piece of policy, to be frequent in the use of Arms: Why should not the laudableness of such martial exercises persuade men to love and embrace the use of them? We read some precedents for it; of Jonathans' shooting for sport that he might be thereby fitted to War. And without doubt the Benjamites attained that dexterity in casting stones out of a sling at an hair's breadth by frequent exercise for recreation. And may I not affirm, by the Exercise of Arms that Empires, Kingdoms and Commonwealths have come to their height and Sovereignty, and have so maintained their State in happiness and prosperity? and by neglecting of the same, they have declined and decayed, and at last have been made Preys to their Enemies: How were those Empires and Monarchies of the Egyptians, Medians, Parthians, Persians and Romans, established and greatly augmented by this Military Art; And how was the Dominion of the Grecian Empire preserved and wonderfully enlarged by the Art and Discipline of great Alexander with small Armies of well ordered and exercised Soldiers? How did he vanquish most great and huge Armies of his Enemies? Nay a great part of the World even contrary then to expectation? Even so on the other side, the forgetting and neglecting of this Art Military, hath not been only the decay but the ruin of many Empires and Kingdoms. Now that people that is not encouraged, or rather compelled by good Laws to practise and exercise Arms, or any thing else belonging to this Military Art; they will in a short time for want of such Manlike, Martial Orders and Exercises, grow into Sloth, to Covetousness, to Drunkenness, and Vicious Effeminacies, and to all other Evils as Nature shall incline them unto; by the which they in a short time do become unfit to be employed in any War offensive, and unable to defend themselves if they should be invaded. Did not God for the sins of the Jews deprive them of understanding of this Military Art? Among other Privileges he deprived them of, he tool from them the valiant men of War, the Prudent and the Captains of fifty, etc. When he made them thus uncapable, than they were first of all conquered and utterly subdued and ●●●ed by the Romans, under their Emperor's Vespasian and Titus his Son: I might tell you of many Nations and Kingdoms that have been ruined for want of Order and Exercise: Spain by the Moors: King Don Roderigo, and many thousands of his Nobility and people were slain by the Arabians and Moors. And about the Year 1353. we read that the Princes of Greece, aided by the Despote or Duke of Bulgaria did revolt against John Paleologus at that time Emperor of Constantinople; who for his safety against those Revolters entered into a League with Amurat the first, and third King of the House of Ottoman, and had his Assistance with ten thousand of his Horsemen; who by their good order and well disciplined Soldiers did prevail against his Revolters, and brought them to obedience: But what followed? Amurat being informed of the great riches those Grecians had, together with their weakness, by reason of their disorder in Military Affairs, transported an Army over the Asian Seas into Greece, and by that Invasion took many Cities and Towns, and did afterwards by battle slay the Duke of Bulgaria and Servia, with many others, etc. and there placed himself over a great part of their Dominion: So about fourscore years after, Mahomet the second Emperor of the Turks seeing Constantine Paleologus then Emperor of Constantinople without any settled Militia, and his people grown luxurious and not able to resist him by Battle, did in the Year 1453. besiege the Imperial City of Constantinople, who within two Months by assault won the said City, and put the Emperor, Empress, and their young Princes, with an infinite number of Men, Women and Children to the sword. I might give a great many more Instances as to our own Country from the Saxons to the Normans; and what History speaks later of ourselves, I must leave that to our Reformers to consider how useful and necessary the exercise of Arms is to the welfare of a Nation and people. The Emperor Alexander Severus that Excellent Prince being very skilful in Government, both in War and Peace, speaking to his Men of War said; The Military Discipline of our Ancestors doth maintain and preserve out State and Commonwealth; but if we do neglect the same, and make no account of the Orders and Exercises of it, We, our name and Reputation of Romans, and therewith all the Roman Empire, are lost and forgotten. Though the frequent use of Arms in Exercise is most commendable, because of the special helps it hath in making us fit and serviceable Instruments of the Public welfare: Yet I advise it with these Cautions. First, have a respect to your particular Calling. God Almighty feeds us, as well as defends us; so if any man under pretence of his Exercise shall waste his time and means, to the damage or undoing of his Family; I say, such will bring a scandal, and an ill report upon this worthy design: He that would manage his Country Affairs with delight and profit, to his preservation and not to his ruin and destruction, must imitate those Builders under Nehemiah, who held their Swords in one hand, and their Trowel in the other; so mind your Military Exercises, as not to forget your necessary Affairs at home; without your dependences be wholly upon it, then to mind nothing more. Yet Secondly, To have such an intent upon their private and particular concernments, making them unfit for Employments, as to impede them in the seeking the Public Good, or make themselves the main end of their Enterprise in what they undertake, doth degenerate so much from being true Soldiers, as to dishonour themselves in all their Services, and will be the sole jet to hinder preferment when it shall fall. And lastly, Sparta's Soldiers (I have read) were Sparta's Walls, by reason of their Concord and Unity amongst themselves; therefore let every Soldier respectively preserve Unity in the Bond of Peace, and in so doing we shall be the better able to pray with our Church, To give peace in our time, O Lord, for there is none that fighteth for us, but only thou, O God. CHAP. XXIV. Conclusion. I Humbly crave pardon for what is here undertaken, knowing my own inabilities for so great a Work; If I had seen any part of Elton's Pieces, before I had concluded these my minor Lines; they should have been turned into oblivious dust: But being commanded by some of our Chieftains, and desired by others of my Friends to proceed thus far (and no farther) accordingly I have both granted and obeyed: It is not in the least to condemn any Person that hath gone before me, or to boast in the least for what is done, or what I know: I have observed that some are most excellent for their Pen; some in their Lingue, and others for execution; now what I do want in either of the two first, the last with my blood shall witness to all the true zeal I bear to my Sacred King, and Countries good, when Commands and Occasions present themselves: In the mean time, to him who is the great King of Kings, Lord of Lords, preserve to his Honour, good of his People, and confusion of his Enemies. CHAP. I. The Original and beginning of Ensigns and Colours. OF this Subject I never thought to have spoken any thing, 1670. but this last Summer perceiving most Ensigns (having that Honour assigned them by Commission) knew but little what belonged to their Office; and think it a thing of little or no difficulty, but only a Rag or Mark, which any man may carry, so it be born up, or swung about men's cars, and sometimes in the teeth of such which are next unto them. And for the Election of these Officers by some new Commissionated Captains; It is not by the greatness of his skill, but the largeness of his body; not how able he is in his mind, but how strong he is in his Arms; not what is his Spirit, Activity, Dexterity, but what is his wealth, and how near he is allied to the Captain in blood, friendship, or service; or some other beholdingness to him, for this piece of Honour: As if this Place deserved nothing else, but a mere Man, or some Friend: For when shall you see an Ensign almost in any Employment, more than in ordinary Marches, or standing still, and observing other men's Actions? When shall you see either Captain or Lieutenant, teach the Ensign his Postures, or the Dignity of his Place, his demeanour before Kings, Princes and Potentates; and other his subjection to his Superiors; his State and Guard to his Equals, and his Humanity and Courtesy to his Inferiors. I am sure that some are so far from making inquiry after these discoveries that you shall see some Ensigns let fly their Colours, when they should sink them; and some to stoop them to Peasants or Comrades, when Superiors have gone unsaluted: There are a great many other absurdities, but I shall hereby endeavour a Reformation; although it may not be to the satisfaction of all, yet I will lay open and plain what I know of these Concerns, as not to puzzle him who is desirous to learn, nor lull asleep with amazement the weakest capacity. Therefore in the first place I shall endeavour to declare the Original and first beginnings of Ensigns (or Colours) in the Wars, and how they have grown up by succession, and continue as now they are. It's true, that the Ancient Historians and Heathen Writers, hold divers Opinions, touching the first beginning of Ensigns: Some deriving of them (especially the old Poets) from Hercules; in imitation of his Lion's skin: Others take the beginning from Perithou●, Persius. the Companion of Hercules in Imitation of his enchanted shield; whereon was painted the head of the Monster Gorgon; on which whosoever gazed was instantly transformed into a stone: But these fictions are more moral than true. There be others which suppose, that the first Ensign was born or carried before Theseus, when he went to combat with Hippolyta, Queen of the Amazons, whom he bravely conquered and afterward married. Now as these, so many other Writers suppose divers other beginners of this Mystery: Some lay it upon Mercury, because of his Caduceus: Some upon Vulcan, when he forged Mars a Shield, and an Armour; and some upon Jupiter, whose Ensign was Thunder and Lightning. But those which go much nearer the Truth ascribe the beginning of this Dignity unto Tuhalca●n the Son of Lamech, who painted in an Ensign the whole History of his Father's Actions and Conquests, when he conquered (or rather tyrannised over) his weaker Neighbours: And that after him Japhet the Son of Noah, did the like, and caused his Actions to be painted out, and born before him in an Ensign. But upon the credit of these old Poets, Historians and Rabbins, we may not rely, but must fly to the truth itself; which is ever a faithful and a constant Warrant. We find in holy Writ that the greatest Chieftain that ever led Army upon the Earth was Moses, the great servant of the great God; He was truly Dux a Duke, a Leader, such a Duke and such a Leader, as after him (Christ excepted) was never the like seen in the World; and the Army which he lead, was the greatest, strongest, and most fortunate in Number, Power, and in all manner of hazardous Actions, that ever the World saw, or the Sun shined upon. Now we find this Duke, this Prince over Israel, by the holy appointment of God himself was the first that began true Martial Discipline; for as himself was General over that huge Body; so for the well disposing and governing of every particular member, he constituted and appointed several Colonels over the several Tribes, and under every Colonel several Captains, as Commanders in Chief over particular Companies, who as Inferiors did execute the Commands of their Superiors, and had also executed under them, by others, whatsoever they lawfully commanded, that was for the good and benefit of the Army. As thus he divided the twelve Tribes into twelve warlike Bodies; so also he ordained them several Ensigns or Banners, charged with twelve several Marks or Divisions, under which they marched; which by solemn oath and protestation they were bound to guard and follow in all places and all dangers. By these Ensigns and tokens of Honour, the Tribes were first of all distinguished and known one from another; and by the carriage of them in the field, and their waving and prospects in their several places, was the dignity of place and precedency of greatness first known; the Elder being distinguished by his Ensign or Mark from the younger, the greater from the less, and the eminent and more superior from those of lower rank and inferior. Although we have a large Basis to superstruct our imitations upon, yet there was not the general use of Ensigns then, as now there is; for these Ensigns were due only to the great Colonel, or chief head of the Tribes, not to every particular Company, but to one Tribe was allowed but one Ensign, and after one manner and form; so as Simeon may not carry that of Levi, nor Levi that of Judah; but were tied to their own Colours: Also if that one Tribe were divided into many Bodies, yet did they not carry several Ensigns, but every Body the Ensign of his own Tribe; so that Companies were not distinguished by their Captains or Chiefs, but by their Tribes; nor could they say there goes such a particular Commander, but there is such a Tribe; not there marches Aaron, but there marches the Tribe of Levi; and thus of the rest. Hence, and from this ground was taken up the use of the Ensigns, or Banners of Kingdoms, by which several Armies display to the World their several Nations; as with us in England, we have the Ensign of St. George, (as we term it) which is a bloody Cross in a white field, which shows to the world not what private Company I follow, but what King I serve, and what Country I acknowledge; for howsoever private Captains are allowed their Ensigns for private respects or distinctions; yet they are not allowed (or to be born on foot) without this general Ensign of this Kingdom: for thus it holdeth in all Christian Kingdoms, and amongst the Turks also, as appeareth by their Crescent or Half Moon in all their Armies, as the Ensign of their Universal Monarchy. Thus you see Moses first (and that by the Commandment of God himself) began Ensigns, which by succession of time, descended and came down with a more general use, unto the days of Maccabees; for the Tribes then being dispersed far and wide, and made Kings of many spacious and fruitful Countries; they took liberty to alter their Ensigns, according to their own fancies: The glory thereof when it came to the cares of the Grecians and Macedonians (for Alexander is supposed to reign in the time of the Maccabees) they took to themselves a lawful imitation thereof, and so commanded their Captains, etc. to carry in their Ensigns, Devices in honour of their Renown and Conquests. Then from the imitations of the Grecians, the Romans took to themselves the carriage of Ensigns; and because they found it the chiefest beauty and ornament of Armies, they made it therefore the noblest and richest spoil which could possibly be taken away from the Enemy; and so made it an hereditary right for any man that should take (in honourable fashion) such spoils, ever after to bear them, as his own, to him and his Posterity for ever. The Romans first brought this custom into the Monarchy of Great Britain, when Caesar first invaded and got footing into the same: Howsoever there is an opinion taken that Brute, when he first conquered this Island, brought in the Trojan Ensigns, and other Ornaments of their Wars; yet it is certain that through Civil Dissensions, and other Foreign Combustions, all these Honourable Marks were lost and forgotten, and only the Romans renewed and brought them back unto memory, partly by their glory and example, and partly by their loss when they were repulsed back; who left behind them many of these spoils to adorn the Britain's: From these times hath the use of Ensigns remained amongst us; and as the Ages have succeeded, and proved wiser and wiser, and one time more than another, so hath the alteration of these Emblems (or Ensigns) changed and brought themselves into the form wherein they are at this instant carried; as the Romans varied from the old Britain's, so the Saxons from the Romans, and the Danes from the Saxons: But the French then being the most refined Nation of all other, altering from them all; and now the English having altered all into this present mode of Uniformity, they may display them to the World for their Gallantry. CHAP. II. The Definition of Ensigns. AFter the Original, Antiquity, and first beginning hath been endeavoured to be made to appear; I shall now descend to the definition and distinction of them; and by what proper names they were called in the best and most renowned Wars of Christendom, and for what reason they have held and retained them. To begin with the first and most ancient name belonging to Ensigns, I think it not amiss to borrow it from the Romans; for although the Hebrews, Chaldeans and Grecians, were the first Inventors, yet the Names and Attributes they gave them, were much incertain and unconstant, and as the experience of Wars grew great, and as the Invention dilated and spread further, so did the signification alter; for what was proper and substantial in this Age, in the next was utterly lost and forgotten, so as I shall not rest upon these Titles or significations. The first than that retained a constant and firm settled name for those Trophies of Honour, is taken to be the Romans, who indeed being the greatest Schoolmasters in the Art of War, are the most worthy to be held for Imitation or Authority. The name which the Romans first gave to the Ensign, or him that carried the Ensign (for to the man was ever attributed the Contents of the thing he carried) was Insigne, or Sign bearing, (and so Ensign-bearer) because they carried in those Ensigns, Marks, Empressaes' or Emblems, best agreeing with their natures and condition, according to their own Inventions; or else the Pourtraictures of their former Battles and Conquests; either of which was so honourable, that indeed they were made Hereditary; descending down to their Children▪ from Generation to Generation: And no more were called Signs, etc. but Coat-Armour, or the Honour of the Families; nor were they of slight or ordinary esteem, as at first; neither had men liberty any longer to make election of them at their own Wills, but this power was incabinated within the breast of Emperors, Kings and Generals, who indeed (under God) are the unbounded Oceans of Honour, they only have the liberty of bestowing and confirming Honour at their own pleasures. Hence it came that Ensigns thus carrying of Coat-Armours, were of such reverend esteem, that men took it for the honourablest place that might be, to fall near or about the Ensign; and for the defence of it, no hazard could be too great, nor any torment insupportable: So that many times the Zeal of those that did defend these Ensigns, etc. and the inflamed desire or greediness of those which sought to conquer and achieve them, was so immeasurable and unbounded, that an infinite of blood hath been shed, and many powerful Armies overthrown, only for the purchase of one of these honourable Trophies. This when the wisdom of the Romans perceived, and that those Insignias were not Bugbears to affright, but rather fires, which did inflame their Enemy's courage beyond their proper natures; they forthwith forbade the carrying of any Coat-Armour or Device in their Ensigns; but only such slight inventions, as might not make the Enemy much the richer by the enjoyment thereof, nor themselves much the poorer by the loss. And hence it followed that the word Insignia was put out of use, and they then called the Ensign Antesignia, and made other Devices contrary to all Coat-Armour; intimating to the Enemy that whatsoever they got by those purchases, was dishonourable rather than any way worthy of Triumph: And from this word Antesignia, or Antesigne, (for it hath been so written in ancient Records) it hath been judged that this word Ancient in many places used amongst us, and given to our Ensigns, hath been corruptly retained by us; for it hath no coherence in signification, nor can any way be alluded unto this Officer, more than to his Antiquity and long standing in the Wars. But this did not quench any flame in the Enemy, for the Romans found them every way as eager in pursuit of these weak and feigned Devices, as the greatest hereditary Coat-Armour they could carry; for when in any skirmish Fortune made them Masters thereof, they took as great Pride, as if they had subdued whole Armies, and bore them with as much Pomp and Triumph, as if they had got all Rome in subjection: which the wisdom of the Romans, and other Nations looking into, it presently became a custom among all their Armies, that thence forth, no Foot Company or Chieftain of the Infantry should carry in his Ensign any Coat-Armour or other Device what ever, more than the mixture, or true composition of two colours, together with the general Ensign of the Kingdom in the most eminent corner thereof. And after this time the Romans called their Ensign-bearers no more Antesignia, Read Markham's Soldier's Accidence. or Antesigne; but of late only Signifier, from Significo, to to signify a thing, as being men of special note and regard; and that the thing signifying was only a Mark of much Honour, etc. The Spaniards and Italians that took all their imitation from the Romans, who were their great Lords and masters, do at this day call this Officer Alferes, and make account of him next unto their Captains, not suffering any second to step in between them. The Dutch call this Officer Vandragon, or Vandragar, which holdeth with the same significations. And we of England properly call him Ensign, and in some Country's Ancient: The first from the thing he carrieth, and the latter from the Honour and Antiquity of the Institution: And both may well be agreeing with the first Titles, conceiving better cannot be invented. CHAP. III. The Original of Horse and Horse Colours. HAving treated of the definition and signification of the several names which belong to the Ensigns of Foot, I will now take leave to speak a little to the Colours or marks of Honour that are born on Horseback; which I find by experienced Soldiers to be full as ancient or rather more than those which belong to the Foot Companies. But omitting all profane Opinions and vain circumstances, I find when the children of Israel passed through the Red Sea, how they were pursued by Pharaoh, and all his Host, which did consist most of Chariots (which in those days were accounted Horsemen) and very properly too) because being drawn by the violent force of Horse, and laden with the strongest and best experienced Soldiers, they had a double power to enter into Battalias to disrank and break their array, and to make their Enemies to run into a rout and confusion; and though they had not the use of our Discipline, nor the true managing of the Horse as we have, yet all their purposes and intents in the use of their Chariots, were to the same ends, to which at this day our Horse are applied. To these Chariots belonged Colours, or Ensigns of Martial Honour; which were called Standards or Standarts, or the King's Imperial Trophy: Indeed these were nothing so general, as those on Foot, but more precious and reserved, as an Attribute only belonging to the King and not to any other. These Standards were charged with the King's Imperial Coat-Armour, and usually born by a Prince or some man of high place and dignity, the imitation whereof we still pursue and follow at this day, giving it a superiority above all other Ensigns. After the use of Chariots was found out, the use of Elephants a warlike beast and of all other the strongest; for these cerried cartain little artificial Houses (in the form of Castles) on their backs in which were some few experienced Soldiers 〈◊〉 with warlike Ensigns, and weapons by which they overthrew the Foot Comp●●● and made passage through them in despite of all opposition; as you shall read in the History of Porus King of India. Not long after the Exercise of Elephants, was found out the use of the single Horse, in those Countries where Horses were most frequent, as in Arabia, Parthia, Persia, and Scythia, for the Asian parts; in Barbary, Egypt and Carthage, for the parts of Africa; and with us in Europe, in Russia, Muscovia, Poland, Hungary, Italy, but principally and above all the rest in France, who were accounted in ancient time the flower of warlike Horsemen, both in number and discipline; therefore from them hath been taken our Authority and examples: But now I conceive we may not go so far for either, referring for satisfaction to the present mode of Discipline in England, for his Majesty's Horse now in Command it is thought none can exceed them. I have read of a Guidon used with the light Horse in former times: Antiquity tells us of Gentlemen at Arms, Launciers and light Horsemen. In the old Wars the Gentlemen at Arms belonged to the Kings own person, or in his absence to his General only; And the Empresa of honour that they followed was the King's Standard Royal, being Damask and charged with his Coat-Armour. The Launciers they had their Cornet to follow, which had Devices in them according to their commanders pleasures. And then the Light-hors-men had their Guidon which was somewhat long and sharp at the end but with a slit which made it double pointed much like to our late Dragooners; but for these Guydons I need not stand upon, only to show all along there were Horse Colours, as Ensigns of honour used. And now the Cornets being most in use with us in England, for the Horse service I need not decipher the length or breadth of them. CHAP. IU. Of the Dignity of Ensigns. 1. THe Dignity and estimation of Ensigns in all ages hath been held most Venerable, and worthy; they have been esteemed the glory of the Captain, and his company; and indeed they are no less, for where they perish with disgrace there the Captain's honour faileth, and the Soldiers in hazard of Ruin; for if the loss proceed either from their Cowardice (or misgovernment) it hath been death by the law of Arms to all that survive; and the best mercy that can be expected is that every Soldier shall draw a lot for his life (file by file) so that one out of every file perisheth for it. 2. The next Dignity of the Ensign is, that every Soldier as soon as he is enrolled and hath received either pay or impress, they anciently took a solemn Oath to be faithful to their Colours, to attend them carefully, and to defend them valiantly; And that upon all summons, of the Trumpet or Drum, or Command of their Officers, to repair to them, wheresoever they shall be lodged, stand, or be; and not to departed or straggle from them until they have received orders. 3. The Ensign hath another dignity, that whensoever he shall enter into City, Town, Garrison, Camp, or other Randesvouze of abode, he is to be first lodged, before any other Officer or Soldier; And not in any mean place, but the best and most spacious for the drawng up of the Soldiers upon any Alarm; and his Quarter ought to be the most secure from danger. 4. The Ensign hath Dignity of place according to the Antiquity of his 〈◊〉 But in one particular case, it hath been judged to be greater than his Captain, 〈◊〉 dareth place to him; as thus, no Captain can receive his antiquity from his enrolment, but from the first hour in which his Colours flew; for if two be enrolled upon one day, and the latter marcheth before the face of his Enemy with his Colours flying, in this case the first hath lost his priority, and the latter for ever after shall preceded him. I have read of another resolve; Three Captains (or more as occasion happeneth) were all enrolled upon a day, and all their Colours flying; presently upon a Truce, Composition or other occasion there is some small cessation of Arms, and these new enrolled Captains are Cashiered (or dismissed) for the present service: Now the two first that had priority of place not only by enrolment but by flying of their Ensigns, because they would not be out of action (to a Soldier the taste of gain is pleasant) took upon them the Commands as Lieutenants of two Colonels Companies etc. which are Captains places in courtesy, retaining those titles, and in some Courts of War have had their Voices; Now the third all this time taketh upon him no place, but remaineth in Statu quo prius; And in revolution of time all these three Captains aforesaid are again Commissionated for three new Companies of their own, the Question was whose Ensign should fly first, and which of these three shall have the priority of place? It was thus answered and adjudged by the old Earl of Essex and Sir Francis Vere, etc. that the two first who had taken upon them Lieutenancies had utterly lost their Superiorities, and the third whose Honour slept, but diminished not, had precedency of place, and his Ensign flew before the other ever after. 5. The Ensign hath this Dignity to have a Guard ever about it, which no other Officer hath; neither is it to be disimbogued, or unlodged, without a special Guard, attending upon it both of Musquetteers and Pikes; (And so for a Cornet with his own Squadron of Horse.) Also in the field if it be in particular Discipline or otherwise upon an Alt, or stand, at such time as the Army or Company are to refresh themselves with victuals or other rest, in this case the Ensign shall by no means lay his Colours upon the ground, or put them in unworthy or base hands, but he shall first furl and fold them up and set the butt end on the ground supported with the Sergeants Holbearts, and the Ensign himself shall not go from the view thereof, unless he shall leave a sufficient guard for them. 6. An other dignity of an Ensign is, If a Noblemen or an Esquire will take upon him the Command of a private Company and have no other superior place in an Army, and a mean Gentleman hath the like equal Command but a great deal more ancient, although there ought to be a respect if they should happen in company unto the worth and quality of the person; yet the meaner Gentleman's Colours shall fly before the other. As this hath been the ancient practice in the Wars, how then do those Captains debase themselves, and their Ensigns, to suffer young Captains to step in, (either by greatness in quality or favour) to fly their Colours before them, etc. 7. Every Ensign hath his Dignity, although he is wholly to be at the Captains Command, yet in justice no Captain, nor other Officer can command the Ensign-bearer from his Colours, for they are as man and wife, and ought not to endure a separation; nor can he be commanded with his Ensign to any base (dishonourable) place or Action: And hence it is that to this day this place, and mark of Honour is held in such a venerable & worthy estimation amongst the Spaniards and Italians that they will not allow of any second between him and the Captain, as the name of a Lieutenant to be amongst them, thinking it to be a superfluous charge and command, because it is in their judgements a lessening and a bating of the Ensigns Honour. But in this although we esteem an Ensign very honourable, we in England differ from them, owning the place of a Lieutenant to be honourable and necessary, who ought to be a man of most approved experience; for he takes from the Captain those heavy burdens, which otherwise would make the Captains trouble insupportable, nor can the Ensign discharge them unless he neglects his care and duty to his Colours. 8. As for the dignity of the Ensign in England (not meddling with the Standard Royal) to a Regimental dignity; The Colonel's Colours in the first place is of a pure and clean colour, without any mixture The Lieutenant Colonels only with Saint George's Arms in the upper corner next the staff; The Majors the same, but in the lower and outmost corner with a little stream Blazant, And every Captain with Saint George's Arms alone, but with so many spots or several Devices as pertain to the dignity of their respective places. But with us in England, placing and displacing is left to the Generalissimo, etc. and so to his substitutes, or deputies: It is to me a riddle that any person who cannot be stained with the least blemish should lose his advancing honour; But kissing goes by favour. CHAP. V Of Disgraces to the Ensign. THere are as many disgraces that belong to the Ensign as dignities; I shall for brevity sake mention but some few: all which must proceed from mistakes in one of these three, Unskilful composure, Negligent government, or Rash actions. 1. Touching Unskilful composure, either in false making, or bearing of Ensigns; and that you may be informed for the composures thereof, I cannot better it than to declare to you Markham's own words out of his Soldier's Accidence pag. 31. He saith, There must be in Military honour nine several faces, or complexions, that is to say, two which be called Metals, as Yellow and White, figuring gold and Silver; and seven which are called proper colours, as Black, Blue, Red, Green, Purple, Tunnis and Ermine. And here it is to be noted that no metal is to be carried upon metal: And for the signification of those colours you shall understand that 1. Yellow betokeneth honour, or height of Spirit, which being never separated from Virtue, of all things is most jealous of disgrace, and may not endure the least shadow of imputation. 2. White signifieth Innocence, or purity of conscience, Truth, and upright integrity without blemish. 3. Black signifieth Wisdom, and sobriety, together with a severe correction of too much Ambition, being mixed with Yellow, or with too much belief or lenity being mixed with White. 4. Blue signifieth Faith, Constancy, or Truth in affection. 5. Red signifieth Justice, or Noble worthy Anger in defence of Religion, or the oppressed. 6. Green signifieth good hope, or the accomplishment of holy and honourable actions. 7. Purple signifieth fortitude with discretion, or a most true discharge of any Trust reposed. 8. Tunnis or Tu●●y, signifieth merit, or desert, and a foe to Ingratitude. 9 Ermine, which is only a rich Furr, with curious spots, signifieth Religion, or holiness, and that all aims are not divine objects. Now from these colours and their mixtures are derived many bastard and dishonourable colours, as Carnation, Orange tawny, Popengie, etc. which signify Craft, Pride and wantonness. So that all Commanders are left at their own pleasure for their mixtures, but with these considerations; As, 1. Not to put in his Ensign his full Coat-Armour. 2. Not to bear one black spot and no more in his Ensign, for it showeth some blemish in the owner, if the spot be round, square, or of equal proportion. 3. If the spot be unequal, it signifieth a Funeral or deadly revenge. 4. Not to carry words in his Colours without a Device; nor a Device without words; but Device with words, and the words not to exceed four in number, for if there be more it showeth imperfection. 5. Not to carry more Colours than two; except it be for some special note, or the Ensign of several Kingdoms, it is a Surcharge and esteemed folly. 2. Having showed the true Colours, and the disgraces that may arise in the composure of them, as mentioned by Mr. Markham, I come to the next disgraces which proceed from Negligence in Government; as in carrying his Colours furled (or folded) up when they should be flying, or to let his Colours fly, when they should be folded up; or to display (or flourish them) when they should be carried without any hand motion; or to carry them without motion when they should be displayed; or to veil them when they should be advanced, or to advance them when they should be vailed. To lodge or dislodge Colours without a Guard; or to suffer any man to handle them that hath not a lawful authority. Now the avoidance hereof is sufficient to keep any man from gross errors. 3. The last disgrace as to the dignity of the Ensign is 1. From the rashness and unadvisedness of Actions; when he is in safety out of a fantastical bravado to thrust himself into danger; as to charge the Enemy when he should stand still: It is not only a disgrace; but the offence hath been adjudged worthy of death, although he may obtain victory by that forward action. 2. If in a March, Battalia, or setting of the Parade, or upon any other Military employments, he shall misplace himself, it is a disgrace. 3. If in a battle, skirmish, or fight where the Ensign is put to retreat, his Colours shall be surled (or folded) up, or shouldered and not flying and held forth and extended with the left arm, and his Sword advanced in his right hand, his Colours are disgraced and such retreat is base and unworthy. 4. If the Ensignbearer shall happen either in battle or skirmish to be slain, and so the Colours fall to the ground, if those, or some of them next adjoining threreunto do not recover and advance them up, it is not only a disgrace to the Ensign, but an utter dishonour to the whole Company; as I have declared, that if the Colours be lost, there must be a severe account given for them: And indeed a greater act of Cowardice cannot be found, than to suffer the Colours to be lost. There is an ancient precedent, but fresh in memory, that in great defeats when Armies have been overthrown, scattered and dispersed so that particular safety hath made men forget general observations; even then, the Ensign being wounded to death, and desperate of all relief, hath stripped his Ensign from the staff and wrapped or folded it about his body, and so perished with it: This Ensign cannot be said to be lost, because the honour thereof was carried with his freed Soul into Heaven, to the possession of the eternal fort for ever: Now in this particular the Enemy cannot boast of any Triumph if then purchased, more than every Sexton may do when he robs the dead of his winding sheet. Thus it hath been reported that Sebastian King of Portugal died at the battle of Alcazar: And I have read of many of our brave English that thus died at the renowned Battle at Newport, and have heard that many have so done in the Army of our late Sovereign of ever blessed memory. 5. And lastly, If any man shall recover the lost Ensign and bring it away flying, etc. no matter how low in condition the man is, if the Captain upon any after considerations bestow those Colours upon some other man; it is a disgrace both to the Captain and his Ensign, for he doth injury to Virtue and discourage Valour. Obj. But some may object that upon composition with the party deserving, the Captain may dispose of his Colours where he pleaseth: I confess it true, but if this composition be forced it is injurious; And if it come by a voluntary consent of the party, it is base and most unworthy in him also. CHAP. VI Of the right use and ordering of the Ensign or Colours; with the Postures and Flourishes thereunto belonging. AS to my best Remembrance, I have given you a Catalogue of the Disgraces, so I shall here insert as to my knowledge the true use of the Ensign, whereby those injuries may be avoided. 1. And first, you shall understand that in all extended Marches (and not drawn into a Body) as when they march either into a Friends or Enemy's Country; or otherwise are conducted to some remote Randesvouz; here the Ensign (or Colours) ought to be half furled (or folded) up, and half flying, shall be shouldered and born a little cross the Ensign-bearers neck, with his hand extended a good distance from his body, and his left hand upon his side or hilt of his sword; this is termed a marching in State. 2. If he shall enter into any City or great Town; then he shall unfold or open his Colours, and let them fly at full length, and carry them in his right hand close under the hose, with a lofty hand and extended arm: This is a marching in Triumph; but if the wind blow stiff, or there is a weakness or wearisomeness in the Ensign-bearer, than he may set the butt end against his waste and not otherwise; and is to have but one hand upon his staff in any march whatever. 3. In all Trooping the Ensign shall ever be furled and carried in the same Postures as the Pikes ought to be. 4. When the Company is drawn up into a Body, the Colours must be flying; and by the Way, in case the General or supreme of the Wars, or any Noble Stranger worthy of respect, do come, immediately upon his or their approach, the Ensign-bearer in all humility is to bow the head of his Colours, waving them with the bow of his body, and to raise both it and himself up again: And as the said person shall pass away, the Drum shall beat, and the Colours shall be displayed: This also the Ensign shall do in all Marching, or other motions of Civil Exercises, where your Superiors pass by you, or you by them: Nay it is expedient and fit so to be done to any Gentleman, that is your familiar; for it is no more but as the vailing of your hat, or giving your friend a courtesy. 5. Now when the Body is drawn up into Battalia and the Enemy within view thereof, than every man being in his place is to express all the Gallantry he can, and especially the Ensign-bearer either in displaying his Colours standing, marching, charging and retreiting (or retiring;) and all these ought not to be done at one time, but when the bodies are joining, and they must be done with great respect, for to use the Postures directly to the motion or standing of the Body; and not to do as I have seen some in ordinary Militia Discipline, that have but one or two motions of their Colours, upon and for all occasions; as if true Honour had such weak inventions; this without doubt is most base and unworthy. To proceed to the Postures of the Ensign. They are in general as followeth, so well as I can express them; for they are better in execution, and to be taught by example, than any pen can describe them. 1. To change them with a plain wave from hand to hand. 2. To change them with lofty turns from hand to hand; each hand performing their turns before you deliver them, as from the right to the left, and from the left to the right, as at first, 3. From the right hand with a wave and lofty turn jutting the Colours upon the left shoulder, and raising up with the same hand again, and with lofty turns to deliver it into the left hand, that so thereby you may execute the same upon the right shoulder, and after the turns, to deliver it into the right hand, as at first. 4. With (and from) the right hand with lofty turns throw your Colours under the left arm, recovering them speedily back with conceived Flourishes, you deliver them into the left hand: you may execute the same with the left hand. 5. With turns or flourishes you bring the butt end of the staff to your left hand turning the palm of your left hand outwards (but not for the reception of it) and with the same hand only throw it off upon its turn with a flourish to deliver it into the left hand, and to perform the same with the left hand, and deliver the Colours into the right hand, as at first. 6. With lofty turns bring the Colours over the head down right (but not too low) before, and raising it again, with the fore-turn and back-turn over the head, changing of hands and delivering as before. 7. From the right hand deliver into your left hand with the palm of your hand, uppermost, the butt end of your staff turning it backwards upon the left shoulder; and turning it over the head with the same hand, you deliver it into the right hand after the same manner, which being performed with the right hand you proceed to the next. 8. From the right hand with lofty turns, fore-turns and back-turns, you deliver your staff into your left hind, and wheel it with the same hand on the same side, and after your recovery to deliver it into the right hand, performing of the same and proceed. 9 From the right hand upon the left shoulder, raising it and turning with its back-turn into the neck; with its returns and lofty flourishes over the head you deliver the Colours into the left, and with the left hand upon the right shoulder you execute the same, delivering them into your right hand as at first. 10. 'Tis by some termed the Figure of eighth; that is with the right hand the half wheel on the left side, and so back on the right side, and then delivering it into the left hand to perform the same. 11. To turn it round the head oftentimes upon the palm with your fingers of your right hand, so recovering it, with lofty flourishes you deliver it into your left hand to perform the same, and so delivering of them into the right hand. And if it be your pleasure to be complete in the Exercise of them, you go back to the tenth, and so conclude with the first. And in your conclusion I have seen some to furl them up as they display them, and so to open them again. But to furl them up in the field it is most ridiculous. Others there are that I have seen to round them oftentimes about their middles, but I cannot justify it upon any Military account. Others I have seen, that thinking to display their Colours bravely delivered them from hand to hand under leg; I must boldly inform such as use it, that 'tis a debasement to the Captain's Colours, and an unworthy Act in the performers of it. I told you of some particular Postures and proper for the Ensign-bearer to observe. 1. Standing, when the Body stands, you are to display the Colours, to and fro in a direct circle, and changing from hand to hand, and no more, without you are commanded to show the excellency of your parts; but be sure to be well guarded when you shall be so commanded. 2. In marching, the Posture is to display the Colours with the right hand only, casting the Ensign still forwards, waving it close over and by the right shoulder, never crossing the Body, but still keeping it flying on the outside of the right shoulder. 3. The charging Posture is to carry the staff extended straight forward before your body, waving it to and fro as high as your bosom, being ready to give the assistance or aid with the left hand for the preservation of your Colours, or to offend the Enemy if occasion require. The retiring or retreiting posture is a mixture compounded of the three former; for in the first retreat, or drawing away of the Company, he shall use the posture of marching: but if the Enemy press near upon him, he shall stand upon his guard, and use the posture of charging; and in fine, having quit himself of danger, he shall use the standing posture a little, and then march or troop away, according to the directions of the commander. And lastly, when the Ensign returns from the field, and is to be lodged; in former times the Lieutenant had the Vanguard; but that I shall not insist upon, because I have observed it to be left off by able Soldiers. The Captain leading them out of the field, and coming near the place intended to lodge his Colours, Converts the ranks of Musquetteers of both divisions to the right and left outwards and joins them; and being so fixed, the body of Pikes stand in the rear, and the Ensign in the head of them, the Captain before the Colours, with the Drums and Sergeants guarding the Colours on each side, and the Lieutenant behind, the Ensign bearer, and all being advanced, shall troop up with the Colours furled to his lodging or quarters; and as he approacheth thereto, he shall with a bow to his Captain carry in his Colours; then the word shall be given to all the Musquetteers to make ready; that being done, they shall all present, and upon the beat of Drum, or other word of command, give one entire Volley; and then command every Officer to go to their quarters, and to be in readiness upon the next summons, either by Drum or Command. It may fall out, that time will not permit this large circumstance; then the whole company being drawn up in a body shall troop up to the place, where the Ensign shall quarter, to see the colours safely lodged, which being effected, the Musquetteers shall with one entire Volley discharge their Muskets, and so departed to their respective quarters; commanding all upon the next summons to be in readiness, etc. And I might here add the funeral posture: if for a private soldier; the Ensign-bearer is to march in his place on the head of the Pikes, with the Pikes trailing reversed, but the Colours furled and reversed only: But if it be a commander that is to be interred, he is then to march just before the Hearse, with his Colours reversed, etc. If I have writ any thing amiss, or omitted any thing as may prejudice the honour of the Ensign, I beg your better advice, for it was in the years 1641. and 1642. that I minded any of these military actions; therefore for any error herein, let the length of time plead my excuse: However, I could wish that every Ensign would but observe these rules, he would then the better know his own worth, and what duty lieth incumbent upon him; and being careful in the performance of them, his own honour will be displayed in his Colours. Sir Francis Vear's notes of Direction how far every man's office in a Regiment doth extend, and the duty of every Officer. 1. The Office of a Colonel. 1. EVery Colonel is to command all his Officers, Captains and other; And all Soldiers, and men of War, of what degree soever they be, that do put themselves, or are by superior authority put and ranked under his Regiment, are all to respect his commands, and obey him as fully as they would the chiefest. 2. Also, He shall see all orders, commands and directions, which are delivered him, by the public officers of the Army, for Guards, Watch, or any thing else, for matter of justice, or for ordering of the Troops, executed. Furthermore, If he himself find any mutiny, or discontented humours tending to mutiny, or extreme outrages, or disorders, or shall by any of his Captains, Officers or Soldiers be informed of any such, he shall forthwith advertise the Generals. And if he find any other fault, negligence or swerving from either directions given, or the policy of the Army set down; he shall straightway acquaint them, by whom such directions did come, or were brought unto him, or some other superior Officer, if he can conveniently acquaint them with it, and shall produce the party so offending, with the Witnesses and Proofs, that order may be given forthwith, and justice done; and if he fail to give this information of any thing he knows or hears, he shall be deeply faulty: Or if any such thing pass without his knowledge, he shall be thought of worse Government than were fit for a man of his place and charge. 3. Also, In Lodging, every Colonel ought to lodge as near as he can in the midst of the quarter assigned for the Regiment, because he may best give directions for the whole. 4. In marching, he shall be at the end of the Regiment that is nearest the Enemy (that is to say) in the head of a Regiment going towards an Enemy, and in the rereguard going from the Enemy; and he shall not go from thence except it be for ordering of his Regiment or some extraordinary occasions. 5. Once every week the Colonel shall call together all his Captains, and shall inquire of all offences in his Regiment; and examine the nature and quality of such offences, to prepare the causes for a more speedy hearing in a Court Martial. 6. All Colonels shall repair to a Court Martial, as often as they shall be warned, and shall be assistant to the Lord Martial, in the causes that shall be there in question; or belonging to the justice of the Army. 2. The Office of a Lieutenant Colonel. 1. The Lieutenant-Colonel, when the Colonel is in presence, is to assist and obey him, in seeing all the directions that are delivered by any public Officer, or such as shall be within the Authority of a Colonel to command, executed. And in the absence of the Colonel, he shall have the command that the Colonel hath himself. 2. He is to lodge ever on the right hand of his Colonel's lodging, as near to the end of the quarter as conveniently he may. 3. In marching or imbattailing, Read Markham's decades fo: 146. and Ward, fo: 200. whensoever the Colonel is in the head of the Regiment, he shall be in the rear; and when the Colonel shall be in the rearward, he shall be in the head. 3. Of the Office of a Serjant-Major. 2. He shall in the presence of his Colonel or Lieutenant Colonel be assistant to them, or either of them, in seeing all orders, and directions executed and performed, and in the absence of them both, to have the same authority as the Colonel himself: He shall lodge on the left hand of the Colonel, as near the end of the quarter as may be with conveniency. 2. In marching or imbattailing he shall keep as near the end of the Regiment as he can, sometimes on the side, that so he may overlook the order of the March. 3. He shall come to the Serjant-Major-General to receive the word from him, if there be no extraordinary cause to hinder him; And when he hath received the word, he shall deliver the word over to the Sergeants of every company in the Regiment, who are to come to him for it. 4. As he doth receive directions for marching, imbattailing and placing of guards from the Major-General; so he is to deliver the fame to the Captains of the Regiment, and call those to whom it doth pertain, and see them executed. 5. Every night he is to visit all the guards of that Regiment, and to keep turn of Watches, marches and going to the Wars; or sending Troops (or companies) upon service, to the end that both the labour and honour may be equally divided. By the way you may observe: whereas the Sergeants of every company are to be assistant to the Serjant-Major of that particular Regiment for the dividing of their several Corporalships or squadrons, files or half files, for the making up of any body, form or figure according to directions, etc. So the Serjant-Majors of Regiments, are to assist the Serjant-Major of an Army, to bring in what divisions or bodies soever shall be called for; and the Serjant-Major General is so to do to the Martial of the Field: And that his duty may be performed with all careful severity, the Serjant-Major is allowed his Hakney to speed it from Company to Company, to see that every Company be in his true form; and not to suffer any man whatever through Pride, Stubborness, Neglect, Covetousness of Pillage, or by any other dilitory, and weak excuse, to break out of his rank, or to disproportion any part of the body, by any rude or uncomely posture, but severely to rebuke the same, and compel a speedy reformation. But out of an Army, both in field or otherwise, than the office both of a Serjant-Major and Marshal shall be in himself; he shall summon Courts of War, with the assistance of his Captains, to proceed to trial against offenders, he shall proportion all allodgments, encamp, and with his best skill fortify the same; and shall upon fight draw the battle (yet with this limitation, to take directions from his superior Officer, etc. And as you see he is to take care of all Watches and Guards about that Regiment: so if there be no greater Officer than himself, there to give the word, and to appoint the Court of guard and Sentinels; but if there be a superior Officer, than the Serjant-Major shall receive it from him, and so give it to the Captains and other such inferior Officers as shall have the guard that night. In short, a Serjant-Major aught to be dutiful to all his Superiors by whom he is to be directed: he ought to be an experienced Soldier, and of a valiant and undaunted behaviour. 4. The Office of a Quartermaster. 1. He shall in all changing of lodging, attend the Quartermaster General, and take the place assigned by him for the quartering of the Regiment, in such form as the Quartermaster General shall direct him, and there he shall appoint lodgings to the Colonel and the Officers according to their places that they are to take in the Regiment, both in town and field. 2. He shall lodge suttlers' of that Regiment in the hindermost part of the quarter, at such distance as the Quartermaster General shall appoint. 3. His place is to lodge on the back side of the Quarter, behind the lodgings of the Lieutenant-Colonel. 4. The Office of the Provost. 1. He shall see all Proclamations, Orders, or Decrees that shall be published by the Provost-Martial of the Army, likewise to be published in the Regiment whereof he is Provost. 2. Also he shall keep all the Prisoners committed to him; and once a week give notice to the Provost-Martial-General of all the Prisoners within his charge, and of the cause of their committance. 3. Furthermore, He shall oversee all the Victuallers of the Regiment, that they shall neither at unreasonable prices, nor at unlawful hours sell their victuals, and shall on the other side be watchful that no wrong be done, and if any be, that forthwith the party doing wrong, shall be brought before some officer that hath Authority to yield redress, and to that end he shall go about the Quarters once every forenoon, once in the afternoon, and once in the dead time in the night, if it may be conveniently performed. 4. He shall have an account given him every night of the victualler, what victual is in the quarter, and he shall carry the notes thereof to the Provost-martial of the Army. 5. He shall when preys (or booties) are brought in, after the Provost-martial general hath divided them to the Regiments, divide them to the several Companies he is Provost-martial of. 6. He is to see the quarters kept clean and sweet; all garbage and filth buried; nothing that may annoy the quarters suffered to be at such a distance as shall be appointed by the Provost-martial of the Army. 7. He shall lodge in the midst of the Victuallers of the Regiment. 8. He shall come to the Carriage-master for directions where the baggage of that Regiment shall march, where they shall assemble, and what ways they shall go, which directions he shall perform: and after he hath given the first place to the Colonel's baggage he shall place by turn the rest as the Companies do march. 9 Also he shall see the ways made for the Carriages accompanied with men sufficient, and with instruments to help and amend every thing that is amiss in the ways, or Carriages, and if any carriages be unable to go, he shall provide that it may be no hindrance to the rest. The Officers of a Foot Company. 1 The Office of a Captain. 1. He hath proportionably the same Command over his Company, as a Colonel hath over his Regiment; and so also all his Officers and Soldiers are to obey him. 2. When he receiveth his Company and his Arms he is to choose his men and to sort them to his Arms as he thinks fit, etc. 3. He shall choose his Officers such as either have had the like place before or are of Experience and good government, or such as have made themselves known to be fit for the like. 4. He shall divide his Company into Corporalships. 5. He shall take care and labour to teach all his Soldiers the carriage and use of their Arms, to keep their order in marchings and imbattailing, and to understand all manner of motions and the beat of the drum, and to this end he shall have usual times of Exercising, which shall be once a day at least, till his men be perfect. 6. In the marching of his Company alone he shall be in the head of his Company going toward the Enemy, and in the Reerward coming from an Enemy. 7. In Marching with the Regiment, he is to receive his directions from the the Serjant-major of the Regiment, (and to carry the several sorts of weapons as shall be by him directed: and to every one of the divisions of his Company appoint such an officer as the Serjeant-major shall direct:) and for his place it shall be where the Serjeant-major shall assign. 8. In imbattailing he is to order his Company as the Serjeant-major shall direct him, and to be himself where his Colonel or superior Officer shall appoint him. 9 In lodging he shall take that according to his degree and place in the Regiment, and see that be ordered according to direction. 10. He shall have his quarter kept sweet for healthfulness, for quiet, for order, especially in the night. 11. If his whole company be to march he shall draw off his company and stand in arms, attending the directions of the Serjeant-major. 12. When he is brought to the place of his guard, he is to take the direction of the Serjeant-major of the Regiment, for the placing the Corpse du guard; setting his Sentinels, and sending forth his rounds, and to see his directions performed, and not to abandon his Guard till he be returned, or whatsoever is discovered or brought to the Court of Guard where he is, shall by himself be sent to the C.— of the Watch; and he shall make good his if he be not by a Superior Officer commanded to retire. 13. If he hear or know of any mutiny, or discontented humour tending to mutiny, outrage, or disorder committed by any of his company, or within the quarter, he shall forthwith advertise the Colonel of it, or if he be in the way, some public Officer of the Army, and shall arrest and bring forth the party so offending, and all such witness and proofs as are to be produced, of which if he fail and know it, he shall be held very faulty, and if such escape him he shall be held unworthy of his place. 14. He shall see those of his Company that do better than their fellows, advanced and encouraged accordingly, and to all he shall do right, both in their place, and things that are due unto them, and shall as far as in him lieth take care for the comforting and preserving them that are hurt and sick. 15 In matter of service he shall do all that is commanded by any superior Officer, that hath authority over him, in the best sort he can; without either exceeding his Commission or doing less. 16. When he is alone with his Company, he shall be very diligent and careful both in his march and lodgings, and if he be put to any extremity, he must look to make an account; therefore he shall do his uttermost both by judgement and by valour to free his Company, etc. 2. The Office of a Lieutenant. 1. He shall when the Captain is present be assistant to him in seeing all directions performed, that are commanded by a superior Officer, or all such as his Captain hath authority to command; And in the absence of the Captain he shall have the same authority as the Captain hath. 2. In a march if there be no Company but his own, he shall be at one end of the Company when his Captain shall be at the other, and if the Company shall march with the Regiment he shall take such place as spuperiour Officers shall assign. 3. He is to lodge on the right hand of the Captain as near the end of the quarter as may be convenient; And shall in all service, and at all times help to keep the Soldiers in discipline and obedience; and shall perform all things commanded him, or upon occasion necessary to be done with valour and judgement. 3. The Office of an Ensign. 1. He shall when the Captain or Lieutenant be present be assistant to them, or either of them, and in their absence he hath the same authority the Captain hath. 2. In his march he is to carry the Ensign, and to take such place as shall be assigned him; and if his Company be alone, he shall upon entering the quarter, going out of his quarter, going upon the guard, or upon the sight of an Enemy, carry his Ensign advanced and flying; and if he march with the Regiment, he and all other Ensigns of the Regiment shall do as the Colonel's Ensign doth. 3. In fight he shall never carry his Ensign Advanced and flying, without offering to use it in any kind of offence, being a sign for a Company to gather by, and therefore to be preserved, for which cause he may use his sword. 4. If he march with other Ensigns he shall take the place as shall be assigned him. 5 The Ensign shall never turn his face out of his order, or start from any danger, or forsake his Ensign upon pain of death. 6. Whensoever the Drum shall beat for the Companies gathering, he shall be in the place and shall see the Ensign well guarded, or be ready to march or do any thing for the service. 4. The Office of a Sergeant. 1. If all the Officers before named be out of the way by any accident, the Eldest Sergeant is to Command the Company next. 2. In assembling the company he shall set every man in his place, and if any be missing he shall seek them out, and have power to correct them (in the absence of his superior officer) and if any be defective and cannot be found he is to acquaint his Captain (or chief officer) of it. 7. When the Company are assembled and set in order, he shall march on the outside, where he may best see the order of the march, and take care and charge of their several Corporalships. 4. Though it be usual to understand the use of Arms, and all things that belong to a Soldier, and though by custom he is to lead the Musquetteers to fight especially in a loan Company, (in all which cases he is to follow the directions of his Captain or the superior Officer in his absence,) 5. Yet for his more particular directions how to lead his Musquetteers after he hath brought them up to that ground, and in that number, and order, that his Captain, or superior officer hath commanded him; he shall make every man to come up close to him, and he shall see that they take their level and discharge to good purpose; And he shall see that they keep their order, as well in going on as retiring. 6. If he be joined with other Companies, he shall follow the directions of him that commands in chief, and carefully look to that part on which he is assigned to attend. 7. The Eldest Sergeant shall lodge in the skirt of the quarter right behind the Captain, and the other in the same sort right behind the Lieutenant, and if more, right behind the Ensign: And in their Quarter they are to visit the Soldiers and their Lodgings, and to see them orderly and quiet. 8. He is to fetch the Word from the Serjeant-major of the Regiment and to deliver it to his Captain, Lieutenant, Ensign, and Corporal that is of the watch; and if the whole Company watch he is to attend, and to see the place where the Sentinels are put out, and to visit them all: If they watch by divisions or Corporalships, than he shall lead them, and bring them to their Guard, where he shall also attend upon any extraordinary accasions by the Command of the Captain of the watch. 9 And while he is there, to advertise the Captain of the watch if any extraordinary discovery or accident of importance happen. 10. He shall deliver such Munition either of Victuals, or of War to the Corporals of the Company, as he shall receive from the Serjeant-Major of the Regiment. The Office of a Corporal. 1. Though it very seldom happeneth that he hath the charge of the Company, yet if such an accident should fall out that all the superior Officers of a Company should be absent, than the Command doth belong to him. 2. To his place belongeth properly the charge of one division or squadron of the Company; he is to see them well exercised in their Arms, and that his deportment with them may be Soldier like: he is to deliver them Munition of Victuals or Arms, he is to govern the Watch, and to divide the labour of his Soldiers equally, either in watch, work or service, and to take care in every respect to do the duties of a good Soldier. 3. When the Drum beateth to gather the Company together the Corporals are immediately to be in a readiness themselves, and to call together their Divisions, and with them he shall repair to their Ensign, and if any of them be wanting without leave, they shall give notice thereof to the Captain and shall prosecute their said absence to the punishment of them. 4. He shall have a third part or a fourth in his division, which being divided into files he shall himself be leader of the chief file; and is with the same always to take place on the right hand of his division. 5. He shall in any case of default either of leaders or bringers up see that they be supplied by the next. 6. In marching or fight the Corporals of a Company have no Command, but of the file that each of them leadeth: they are to see the opening of their files, or ranks, or to double the same, to follow the sound of the Drum, and to observe every other motion that shall be commanded by the chief Officer; Always provided that he start not out of his place nor use any Command of himself. 7. He is to observe the beat (or sound) of the Drum, and shall see them fully furnished of their Arms, Powder, Bullets, Match (or Flints) and all things else that shall be necessary for the Arms they carry: whereof the Sergeant is to supply them. 8. He is to be lead by a Sergeant to the place of his watch, and from him to receive the word, and directions in what manner and where he shall place his Sentinels, as well by day as in the night, which he is to see performed. 9 His Sentinel being placed he is to let none to pass his Guard without the Word, unless it be to the Captain of the watch, or the Serjeant-major, to whom after he knoweth them, he is to deliver the word to the first Round. He shall direct the Sentinels that every one do the like; he shall see them changed at due time, and shall now and then visit them unlooked for. 10. He must warn his Sentinel to give no false Alarms, but with as small a noise as is possible to advertise his said Corporal, who upon an extraordinary occasion shall put his division in Arms and give notice of the danger discovered to the next Guards, and to the Captain of the watch. 11. He shall make good the place of his guard until he be called from thence, and not to suffer any of the Corporalships to leave the same till he be relieved; And he shall fulfil all commandments for the entering or going forth of any Soldiers. 12. At the coming of his relief he shall put all the Soldiers in his division into Arms, and stand ready to receive them, and when his Sentinels are relieved, march to his quarter. 13. If during the time of Watch, any of the Soldiers under his Corporalship shall offend, he is to commit him, or to acquaint his chief officer therewith. 14. If by any occasion the Company remove, and he be drawn from the guard before the twenty four hours be expired; and that the same Companies lodge again within the same time; then shall the said Corporal with his Soldiers be in readiness to watch out the residue of the time, and in such place as shall be appointed. 15. As a Corporal is next in degree to a Sergeant, so in behaving himself well he may pretend to the place of a Sergeant when by any accident it may be void. The Office of Lansprizado. 1. Next to the Corporal is the Lansprizado, who is in the absence of the Corporal to do his office. 2. His own proper place is to lead the left hand file of the same division and to have his own and the files adjoining to the same in care observing their orders, as is specified in the Corporals office. The Office of a Drum. There aught to be two Drummers at least in a Company, both of them perfect in every necessary beat (or sound) thereof, which by turns are to do all the service belonging to their place; and therefore in the field or Garrison, one of them is to give attendance to the Quarter, though the Company were at that time free from any duty. 2. The Drum having warning to beat for the gathering of the company; shall go beating from one end of the quarter to the other, twice; and then he shall repair to the Ensigns lodgings. 3. While the Company march the one must beat constantly and by turns ease each other. 4. When the Company shall be joined with others, the Drums shall take place by the appointment of the Drum-major, and shall beat the same point of War, and observe the same time that Drum doth, that is next to the Colonel or Chief Officer. 5. It is the Office of a Drum; when any of the Company are taken prisoners, to inquire after them, and carry their Ransom, which he may do boldly, after he hath received a Passport from the General, or Commander in Chief of the Army where the Company is: And when he shall come near any place of the Enemies, he must beat (or sound) thrice, and not approach too near till he be by some of the Enemy fetched in. 6. He is only to make his errand known, and not to discover any thing of the estate of the place from whence he was sent which may be prejudicial to him. A Military discourse, Whether it be better for ENGLAND To give an Invader present battle, or to temporise and defer the same. AS it is familiar and common amongst men to be divers and contrary in opinion; especially in every doubtful and questionable matter, according to the old saying, so many men so many minds: every man must therefore prepare himself with a good and equal contentedness to endure what others do censure and judge of his position, as either their reason shall lead them or their sense and humour carry them. Neither ought any man challenge greater prerogative to his opinion than he bringeth with him authority of reason for the same: And seeing that reason, joined with experience, is the only guide to direct us in all affairs of Action, whereunto all our opinions and judgements must be restrained, we must submit our private conceits to be ruled by reason and experience. In things of great importance and weight, as it behoveth us to be very considerate, before we resolve and set down a certainty which we intent to pursue; so in this matter of War, are some points so difficult as may minister occasion and question of long debate, unless those controversies be commended to men of stayed and approved Judgement, who are not carried away with corrupt and common opinion, but advised and persuaded by the greater strength of reason, confirmed by experience, and precedents of the like examples: And by the way give me leave to declare my opinion, that no man can set down in writing a rule or method, precisely to be observed in War, the same being rather to be printed by a long practice and experience in a Soldier's breast, to be executed, as time, matter and place may minister, that upon the accident of any (in which there may be then required a new form and order to be used accordingly) It is held for a maxim That a Prince cannot any way more dangerously hazard his Realm and Country, than by giving an Invader Battle at his first landing, as hath been heretofore an usual custom. And since it is amongst things of the greatest importance that may concern a Prince and his kingdom, a people, their liberty and goods, it is to be considered and resolved upon beforehand by what means an Army Royal coming to invaid and conquer, might be best prevented and defeated. The accustomed Order hath been by firing of the Beacons to put the Shire in Arms, Short answers to the old accustomed Orders. and presently all the forces to repair to the landing place, and these without delay to give them battle. But because there are other opinions, the reasons of each opinion shall be set down, and then a resolve with submission to better Judgements shall follow. Such as hold (or maintain) this old accustomed order allege (besides the good success that many times it hath taken) in reason also it is the best dealing with the Enemy at his landing, before he hath firm footing, and before he shall have leisure to rank his men in due order of battle, and before he shall be able to land his Ordnance, Horse and Carriages, It might be so if the Enemy would acquaint you before where he would land. and that a very few men thus in time shall be able to give greater annoyance, and do greater service upon the Enemy than ten times so many, when the Enemy is landed and settled in strength and order with all his Horse, Ordnance and Carriages. They also add these reasons ensuing for confirmation of their custom. The Reasons. First, The greater fury, the lesser reason; therefore to be suppressed in an Army, as a breach of Order, and not to be inflamed. The fury of the Country upon the first firing of the Beacons is great; every man (pro aris & focis) violently running down to the Sea side, to repel the disordered Enemy at the first confused landing; which fury, if suffered to grow cold, we shall not so easily inflame again. Secondly, While the Enemy is landing, He is a silly Invader that upon a difficulty will make a retreat. if he find any difficulty or danger (being in boats) they are ready to retire to their ships again: But if they be once landed with their Artillery, etc. it is not then possible for them to retire to their Ships again, without extreme danger of their lives upon the retreat, and the dishonourable loss of their Munition, etc. And therefore necessity compelling them to fight, and all hope of escape by flight being then taken away from them, they become ten times more dangerous Enemies to deal withal than before. Thirdly, Every man knoweth what great advantage they have, It is no great difficulty to land men both strongly and orderly. that have a firm footing on land, to encounter an Enemy that must land out of boats, in confused straggling manner, and therefore ever, and speedily will go to enjoy the benefit of this advantage; whereas, if we suffer the Enemy to land, and put himself in Military order, he becometh more terrible unto us. Fourthly, It is not the fight of the Enemy which will cause them to discover themselves, but his prosperous success upon the first combat, which for that respect is to be avoided. There is in this Realm (as in all States divided in Religion) no small number of Traitorous minds, who having time to confer, and seeing an enemy of force then landed, may and then will discover their Malice, which on the sudden they dare not nor cannot. Another Opinion. Some others hold this old custom of running to the Sea side to be but a barbarous custom, void of Order, and Warlike Discipline, very perilous to ourselves, not hurtful to the Enemy, but rather a means to lose all; and therefore wish by special Command that order of repair to the Sea side be restrained and the Enemy suffered to land quietly: Suffered to land quietly because the Enemy would land whether you would or no. and in the mean time to drive and carry away all , Victuals, Forage, Carriages, etc. and certain places of Randesvouze appointed, (some distance from the Sea side) from whence they may march in a Warlike manner and Order; and so by carrying away all victuals and fortifying of straits and Passages to weary the Enemy in time. The Reasons of the Second Opinion. First, It is said the invading Enemy bringeth a select Company of Disciplined and well trained Soldiers whom we seek to encounter with a confused multitude of men untrained, in which match there is no comparison, but loss certain. Secondly, It is said an Enemy of force meaning to land will do it in despite of us, and then the Country offering to repel them, and finding themselves not able, grow much more fearful, than if quietly without resistance we had suffered the Enemy to land. Thirdly, Where we suffer the Enemy to land we may drive away all provision and further into the Country, and then maintain straits and passages well fenced and fortified; so as the Enemy shall be enforced to approach us upon our own strengths and fortifications to his great peril and danger. Fourthly, They say, in this manner we keeping Victuals from him by land, and his Majesty's Navy also in the mean time keeping the Seas, the Enemy for want of Victuals only shall be forced to retire, and glad to withdraw himself if he can. Further, It is alleged how doubtful a thing Battle is, and how dangerous a thing for a King to commit his Crown upon it, and therefore is that temporising course extolled. These are thought most effectual reasons to impugn the speedy repair to the Sea side, and to maintain the other Opinion for suffering the Enemy to land quietly, and by driving and carrying away Victuals, and forage and fortifying the straits and passages, by time and famine to weary the Enemy. But having weighed the reasons on both sides, and by experience of former invasions examining the success and sequel of the like attempts, it is adjudged not safe, and therefore not to allow of confused and disorderly running to the Sea side, to encounter a select well trained Enemy invading; and secondly, neither is it safe to suffer the Enemy quietly to land all his forces, munition, etc. It is by some conceived that a middle (or a mean) course far more serviceable than either of them both may be taken, whereby the benefit of that old custom may be embraced, and the disorders of the other (well noted) may be reform, and no advantage to annoy the invading Enemy omitted, as by these following reasons may be judged. Reasons and Resolutions against the second Opinion. It is subject to invasion notwithstanding: it is not meant but our Navy should annoy them both before, and in landing if they can. First I say one of the chiefest forces of this famous Island of England consisteth in this, that it is fortified naturally with such a Trench (or ditch) as the Sea is, whereby it is not so subject to invasion as other Countries lying on the main; which singular benefit and peculiar advantage to our Country is utterly lost if we suffer the Enemy to land all his forces, etc. and take firm footing on the Main. A reason made where there is no contradiction. Secondly, Whereas this noble Island hath such a number of Mariners and good Shipping both of his Majesty's Royal Navy, and also of Merchants, as may hope with good success to encounter on Sea the force of any foreign Enemy: Now if we suffer the Enemy quietly to land, and then temporize afterward (according to the second opinion) we lose a great part of this our strength. Rather by supposition than by experience. Thirdly, There is no man of any experience, but knoweth with what danger men land out of boats, if there be any ordinary force (before landing) to resist them; for if any storm arise the Sea alone fighteth for us, and with but small resistance on land may drown great numbers of our invading Enemy. Fourthly, No small work to entrench all the landing places about England. Any small Trench on land shall lodge Musquetteers enough, to spoil as many of our Enemies as in boat shall offer to land, before they can approach the shore. Also, In landing, True, if the Enemy would not resist you with a far greater force than can possibly be gathered together on such a sudden to encounter him. before they can have time to put themselves in Order, what an execution may a far less number of well armed men do on them, before they shall have time to unite their forces. Again, After the Remnant shall land, if they be not all drowned slain, or repelled in or before their landing, how easy a matter shall it be for a few well Armed Soldiers, to put such a confused, dispersed, scattered, Sea-beaten Company to the sword, A strong Imagination upon a weak supposition. before they shall be able to advance a Standard, or put themselves in order of battle? Besides all this, No intendment but our Navy should impeach them upon all assays. if his Majesty's forces should not in time be assembled of such strength as to be able before landing to give them battle, yet any mean force (assailing their Ships while their men are in landing) cannot but greatly annoy them, if not utterly defeat them. Again, An Invador will both forecast and prevent those dangers. In most places if (except the Enemy bring his tide justly with him) he cannot land, and then if part land, and any mean resistance made to give impediment to the rest, till the tide pass, their divided forces may more easily be defeated. Also, You grant him victuals enough if he can land, you say he shall find houses, and Barns full. It is no small time that is requisite to land an Army with Horse, Carriage, and Ordnance, Munition, and Victuals: without which an Invader shall never be able to prevail: And then if any mean resistance be made at the landing, it much prolongeth the same time, so as any storm happening, the Winds, Tides, Shelves, Rocks, Bars, and Seas fight for us, (in our favour, and to the ruin of our Enemies;) and therefore I utterly disallow that opinion, to give an Enemy leave quietly to land, and then by device to temporize afterwards. It behoveth an Invader to be as wary of burning and spoiling as yourself, lest he make himself odious to his own party. Further, If any such resolution by the Prince and people be taken, that the invading enemy should be suffered to land quietly to spoil and burn at his pleasure; and the inward forces of the Country not permitted, even at the first landing to come to their reskues, Let the Company come down to the Randesvouze as fast as they can so they give no battle. it would cause (no doubt) the Inhabitants of the Coasts to abandon their Towns, and leave the Frontiers desolate; which the wise Kings and grave Counsellors of this Land have everto sought to make populous, by granting many privileges and immunities to allure Inhabitants on the Frontiers. But touching driving, or carrying away of Victuals, No great difficulty, though not easily done as wished. and leaving the Country waste, thereby to famish our landed Enemies, it is a thing more easily wished than performed. By which retreiting and driving away of Victuals and keeping of straits and passages they starve and weary them that follow them. I confess in Ireland where most of their substance consisteth of Kine, it is easily done. But in this rich and wealthy Country of England it is not possible but that the Enemy (if he be once landed with all his force) shall find houses full of provisions, and barns full of all kind of Forage, That is where the prince is a Tyrant otherwise he shall be obeyed in all things that tend to the preservation of the Country. and Corn all the Country over, unless the King should command all to be wasted with fire, which precedent we see seldom or never put in use, neither in the Wars in France, Flanders, nor in any former invasion that we read of, for it will make the Prince odious, and alienate the Subjects minds, therefore not to be used but upon a great extremity, when all other means fail: and here in England above all other Countries it may worst be done, for our Towns be poor, weak, and unprovided and unfortified; the Country full of habitations, populous, rich, and abundance of all commodities. In the Low Countries by reason of their great store of strong well fortified Towns, they might much more easily drive and carry to their Cities (at hand) all victuals and forage, etc. And yet when the great Army of the States and Don John were in the Field, I grant for Forage because they came in harvest, but all other victuals came out of the Towns behind their backs. notwithstanding all the Boars and Country People were fled and retired, to the next walled Town, and had knowledge long before of the approaching of the Armies, yet were they not able so to drive and carry away their Victuals and forage, but that the Enemy found Barnes full in every place, as the Enemy was never forced to forage four miles from their Camp: So difficult, or rather impossible a thing it is to carry away our victuals or forage, or leave the Enemy a waste Country. But if here in England we should drive or carry away our Victuals or Forage to the next walled Towns, Here he speaks as if the Enemy by his landing were strait master of the Field, and no place left us but walled Towns to guard our and Victuals. the Enemy being quietly landed with all his Munition should have his chief desire, knowing not only how weak and unfortified our Towns are, but also how unprovided of all necessaries to abide a Siege; as if fortification on a sudden could be made. Wherefore it is wished that all provident means should be used to give the Enemy all possible annoyance before and at his landing. By reasons and precedents it is proved that an invadours landing cannot be prevented. And by no means to suffer him to land quietly, or to trust to that temporizing course, which is rather to be practised when all other means fail, than to be relied upon at the beginning. Too late to shut the Stable when the Steed is stolen. It is granted perilous for a defendant Prince to hazard his Crown upon a Battle, and more dangerous for men untrayned to encounter expert Disciplined Soldiers, and most perilous to us that have no strong Towns to make head if we lose the Battle: Therefore it is no part of judgement to wish our Prince to give an invading Enemy Battle with all our forces, how well prepared and ordered soever they be; but the meaning is to have such provisions in every Shire, as we may be able readily on a sudden to give the Enemy all annoyance possible before, and at his landing, whilst the inward forces of our Country may the better assemble, and put themselves in Military order to proceed after as shall be most convenient. A Reply to the reasons aforesaid. Now to come to the question, and matter propounded, whether it be better to fight with an Enemy at his landing or to defer battle. A Distinguisher betwixt an Enemy Invador, and an Enemy Borderer. I will first distinguish between an Enemy Invador, whom we do presuppose would be a conqueror to alter and change the state; and another Enemy Borderer, who either to procure a new quarrel, or to revenge an old wrong, may support some small company by shipping (or dwelling upon the main) and make incursion into a Country only to burn, and spoil some part thereof, such an Enemy may be fought withal at his first appearance or landing, because there is a means and likelihood to repulse him again, with the only aid and strength of the Frontier forces, as hath been already alleged, Viz. That if the Enemy should intent but to land and burn some houses, and villages near the Sea coast; for the prevention thereof as much as may be, it were good to appoint only those, that dwell within two or three miles of the Sea side to repair thither to make resistance, These may be termed the forelorn hope. and for their succour to appoint the Horse men to draw down to the Plains next adjoining, who may also give them stop for straggling far into the Country, and though you should receive a foil, there is no danger, for his intent is not to dwell and tarry by it. But for an Invadour as there is difference of his intention and force, so must you make also a difference in the encounter and prevention accordingly, who if he cannot be defeated by our Navy (is always preferred by the first trial, although it be hardly gathered to the contrary against me) which either I say might by contrary winds or other accidents happen to miss each other, and so the Enemy come undiscovered upon our Coast, As the Earl of Warwick did out of Normandy in Edward the fourth's time. or otherwise might land in despite of our shipping, than my opinion was to restrain the Country's disorderly running down to the Sea Coast, as a thing very dangerous, being not able to withstand their landing; first, because it was said, such an Enemy would land more men within three hours, than would be meet in reason for you to fight in three days; such a while will it be, before the Country can come down to the Sea side, as hath been seen by many false Alarms given to the Country for trial of the readiness thereof. Next because it is Impossible so to man the Sea coast round, as that an Enemy (meaning to land and burn only) might be prevented, for that he will make show to land in one place, and (the Country being drawn down thither) may suddenly weigh Anchor and Sail further in few hours, than your Army that you have provided in a readiness, can march well in two days. As for example, How your prepared forces may be prevented. The French made a show in King Henry the eighth's days as though they would Land in the Isle of Wight or Portsmouth, & finding the Country drawn down thither by means of the Kings being there, hoist Sails, landed & burnt at Brighthmesteed in Sussex, & in the Downs in Kent, and after returned and landed in the Isle of Wight. Then seeing the Enemies remove from place to place, is so speedy, and his landing place so uncertain, and the knowledge thereof before hand impossible; I would fain know how strong a resistance the Country can be able to make upon the sudden, against an Invadour, that will land a thousand or two, at one instant, or rather which hath embarked his men invessels of so small draught, as the men may leap a shore out of them. The Opponent meaning to sail safely betwixt the two Rocks of Scylla and Charybdis, imagineth he goes clear when as he striketh upon both; who seeing to dislike of giving Battle, would have the Country drawn down to make resistance and impeach their landing. I would thereupon ask this question; if the men you send down be once in fight, whether you think it not requisite to second them, and if you second them, what do you else, but engage yourself to Battle; if you will not second them, then do you most barbarously expose your men to the slaughter and butchery of your Enemy: How great a discouragement that would be to your people, and what inconvenience might follow, I leave to your Judgement to consider. But from whence proceedeth this opinion of the necessity or convenience of a rash and sudden encounter with an Enemy at his landing, but from an excessive fear and doubtfulness conceived beforehand that all the Realm should be in hazard to be lost, if the Enemy were but once suffered to land, and have firm footing. Which imagination groweth for want of skill and judgement in Martial actions, and therefore we seek to prevent that by a desperate and disorderly fight, which we might more safely remedy by a defensive, and less dangerous course, as may appear by the examples of a weak Ship, and a battered Town; which both by suffering themselves to be entered and assaulted, the one by her close fights, the other by new intrenchments, do give the entered Enemy the greater foil, even then when they think themselves possessed of all. Besides a King that is in his own Country may be supplied with infinite Numbers of Pioniers, who in few hours may rear earth works to triple his force against an Invadour (as is well known to him that is a Soldier) whereof he should be utterly deprived, by that most barbarous custom heretofore used and yet maintained; I mean of that disorderly running down to the Sea side, to give an Invading Enemy battle, at his first landing. What reason had Spain to attempt the Conquest and subversion of this Realm, but that they presumed, The only hope of an invador is to prevail by Battle. we would assuredly rely upon our old Custom of giving them Battle at their landing: which if we should do, there would be great likelihood; first that we should lose the same, and next having lost the Battle, I fear that the subversion of this famous Island would ensue. For an aspiring King that hath a great faction within a Country may presume beforehand to carry the same, if he be assured, that the people thereof will give him battle at his first landing. Therefore if you will avoid an Invasion and the danger of a Conquest, let it be known to the world that it is an error, whereby you might embrace those advantages, and the benefit that our Country affords, and you shall undoubtedly avoid the trouble of the first, and be free from the danger of the last. Scanderbegg against the Turk. We read that Scanderbegge (never theless that he expected the Invasion of so puissant an Enemy, as was the Turk) thought it not good to leave any great Army of Force to give him Battle; but only certain select bands (or Companies of Foot) with Troops of Horse, & the foot too lightly armed, & causing all the frontiers to withdraw themselves, their , Corn and Substance into the strong and fortified places of the Country; did with such select forces face the Enemy on the frontiers, by keeping of straits & passages, making sudden attempts in the night, & such other times as by Spies he found the Enemy careless, and so with a few people (or small force) by time, famine and expenses he wearied the Enemy and caused him to retire, that otherwise in Battle might have gotten the victory, and so in short time commanded the whole Country. Wherefore I would not wish any Prince to adventure his Kingdom that way, unless he be weary of the same Battle being the only thing for an Invadour to seek; and on the contrary for the invaded to avoid and shun, for the one doth hazard but his people, and hath a lot to win a Kingdom, and the other in losing of the Battle endangereth his Crown. The Opponent disalloweth of a confused disorderly running down to the Sea side, and yet would fight with them in their landing, which is a thing impossible. For if you tarry time to put men in order, (which you must of necessity do by reason of the Country's slack assembly) then will the Enemy land in the mean time and frustrate your purpose, unless you were made acquainted long beforehand, when and where he intended to land, and where you may make your supposed Trenches you have declared, to lodge your men in. There be some also that conceive a great advantage of the Enemy's weakness coming from the Sea, and of their landing out of Boats disorderly, which when it shall happen to come to trial, it will easily appear how far they are deceived of both: for who knoweth not that even all men coming near the shore, and smelling land, become well and sound again of their Sea sickness. Also, what numbers of men will be landed at one instant in Boats, Galleys and other Vessels of small draught, and that safe enough, those that have been employed in like actions, can testify. And as touching Rocks, Shelves, contrary Winds, etc. which is said may fight for us, we must not build upon such uncertainties, for an Enemy will beforehand so set down, and lay his plot, where he will make his descent, as that none of all those accidents shall give any impedement to the same. What other advantages our Country men may have either of their Courage, or goodness of their cause, Strength and courage availeth much being joined with skill and order to dispose of them. without knowledge, and order, how to dispose thereof, will rather be an occasion of their overthrow, than means of the Victory. But especially a few to fight against many, disordered against ordered, Country men against experienced Soldiers; the odds that the Enemy hath of you therein, will be much greater than your imagined advantages. And albeit that I confess, our Country men have a show of desire to fight, (as having as great, natural help of strength, courage and ability as any other Nation) yet can it not be denied, but that in the Artificial we must needs be defective, for want of use and Practice, therefore not to be suffered to run down to the Sea side, in that confused and accustomed manner unless it might be done with a complete number of choice men; conducted by a skilful leader that knoweth how to make his fight upon the best advantages, and to retire them orderly again to their least hurt and discouragement; otherwse I do altogether disallow, of that general repair to the Sea side. But rather to make your assemblies five or six miles distant with all your Foot forces, and to attend them in the plains, with your Horse; for whatsoever men resolve with themselves before hand, and what minds soever they may seem to put on, when they shall be driven to make their ways through the volleys of shot, having never been acquainted with the game before, it may either make them pinch courtesy through the strangeness thereof, or at least having tasted of that sauce (and finding it bitter) may spread rumours to discourage a whole Army; for oftentimes the same and bruit of a repulse maketh others as fearful that but hear of it, as those that have been in the Action and born the blows themselves. How unlikely then it is, that you should profit yourselves by that means or impeach your Enemy, may easily appear. But let us come to examples, for it is not sufficient to say by experience of former invasions, etc. not alleging any. Where can it be remembered that a strong Enemy proffering to land, hath been prevented by the Frontier forces? I think few or none, who be avouched, The Priest of Saint Margaret with his Bow and Arrows. unless the precedent of the Priest of Saint Margaret's near Dover shall be admitted for one, of whom the old Fletcher's retain a memorial in honour of their Bows; who is said with his Bow and Sheaf of arrows to have kept down the French men that offered to land in a narrow passage up the Clift near Dover, Who came for fresh water as was supposed. where they found a gate fast barred and locked to stop the same. And he standing over them, on the top of the Clift, played a tall Bow man's part, when as in these days the French had not any shot but some few Crossbows, that could not deliver an Arrow half way up the Clift to him; and so it was given out that he kept them down till the Country was come down to the Sea side to repel them back to their Boats; or rather I suppose (my self knowing the place) when they saw the gate was so fast, as they could not suddenly break it open, they returned before their coming. But yet I must confess the Bow bore the bell, before the Devil (I suppose) sent the musket, etc. out of Hell. But here lest the Author be mistaken, he prefers the force of the Harquebuz and Musket, far before the Bow, yet in judgement doth not disallow the Bow but rather judge the same to be a serviceable and warlike weapon, as well in Town as Field, and although it be not greatly pertinent to this question, yet it may be convenient to consider here, how and wherein good use may be made of this weapon: first in the field against the Horse men, The use of the bow how serviceable. though it be shot at the highest random, only with the weight of the fall it galleth both Horse and Man; and though the wound be not mortal, yet both Horse and man are hereby made unserviceable then and long after; if they escape death. Secondly, in rainy weather when men come near together it is a good weapon. Thirdly in the night time it is a ready and a secret shot, etc. and the use of it may be good in the forcing of the Enemy's Trenches, in sallying out of Town: or else, Fourthly, at an assault when all the defences are taken away in any Town, you may deliver your Arrows over the wall and shroudly gall your Enemy with the fall of them. Fifthly to shoot Arrows with wild fire, to burn gate or draw bridge, to fire thatched or shingled houses. When our English Army was before Paris those of our Commanders wished they had brought Bow men over with them; and I see no reason it should be wholly laid aside, for the worst Bow man that can but draw his Bow is better than a bad fire man. But if we should not make use of our Bow in any of our warlike enterprises; it should be every Commanders care to choose good fire men, for Ammunition is much wasted by the unskifulness of the Musquetteer, and execution not to expectation; Mustermasters cure. and as we have an order established for our Musket bore, I could wish the Mustermaster in every County would look so to it, that they may not be too big, as well as too little. But now touching landing let us see what may be conceived out of the former experience. Examples and precedents of landing. Did not the Earl of Warwick notwithstanding the Duke of Burgundy's great and puissant Navy which he had provided to join with Edward the fourth, for the impeaching the Earls landing from out of France; and the fleet being before the Haven in Normandy, out of the which the Earl must come; the Duke having also warned the King, into what part and Port of England the Earl meant to make his descent, whereby in all likelihood he was or might have been provided sufficiently to withstand the same; yet (I say) did it not so fall out that the Earl of Warwick escaped, their Fleet landed in England, and drove the King to flee for secure into the Low Countries, and enlarged Henry the sixth, and set him in his former estate? After this did not Edward the fourth with some small aid from the Duke of Burgundy given him, Edward the fourth relanded in England and deposed Henry the sixth. and that under hand, both of shipping men and money, transport himself into England again, and in Battle slew the Earl of Warwick, and his adherents, deposed Henry the sixth, resuming again unto himself the Kingdom of England? Have not the Kings of England many times entered France, by Navy; and Scotland during the time of Wars betwixt them? Queen Mary landed 5000. in Britain and burned Conquer. Did not Queen Mary land 5000 men in Britain one of the most popular parts of all France, and there sacked and burnt Conquer, and other places, our men remaining on shore two days and a night, burning and spoiling, and were not, or rather could not be resisted upon the sudden? Have not our English (though but small) forces in Queen Elizabeth's days landed in the Indies, English landed in the Indies. at sundry times, sacked, and ransacked their Towns, brought away their Munition, with other great spoils and riches, yet at their landing were not withstood? English in Spain and Purtugal. And did not our Army land in Spain and Portugal at sundry times, and in sundry places; they having knowledge a long time before of their coming, whereby the Country was or might have been in that readiness themselves would have desired, and yet by a temporising course used against them they were driven to retire; both feeble and broken: whereas if they had been fought withal at their landing, and had won the field, there had been a great hope, they might have prevailed in that enterprise? The Spanish Forces landed in Portugal. Did not the Spanish forces also land in Portugal & his other Army by land, under the conduct of the Duke of Alva who by winning the Battle won the Kingdom withal, and drove the King quite out of his Country? The French in Terceras. And did not the French forces likewise land in the Terceras in despite of the Country? And did not the Spanish forces after reland, slay and drive all out again? The Spanish relanded there. Infinite are the precedents of landing, and a rare matter to find any example of an Army coming to invaid, to be prevented of landing, by the Country's fury, and running down to the Sea side; and what Soldier (or man of War) would not undertake to land even a few men in comparison of a royal Army in any Prince's Realms and Dominions, spoil and burn at his pleasure, until such time they had assembled greater forces than the inhabitants of the Coasts. Whatsoever a man cannot resist, he must give way unto. Reason and experience do plainly prove, that it cannot be withstood, but that a forceable Enemy will land. Therefore the best remedy will be to give him way, and withal to remember to do all things like wise men and Soldiers as hath been said already, by driving and withdrawing the Country's and provisions that your Enemy may not be relieved and nourished. Duke of Alva against the Prince of Orange. Did not the Duke of Alva defeat the Prince of Oranges great Army, by forbearing to fight with him, and leaving him a vast Country to walk and way himself in? Did not the Constable of France defeat the Emperor's attempt upon Province, France against the Emperor. by this only temporising course? Did he not burn the Mills, destroy the Ovens, spoil the fruit, etc. himself retiring to Avignon; there to join with his forces after that he had provided for the frontier Towns; leaving nothing but a waste Country, for his Enemies to spend themselves in; whereby he drove the Emperor in the end to make a most dishonourable retreat? Monsieur de Langey doth allege that example of the Constable of France, proving greatly his device and policy therein. Notwithstanding there were divers who did not stick to blame him for that he did not seek to stop the Enemy's passage, through the mountains, which they supposed he might have done very easily, and with few men. But he foreseeing the mischief that might grow by a small foil or loss received at the first, thought it the safest way to prevent all dangers, by temporising, until his forces were assembled in full strength and his Enemies weakened; saying moreover, that it is a great point of wisdom for a Prince, or Captain General, to defer fight when the Enemies are entered in his Country! for saith he, if the battle should be lost through the encountering of them, the Country would also be in hazard to be lost, and this may appear by divers examples. First, The King of Hungary against the Turk. the King of Hungary being assailed by the Turk in the year 1562. thought it better to hazard the Battle and to fight with the Turk at his arrival, than to forbear and stand upon his guard, which was the cause he himself was slain, and a great part of his kingdom lost. William the Conqueror, and Henry the seventh got the Crown of England by Battle. And did not William the Conqueror and King Henry the seventh become kings of England by reason the defendant gave them battle at their landing, and lost the same. Obj. But some may here object, that the Parties and Factions within the land, were cause thereof. And doth any man think that a Foreign Prince is so void of Judgement as that he thinketh to prevail by way of Conquest without a party? The Duke of Burgundy won the Country of Leigh by Battle. Did not the Duke of Burgundy get the Country of Liege, by reason of some Battle he won against the the people thereof? Philip de Comines saith, that a man ought greatly to fear to hazard his estate on a Battle, when he may otherwise avoid the same: for faith he, of a small number of people lost there followeth a great change to him that loseth them, not so much by the fear they conceive of the Enemy, as in the little estimation they will have of their Master afterward, being ready still to enter into mutinies, demanding things more boldly than they were wont; alleging further, that one Crown before, will do more with them, than three will do after. Whosoever will read the Book of the actions of Lewis the eleventh King of France (who was both a very wise and valiant Prince) shall find, Lewis the eleventh against Charles the Duke of Burgundy's Son. that after the great encounter between him and Count Charles the Duke of Burgundy's son at Mountleyrre, notwithstanding, that the conflict went so indifferent, as neither side knew almost by the space of three or four hours after who had the Victory, so soon as each party had rallied their broken Troops, etc. having some good means so to do by reason of a great ditch and long hedge that was between their two Armies, where the fight first began, although the King's power remained still great, by reason of so many Princes, as he had assembled together, yet then, and ever after he determined, no more to venture so great a Kingdom as France was, upon the uncertain event of a Battle. And therefore the night following he dislodged and retired to Corbel; after which time he carried all his Wars, with such a Temporising course, as thereby he wearied his Enemies, and became a mighty Prince, making his Army so great as his adversaries at no time after durst attempt to give him Battle. Although Philip de Comines doth write that our Nation hath been wonderfully fortunate in Battle, and are much addicted thereunto; yet he doth more allow of the politic and wise temporising of Lewis the French King in forbearing to fight with Edward the fourth when he entered France, proffering him Battle near Amiens. Lewis against Edward the fourth. The King considering how dangerous an adventure it was to his estate, If it should not succeed well with him, looking also back to the great thraldom and subjection, that his predecessors had brought the Kingdom of France into, under the English Nation, by such like rash acceptance of Battle, he determined to temporize, though it were to his charges, thereby to weaken the King of England, the winter season drawing then on: In the mean time sending great presents to those that were near about the King, and Victuals of free-gift to relieve his Army; condescending also to pay a yearly sum of 50000 Crowns into the Tower of London, thereby to hasten the peace, and to get our Nation to return. After all was concluded and the King returned home; one of the King of England's men being with Philip de Comines in discourse, he told him he had been at the winning of nine Battles, and how many said Philip have you been at the losing? Only one said he; and that was at the last forbearance of my Master to fight with yours at Amiens; whereby we have gotten more shame unto ourselves than honour by the first nine. When Lewis the King heard of this speech, he said, this is a shrewd boy, and sent for him to dine with him, and after gave him 1000 Crowns with other great promises to the intent he should be a means to entertain the peace, begun between the two Kings. What success had the French at the Battle at Poytiers and Cressey, The Battles of Poytiers and Cressey. who although they were in number far greater than the English, and in the heart of their own Country, yet they tasted nothing but the bitter effect of a lost field. And we by other such manifold examples might be warned not to commit the good estate of a Realm to so tickle and dangerous a trial as is the uncertain sway of a Battle. Spanish Fleet defeated. 88 And now never to be forgotten, did not our English Navy defeat the great Spanish Fleet by this temporising course? which had been so easy (as it was thought) to have been performed by main force, in boarding them at the first. Yet some would have this temporising course not to be used at the beginning, but when all other means do fail: and then it may be too late to temporize when you have fought and received the foil; and it is against the name of the word and thing itself to use it in the end when time is past. Infinite are the examples to confirm these temporising courses, by means whereof great and huge Armies have in a short time been dissolved and come to nothing. As namely the Germans sundry times in France, Duke of Pama's Army and the Duke of Parma's Army in France, when he came to the relief of Paris Anno. 1590. Lastly, The better to remove this old impression of rash encountering of an Enemy Invador, remember the unadvised encounter of the Duke of Burgundy who besieged a certain Town in the Savoy, The Duke of Burgundy's fall. called Granson, with a very great Army, to the relief whereof came certain Swissers, (though not great in number;) the Duke hearing of their approach, sent some forces to them to give them all annoyance possible, as also to prevent their entry and descent into the Country (for the passage they should enter by was through a certain narrow strait betwixt certain Mountains) and himself followed with some greater forces to second them. And this was done by the Duke, contrary to the advice of his counsel who persuaded him, rather to attend their coming with all his forces in the place where they were; for the place both by Nature and also by Art was strongly enramped, and it was so that in all reason he could sustain no danger. To make it short, the Duke's Vanguard was not able to withstand the Swittzers entrry, but retired; the Duke's rere-guard seeing this, supposing they had fled began also to fly; in fine his whole Army retired toward the Camp, although some behaved theselves very well in this retreat, yet when they came into the Camp they durst not defend it; but all betook themselves to flight, leaving their rich and pompous Camp and their Artillery to the spoil of the poor Swittzers, who slew but very few of his people for want of horsemen to follow the chase. The Duke, who the day before was lifted up to the skies in pride, through the seeking to himself so many great States and Princes, that desired to ally and confederate themselves with him in league and friendship, presently after the loss of this Battle found a great deal of alteration and change, for there fell from him four sorts of people, who became his Enemies. The rage of the Duke was still so great that he would not thus give over, but would try a second Battle at Morat: Upon the loss whereof divers others of his Allies fell from him also. And lastly after the Battle of Nansey where he himself was slain, a great part both of his own proper Dominions, and of Burgundy itself, fell from his house also. Thus you may see what a long and evil tail a lost Battle hath; as Lewis the French King was wont to say. If you desire examples of greater Antiquity, you are referred to the reading of the Roman Histories; but because brevity is required, I will remember you only of this one; Namely of Caesar, who never could attain to the sole government of Rome, until Pompey (opposing himself against it, on the behalf of the State and Senate of Rome) gave him Battle and lost it: after which he was driven to fly into Egypt, where Ptolemy the King sent his head unto Caesar, whereby there were left none able to withstand. By the which he got not only the absolute government for himself, but also brought and reduced the free State of Rome to a Monarchy. But if the defendant chance to win the Battle, than indeed he removeth the cause and endeth the danger. As the Moors against the King of Portugal, The Moors against the King of Portugal. who landed without any resistance: But the defendants finding themselves the stronger as well in Foot as in Horse, thought it no danger to give Battle, which grew by temporising, until their power was come together: for it is most certain, that as long as you abstain from coming to fight, the Enemies shall always be held in doubt of winning, and you shall be in no hazard of losing the Country, and your malcontents and evil disposed persons will be kept from revolt, who no doubt will see a Battle fought before they will show themselves open Enemies; yea, whatsoever they had promised beforehand, as the Portugals did to Don Antony, and performed it not. By which dilatory manner of proceeding, you may be at choice either to accept or refuse the Battle, as shall be most for your advantage, when by time you have made yourselves strong and your Enemies weak. And this defensive War, and these temporising courses, we see that all Princes and men of War that are, or have been of late of Judgement do imitate and follow. As whosoever will Look into the Duke of Parma's actions shall seldom see that ever he came to fight a set battle, but when all other means did fail to accomplish that which he intended. And no less noble and glorious is that victory holden, which is obtained by Counsel, device and policy, than that which is won by the sword, violence and Blood. I have now answered to the question first proposed. & given the reasons on both sides, leaving my superiors to their better judgements. Although the people of this Nation heretofore ran headlong upon the invador to the Sea side, without sufficient arms, advice or command; such furious actions the discreet Soldier is against. But in these our later days the people being more civilised, better armed and disciplined; and the whole Nation in a better posture of defence; If any advantage is offered not to temporize. it may now be granted that in some cases, to defer and delay your fight may be dangerous, as in letting slip some notable advantage; from which you are not restrained but only to be advised in this case, not to join Battle rashly and unadvisedly with the Enemy. The which (besides the danger of rash attempts) doth cut you off from advantages and supplies, that may be had, by time, deliberation, and counsel; for their is nothing in which true fortitude may be showed more than in this action: for to fight, courage doth not naturally provoke; but to refrain upon good cause, is the advice of wisdom; and he that will fight upon every call of the Enemy when offered, shall be sure to do it to his disadvantage; and thereby shall show that he hath no experience of Wars, and is ignorant of the chances and mutability of fortune, or as I may say more aptly, knoweth not how to use his fortune: yet what is the common voice of the Country? which heat and fury as it riseth suddenly, so may it be cooled quickly again. But that which increaseth and confirmeth courage best and maketh men resolute and constant indeed, is when they shall see themselves accompanied with numbers able to resist, instructed with knowledge how to use their arms and weapons, and fortified with order to be able to withstand and repel an Enemy: This is it, which will make a coward valiant: For as one saith, the fierce and disordered men, are much weaker than the fearful and ordered; for that order expelleth fear from men, and in the end disorder abateth fierceness; so than it is not fury that prevaileth in War, but good discipline and order. The chief scope is to persuade a restraint of the violent and disorderly running down of the Country to the Sea side to fight and give Battle to the Enemy at his landing after the old custom, showing the danger and inconvenience that may follow. And for the other part it is granted by all that it is perilous for a defendant Prince to hazard his Crown at a Battle; and more dangerous for men untrained to encounter expert disciplined Soldiers. Put the case that Battle be given, and loss received; then if we have no strong Towns adjacent to give the Enemy stop, to make head and rally again, it will prove most perilous to us. Therefore moderately it may be concluded dangerous (unless advantage might be obtained) for any Prince to give an invading Enemy Battle. And here by the way (occasion being offered) to speak of strong Towns; some there be of that opinion that a Country well peopled, that hath not, or few strong Towns, is in less danger of conquest than that Realm that hath many: because (say they) an Enemy cannot any way nestle himself, but that you may at all times force him to Battle at your pleasure. To that may be answered that a Battle being the thing that an invadour is most desirous of, and which a defendant ought to shun; your strong Towns in that case are most available for the defendant Prince in his own Country against an Invador; because he may only with one strong Town weary an Invadours' Army and consume it: especially if he be but able with a small force to encamp near his Town besieged: for the Invador is thereby restrained from assaulting the same, for fear the defendants Camp should assail him in the mean time. The which worketh all for the defendant, in winning of time to the weakening and ruin of his Enemy's Army: the date whereof (as by daily experience is found) is not above twelve or thirteen week's continuance; so as your strong Towns avail wholly for the defendant; In our late Wars. and are dangerous only in Civil and Intestine Wars, for that such Towns revolting work the like contrary effect against their Lord and Master, as they did before for him: for examples & precedents of this, you may behold what the strong holds of France, and the Low Countries, and England itself did against their Lords and Sovereigns: Insomuch as we may truly say of them They are a dangerous good: Wherefore I think it matter of Joy to all loyal hearts that our most Gracious Sovereign hath a Kingdom so well replenished with a warlike people, whereby to be enabled at all times to front and give a stop to an Enemy Invadour: And as touching a rebellious number, I hope we shall never doubt or fear them, as long as they shall want skilful leaders and Governors to direct them; pay, armour, Munition, and other necessaries to uphold them; wherewith His now most Royal Majesty is plentifully furnished; the want whereof shall force Rebels in a few days to disperse themselves, who being once broken may presently be followed in gross; in such sort as they shall never be able to assemble and make head again. And what leader of skill and judgement will undertake such an enterprise in these days; and not forecast that a power and force assembled cannot long stand without rich and strong Towns to supply their wants; or at leastwise, without so much as is requisite to retain and keep an Army together in due order and obedience; without which there can grow nothing but confusion and ruin; be their numbers never so great. THE CONTENTS. For the service of the Horse. Chapt. 1 Introductive Collections for the exercise of the young Soldier in the Art Military. folio 1 Chap. 2. Of the Soldier and Officers in general. 4 Chap. 3. Of Arming the Cavalry. 7 Chap. 4. Of Military signs. 9 Chap. 5. Of marching and drawing up of a Troop of Horse. 10 Chap. 6. Of exercising a Troop as armed with Carabine and Pistol. 13 Chap. 7. Of Distance. 15 Chap. 8. Of Motions. 16 Chap. 9 Of firings. 21 Chap. 10. The conlusion for the Horse Service. 23 For the service of the Foot. Chap. 1. By way of introduction. 33 Chap. 2. Of the postures of the Pike, and of the Musket. 34 37 Chap. 3. Of places and dignities both of files and ranks. Some Objections answered in dignities etc. 40 43 Chap. 4. Of the Drum. 45 Chap. 5. Of distances. ibid. Read Chap. 7. for the Horse Service. Chap. 6. Of Marching and drawing up of a Company, Deciphering their Dignities in place. 48 49 Chap. 6. Of Face. 50 Chap 7. Of doublings. 53 How the Front is strengthened, 1. By entire doublings of Ranks. 54 2. By Bringers up. 57 3. By half files. 58 4. By divisional wheelings. 61 Chap. 8. Showing that several Commands produce one and the same figure. 63 Chap. 9 How the Rear may be strengthened. 65 Chap. 10. How the Flanks are to be strengthened 1. By Files. 67 2. By half ranks. 72 3. By divisional doublings. 77 4. By Wheelings. 78 Chap. 11. Showing how that several Commands produce one and the same figure. 81 Chap. 12. Treating of Inversion. 1. Of files filing. 84 2. Of Ranks filing. 90 Chap. 13. Of Conversion, etc. 93 Chap. 14. Showing also their several commands producing one and the same figure. 106 Chap. 15. Of Countermarches. 110 1. Of maintaining ground. 111 2. Of losing ground. 115 3. Of gaining ground. 122 Chap. 16. Of Wheelings. 127 Chap. 17. Of file leaders to be made successively six deep. 136 Chap. 18. Of firings, and firing in the Front. 137 Chap. 19 Of firing in the Front and Rear: and Rear alone. 151 Chap. 20. Of firings in the flanks. 153 Chap. 21. Of divisional firings. 160 Chap. 22. An excuse for not proceeding farther. 169 Chap. 23. Showing the Necessity of exercise of arms, with their Antiquity. ibid. Chap. 24. The Conclusion. 174 Chap. 1. The Original and being of Ensigns and Colours. 175 Chap. 2. The definition of Ensigns. 177 Chap. 3. Of Horse and Horse Colours. 179 Chap. 4. Of the dignity of Ensigns. 180 Chap. 5. The disgraces to the Ensign. 182 Chap. 6. The use of the Ensign with the postures and flourishes. 184 Sir. Francis Veares notes of directions how far a man's Office and duty in a Regiment doth stand. 186 FINIS. HOC MUNIMINE TUTVIS VERO NIL VERIUS WF fec. He that heareth the sound of the Trumpet & will not be warned if the sword come to take him away, his blood shall be upon his own head for he heard the sound of the Trumpet and would not be admonished; but he that receiveth warning shall save his Life. MILITARY OBSERVATIONS Or the TACTICS PUT INTO PRACTICE, BY "TV" (monogram of Thomas Venn) MILITARY ARCHITECTURE, OR THE ART OF Fortifying Towns; Together with the ways of DEFENDING AND BESIEGING THE SAME. By ANDREW TACQVETT, of the Society of JESUS, and Translated out of the Latin by J. L LONDON, Printed by S. Simmons, for Robert Pawlet, Thomas Passenger, and Benjamin Hurlock, MDCLXXII. To the Right Honourable AUBREY de VERE, Earl of Oxford; Baron Bolebec, Samford, and Badlesmere; Chief Justice, and Justice in Eire of all His Majesty's Forests, Chases, Parks, and Warrens on the Southside of Trent; Colonel of His Majesty's Royal Regiment of Horse-Guards, Lord Lieutenant for His Majesty in the County of Essex, Knight of the most Noble Order of the Garter, and One of His Majesty's most Honourable Privy Council. My Lord, I Shall not be tedious in informing Your Lordship of the reasons which induced me to this Dedication. Your most Heroic Ancestors being always the truest defenders of Loyalty, and eminentest Patterns of Valour; your Lordship's particular disposition and affection to Martial acts, the Experience you have had in the Fortifications abroad, have Entitled you to the Patronage of these my Addresses, and given you the undoubted right to be a fit Judge of all Military designs whatsoever. And though the particular favours and kindnesses which I have received from your Honourable Family (as owing my Education to the bounty of it) have sufficient force to oblige me to a most humble and grateful acknowledgement, yet in this case I laid aside those considerations, and had respect only to your Lordship's self as a Soldier, furnished with all that may render you capable to examine either this, or any other Martial Treatise. I am confident, My Lord, the Book in itself, how meanly soever by me Translated out of the Latin, will not be unworthy your Lordship's favourable aspect, it being the Easiest and Exactest of that Nature that ever yet was Extant, having been compiled from all Authors that have treated of that Subject by Andrew Tacquett of the Society of Jesus, for the use of his Pupil Count d' Horn of Flanders. The new Corrections of the Count d' Pagan, and Van Ruse, that we all so admire, but no body practices, is not here so much as spoke of; he thinking it best that men should be well grounded in the old ways; afterwards for divertisement they may follow what Novelties they please. I shall not insist further on the praises of the Author, or obtrude him upon your Lordship by numerous commendations: If at your vacant hours you shall vouchsafe to cast an Eye upon him, I do not doubt but you will give him the esteem he deserves, and favourably accept the poor Endeavours of him who is willing to omit no opportunity of testifying himself, MY LORD, Your Honours most Obliged humble Servant John Lacy. THE FIRST PART OF Military Architecture TREATING OF REGULAR FORTIFICATION. CHAP. I. Wherein is contained the Definition, Beginning, Progress, and Perfection of Military Architecture, etc. MIlitary Architecture is a Science how to defend and fortify any place against the force of an Enemy. Towns and Castles (says Vegetius) are either fortified by Nature, or by hands, or else by both. By Nature as being situate in some high abrupt place, or being encompassed with the Sea, Lakes, or Rivers. The Mountains about Cilicia in Asia, and Helvetia of Germany, almost render them inaccessible. The Rock Aornis baffled the force of Hercules and Alexander. The Castles of Namur, and Hermenstein, and many others in Europe, are almost invincible by reason of the Rocks which lie underneath them. Venice, Straltsound, Custrine, and almost all Holland, are defended by the waters that flow about them. So that you may see Nature in her fortifying of Towns, either casts about them the Element of Earth or Water. And Art imitating Nature (as it uses to do) placed Walls and Ramparts instead of Rocks and Mountains; and Moats or Ditches, where the Sea or Rivers have been wanting. Fig. 1 But as all beginnings are wont to be, so this of fortification was altogether simple and unskilful. They raised their walls to such a height as might seem to deny the enemy an easy ascent by his Ladders. The breadth was such as would hold six or seven Ranks of armed men; nay Curtius reports the walls of Babylon were 32 feet broad. But this Structure had two faults in it, and both of them very dangerous. The first was that the defendants standing on their wall without any covert lay open to their Enemy. The other was that the Enemy approaching under their wall, was so secured by the wall itself, that he could not be hurt by the defendants that stood on high over him. These Errors at length they endeavoured to remedy, by building throughout upon their wall a brestwork B C Z, the top of their brestwork they distinguished with Battlements Z Z Z, not joined together, but left open at certain distances, so that the defendants, covered with these Battlements, could beat off the enemy through their open intervals; so was the first Error in some manner sublated. Fig. 2 To mend the other they caused loopholes to be cut in the wall at a man's height from the ground, marked with the letter P P P. Nor yet were these inconveniences perfectly taken away, for the Enemy lying within the triangles D E F, G K H, would escape the shot of the Townsmen. Therefore they began to look on a flancquing or side defence, and still keeping Fig. 3 their battlements and loopholes they built round their work square Turrets that ran out beyond the thickness of the walls, and so they added to their foreright defence (which was only then in use) a flancquing or side defence; but this same side defence was as yet imperfect, because the Enemy could be hid within the triangle I P K; besides square Towers were not thought able enough to bear the brunt of Engines and and battering Rams. Fig. 4 Therefore slighting their square Turrets they made round ones; so the Triangle A C B, in which the Enemy was hid, became so much lessened, that now he could not traverse his battering Engines within it; and the Round form of Turrets was found to stand firmer than any other against the force of the batteries. And here the Art and endeavour of the Ancients rested, till Gunpowder being found, men began to imitate Thunder and Lightning. And indeed this last way of Fortification was far better than the former. Nevertheless the business went yet suspected, for the Triangle A C B, was found large enough to shelter Pioners, besides the flancquing defence F C, D E, could scour only one point of the round Towers, B C A, because round bodies cannot be touched by right lines but in one point only. At last Art conquered itself, and found out that way of defence which we now use, turning the Walls into Ramparts, and the round Turrets into Bulwarks fitted with face and flancque; and enclosed the whole Fortification with right or straight lines. To conclude, it is brought so to pass, that the Enemy let him stand where he will, shall lie open to the Shot of the defendants, and all the parts of the Fortification mutually defend one another. Being about to treat of this last manner of fortification, I will keep such Order, that when I shall have expounded the terms that are used in this matter, I shall then propose the Rules and Principles of the Art; and thus instructed, at last, God willing, we will fall upon the practice itself. CHAP. II. The Terms of Military Architecture are Expounded. 1. A Fortification is a Place having such a Circumference, whose each part receives from other parts a Flancquing or side Defence, besides the foreright Defence they yield themselves. So that all parts mutually scour one another. One part is said to scour or flanque one another, Fig. 5 when it can defend it with the parallel shot of a Gun. So the part of the Circumference X B C scowrs the part F G; the part A E F scowrs C D: So of the rest. 2. To delineate a Fortification, is to describe the out-lines of the Fortification. 3. A Regular Fortification is built upon a Regular Figure, hath all its parts equal and like placed. 4. A Regular Figure, is that which hath equal sides and angles; such is the Figure H K R P M N, all whose sides K R, R P, P M, M N, N K, and angel's N, M, P, R, K, are equal among themselves: About this a Circle may be circumscribed, that shall have the same Centre H, as the Figure hath. The Angle of the Centre is that which is contained between two Semidiameters K H, R H. The Angle of the Circumference, or of the Figure, is that which was contained between the sides of the Figure, as M, P, etc. 5. An Irregular Fort, is that which is built on an Irregular Figure; an Irregular Figure is that which hath neither Sides nor Angles equal. 6. A Bulwark or Bastion, Fig. 6 is that part of the Fort B D H L M which most of all runs into the field. 7. A C, B D, Are the flanques of the Bulwark. 8. D H, C G, The face of the Bulwark. 9 B F, M F, The gorge or neck of the Bulwark. 10. F H, E G, The Capital lines. 11. A B, The Courtine. 12. If the flanque of the Bulwark be divided in the point 2, and on the inside you take 5, 3, equal to 2, B, and join the points 2, 3, the part 3 D, or that curved Line within it is called Orillon, or ear of the Bulwark; and the rest of it 3, 5, is called the Flancque Couvert; but the use of these orillon's are almost out of date. 13. C Q. The flanque prolonged. 14. Q G, The front or surface. 15. B G, The fichant line of defence, 16. R G, The flanquing line of defence. 17. K B, The flanque of the Courtine, called by the French, the second Flanque; it is that part of the Courtine which lies betwixt the flanque of the Bastion D B, and the flanquing line of defence KG. 18. E F, the side of the inward Polygon or Figure. 19 G H, The side of the outward Polygon, or the distance of the Bastions. 20. P E, P F, The Radius of the inward Polygon, or Figure. 21. P G, P H, The Radius of the outward Polygon. 22. E P F, The Angle of the Centre. Vide def. 4. 23. A E O, The Angle of the Figure. Vide def. 4. 24. N G C, The Angle of the Bulwark, called in French Angle Flancque. 25. K C A, I D B, The Angle of the flanque, and flanquing line of defence, called in French, Angle de laflancquant & du flancque 26, C K A, D I B, The Angle of the flanquing Line of Defence and Courtine, called in French, Angle flancquant interieur. 27. A C G, The Angle of the flanque and face. 28. G T H, The Angle of defence, in French, angle flancquant exterieur; Angle de tenailles. 29. D S H, The Angle determining the flanque. Angle form flanque There are several sorts of Fortifications, as to their Magnitude. 30. A Fort Royal, Is that whose fichant line does not exceed a Musquet-shot, and is used most in fortifying Cities and great places. 31. The middle sort of Fort Royal, Is that whose fichant line is less than Musquet-shot, but the distance of the Bulworks more. 32. The lesser sort of Fort Royal, Is that whose Bulworks are distant just Musquet-shot. Those that are less, are called Castles, Forts, etc. We shall expound the Orthographical terms, or the Profile, commonly called the uprights, in the 7th Chapter following. CHAP. III. The Canons or principal Rules of Fortification. 1. THe end of Fortification, is that few may resist many. 2. The form of the Fort must be such, that all its parts may receive an obliqne flanquing-side defence, beside the foreright defence they afford themselves. 3. Therefore each part of the Fortification, must flanque and be flanqued. The manner of flanquing is this: The face, which is the weakest part of the Fortification, is defended by the flanques of the Bulwark and Courtine, as also by the opposite Fig. 5 face: The flanque of the Bulwark are defended by the Courtine, and the Courtine by the Flanques. Vid. fig. 5. Fig. 6 4. The shorter and obliquer the defence lines are, so much the stronger and surer. Now the Lines of defence will be so much the obliquer, as the Angle of defence G T H, shall be acuter. Fig. 5 5. The Fichant line B G, A G must not exceed a Musquet-shot, that is 750 or 720 feet. The Bullet may be carried farther, but not to do execution at a mark. The Fichant line among all the Lines of the Fort is the chief, and doth itself determinate the bigness of all the rest. Note. When we shall make mention of feet, you must understand them to be Rhyneland feet. 6. Above all, care must be taken to make the flanquing parts of the Fortification as large as you can. 7. Therefore let the flanque of the Bulwark be of a just bigness, and make the second flanque as large as you can: For that Fort is far the strongest, which keeping the Rest of the Maxims, hath also flanques in the Courtine. 8. Let the Courtine be of a just length, let it be more than the face, and the flanques of the Bulwark joined, because it is the strongest part of the Fort. Fig. 6 9 Let the Angle of the Bulwark N G C, be able to resist the force of Canon, and consequently not less than 60 degrees; for experience hath taught us that such a one will suffice. 10. A Right Angle for the Bulwark is the best, but to gain it you must not omit or cut away too much of the second flanque. 11. The Angle of the Flanque and Courtine C A K, Fig. 6 must always be a right Angle: For so, as well the Courtine as the Face will be more largely flanqued and defended, and consequently more sure and commodious, and the Angle of the Face and Flanque will be bigger, and therefore stronger. 12. Let the Gorge or neck-line A C, F H, be large, Fig. 6 lest the Bulwark be straitened. 13. Let the quantity of the Bulwark be such as may receive a sufficient number of armed Men, and yield room enough for the traversing Guns, and performing other Military duties. The Bulwark is chief straitened for these reasons; if you lessen the Face, and keep the same Angle for the Bulwark, and consequently increase the Flanques: Or if you retain the same Flanques, and increase the Angle of the Bulwark. 14. At length, that I may contract the Rules , and many others into one, that form of a Fortification will be the best, that hath the largest Flanques in the Bulwark and Courtine, the Gorge Lines very spacious, the Angle of the Bulwark a Right Angle, or near a right Angle; and the Fichant Line, at most, not to exceed a Musquet-shot. That this form may be had in Regular Figures, the proportion of the Courtine, Face, Flanque and Neck, will be as follows. 15. Let not the Face be less than half the Courtine, nor bigger than the whole. 16. The Flancque must not be less than a fourth part of the Face, nor bigger than half the Face. 17. The Gorge Line must not be less than the Flanque. In these three Dogen and Goldman agree: The reason of them you may see in the Account of the Fifth Chapter. CHAP. IU. Being an Explanation of the foregoing Maxims. ALL the reason and proportion of our Fortification will rely on the Rules delivered in the last Chapter. Therefore 'twill be here necessary more fully to declare them; especially those which sometimes all Ingineers did not approve of. The first, second, and third want no exposition. About the 4th and 5th, although now no body disagree, yet there was a time when men did doubt them. Some Military Architects, those chief that flourished in the former Age, did order such a distance for the Bastions, that the Fichant Line, or the longest Line of defence, should not a little exceed a Musket shot. The Reason they brought was, that the place might better be defended with great Guns than with Muskets: And therefore, because great Guns cannot be so well levelled against an Enemy that's near, they required a greater distance for their Bulworks, and so the charge would be the less, the Town being defended with fewer Bulworks. But this way, by all modern Ingineers, is neglected, who with one consent remove the Bulworks to such a distance, that the Fichant Line might be measured with a Musquet-shot. What reason our former Architects brought for their opinion, is plainly none at all. For both by Reason and Experience 'tis evident, Towns may be better defended with Muskets than with Cannons; for the use of great Guns is very costly, slow, difficult; the execution they do, very rare and uncertain, so that 'tis become a Proverb, He is cursed in his Mother's belly, that's killed with a Cannon bullet. And if a great Gun should be made useless, by being dismounted, or by the death of the Gunner, or some other mischance, all the Flanquing defence is lost, to the great encouragement of the Besiegers. On the contrary, the use of Muskets is not costly, but easy, ready, quick, and sure. For who will deny, that an Enemy may not better be beat off with a thousand small Shot than one great Gun? A thing so clear needs no more arguments. Therefore let stand what we have appointed, the Fichant line to be measured by a Musquet-shot. Nor do we exclude the use of great Guns from our defence; for in this modern way of Fortification, they may and aught to be admitted usefully: We only persuade, that the chief of the defence may rather be committed to Muskets than to Cannons. What we ordered in the 6th. and 7th. Rules, is the chiefest concern in the whole business of Fortification. The Faces of the Bulworks, because they lie farther out than any of the other parts, are the weakest parts of the Fortification: The Flanque and Courtine are the strongest, for they lie farther from the Enemy, and being near to one another, stoutly defend themselves. Since then the Face is a place weaker than the rest, and which the Enemy most usually attaques, we ought with our chiefest care to help it. Fig. 7 There are two sorts of Bulworks. In the first, the Face G V C, produced, falls upon the end of the Courtine F; for which reason the Face G C can only be defended from the Flanque of the Bulwark. Fig. 5 In the second form of Bulwark, the Face G F produced, does not fall upon the end of the Courtine, but in another point of it X, so that it leaves out a part of the Courtine X B, which is called the Flanque of the Courtine, from which the Face may be as well defended and scoured as from the Flanque of the Bulwark B C. The first they follow, that would have the Angle of the Bulwark a right Angle, in all Figures above a Pentagon. The latter the first received, and made use of; who judged it best for their advantage to add to their defence second Flanques in the Courtine, though with the loss of a right Angle even in a Duodekagon. Neither is there any doubt, but this method is far better than the former, since it doth not only sufficiently provide for the Angle of the Bulwark, which it never makes less than 60 degrees, but also increases the defence of the Faces often to twice as much as the former. The Reason of the 8th Rule, which bids the Courtine be of a just length, is, that among all the parts of the Fortification the Courtine is the strongest: For it lies distant from the Enemy farther than any other of the parts, and placed betwixt two Bulworks, is very strongly defended. Now 'tis very agreeable to reason, that the strongest parts of the Fortification should be longer than the weaker: Yet do not extend the Courtine so far as to make the Fichant line above Musquet-shot, for that is against the 5th Rule. The fittest proportion will be, if with Dogen or Fritach, you give it 432 feet, or with Goldman 480 feet. The 9th and 10th Cannon treats of the Angle of the Bulwark; where a right Angle is preferred before any other, provided it do not too much obstruct the rest of the Rules. For the better understanding the Reason of this Rule, you must note, that right and obtuse Angles do resist the Cannon shot with their whole bodies, but an Acute one doth not with all his body. Fig. 7 Fig. 6 Fig. 7 Let there be a right angled Bulwark F O B Q P; and another Acute angled M L H D B. Now suppose the Bullets to fall in B O, the Face of the right angled Bulwark F O B Q P, from the Guns planted in R, by perpendicular strait-lines R B, R S. Therefore because the two straight Lines R B, B Q. are both perpendicular to B O, by supposition, in the same point B they will make one straight Line R B Q. by the 14. l. 1. Euclid. From whence it is manifest, that the side of a right angled Bulwark B Q, objects its whole self against the perpendicular shot R B: and so consequently a rightangled Bulwork doth with his whole bulk oppose and resist all the perpendicular shots R S. The same thing may be demonstrated by stronger reason in an obtuse Angle: Fig. 6 But in an Acute Angle M L H DB, the perpendicular shots S H, S Q, being continued on, or protracted, in a little space falls within the Bulwark, and so it appears the Bulwark doth not object its whole body against the shot. From whence you may gather, that an Acute Angle is weaker than either a Right or obtuse Angle. These things being known, 'tis plainly manifest why a right Angle should be preferred before an acute Angle; that is, if it can be had without prejudice to the rest of the Maxims: And why it should rather be chosen than an obtuse one. These are the Reasons. The first is, that keeping the same Hancques Q P, O F, Fig. 7 and the same Gorge Lines P E, F E, the Bulwark will be very much straitened, which is against the 13th Rule; and the Angle of the shoulders P Q B made so much the less. The other and chiefest reason is, that the obtuser the Angle is, the lesser will be the Flanque of the Courtine, or else all lost. Therefore a Right Angle, or one near a Right Angle, must be given to the Bulwark as oft as may be, but so that one clause in the Rule be not neglected, which forbids you to spoil the second Flanque for the desire of a right Angle: And because in a Hexagon, and the figures following to a Duodekagon, a Right Angle in the Bulwark will cut off the second Flanque in the Courtine, we judge it better, with most of the famous Engineers of this Age, to detract something from the Angle of the Bulwark, keeping notwithstanding a due strength for him, than to want the Flanque in the Courtine to the prejudice of our defence, which will be so much lessened. Barleduc and others followed the contrary; but most people now a days being taught by Experience, the School-mistriss of all things, have forsaken them. The reason and sense of the rest of the Rules is so plain, that they need no farther Explanation. CHAP. V The constitution of Regular Fortifications. THe Definitions and Principles of the Science being now expounded, we will come to the thing itself. That the Constitution of a Fortification may be found, Fig. 6 some things ought to be given. Those things here are said to be given, which we take at our discretion, so that none depend on, or prejudice one another. Now from these Data once ordered, the proportion of the rest of the parts follows sure and determined according to the Reason of the things given. Therefore 'twill be the part of a skilful Engineer to choose those Data which may best agree with the Rules established in the third and fourth Chapters, and make the parts agree which depend on them. Furthermore, because these Data may be varied without any prejudice to our Maxims of Fortification, the Constitution also of Fortification will be various. I shall choose and propose six of the best and most approved. The proportion of the Lines will serve for any form, the quantity for the Royal only. The First Manner Is Goldmans. Let the Face be half the Courtine in what Figure soever. Feet The Courtine 480. The Face 240. The Flancque in A4 Ang. in A5 Ang. 60. That is ¼ of the Face. 80. That is ⅓ of the Face. In the rest of the Figures up to a nine-angled Polygon 10 feet are always added to the flanque, till in a Nonangle the Flanque becomes 120 feet, that is 1/● the face, which quantity is retained for the flanque in all the following figures. The Angle of the Bulwark is made of half the Angle of the Figure, increased with 15 degrees. Therefore it will be Degr. 4 60. 5 69. 6 75. 7 79. 17′9″. or in decimals 79, 286 In a 8 angled figure 82. 30. or 82.5. in decimals. 9 85. 10 87. 11 88 38′. 11″. or 88 63.64. in decimals 12 90. or a right Angle, which is retained in all figures following. From these Data, or things given, the proportion of the rest of the lines will arise, which the following Table shows you. Radius. Capital. Gorge. Flanque 2. Fichant. IV 494.5.5.8. 172.6.9.9. 109.7.0.6. 256.0.7, 7 722.2.2.2. V 595.2.9.3. 197.9.1.1. 109.9.0.2. 254.0.8.7 724.1.5.7. VI 713.4.8.6. 209.9.7.6. 116.7.5.3. 262.7.2.1 724.9.0.9. VII 833.8.5.8. 222.0.5.6. 121.7.9.3. 262.0.1.1. 726.2.5.4. VIII 955.6.6.1. 233.9.6.4. 125.7.1.3. 256.9.4.2. 728.0.7.4. IX 1078.5.0.8. 245.6.2.8. 128.8.7.0. 249.4.8.2. 730.3.1.7. X 1212.6.0.7. 246.5.9.2. 134.7.1.7. 258.9.8.8. 729.6.3.3. XI 1347.0.8.3. 247.5.4.3. 139.5.2.1. 266.3.2.1. 729.0.3.5. XII 1481.8.8.6. 248.4.6.0. 143.5.4.0. 272.1.5.4. 728.5.1.5. In this Table the figures before the separating line are Rhynland feet; the rest are 10ths, 100ths, 1000ths, parts of a foot, etc. In this first manner of Fortification there are four things given besides the species of the Figure. Viz. The Courtine, the Face, Flanque, and Angle of the Bulwark, who themselves agree with our Rules, and also the rest of the Lines which follow from them; as the Gorge, second Flanque, and the flanquing and fichant lines of defence, which you will find to be true, if by the help of the trigonometry you calculate the quantities of each of the parts out of the Data, or things given; of which we shall speak in the following Chapter. I shall here only mention two things: That is, the second Flanque in this way will be larger than in any other, so as to exceed half the Courtine. And the Gorge line be always above a 100 feet. The Second Manner Is Dogens. The face is 24 perches, or 288 Rhynland feet. The Courtine 36 perches. Therefore the proportion of the Courtine to the face is sesquialter or as 3 to 2. which is observed in all the following methods. The Angle forming the flanque is 40 degrees always. The Angle of the Bulwark is ½ the Angle of the figure increased with 15 degr. as in the first manner. Goldman, Marolois and Fritach, agree in the Angle of the Bulwark. Note, that the Perch we speak of contains 12 Rhynland feet. The Third Manner Is Dogens second. It differs from the second in the last datum only, for it makes the Angle of the Bulwark equal to two thirds of the Angle of the figure, therefore 'twill be degr. 4 60 5 72 In a 6 Angle 80 7 85. 42′. 51″. or 85.71428 in Decimals. which will serve in all that follow. 8 90. Rad. Capital. Gorge. Flanque 1. Flanque 2. Fichant. iv 38. 50 19 73 9 23 7. 74 7. 10 60. 80 V 49. 05 20. 40 10. 83 9 09 8. 03 61. 10 VI 60. 00 21. 10 12. 00 10. 07 8. 33 61. 34 VII. 70. 80 21. 75 12. 9 10. 83 8. 41 61. 54 VIII 82. 66 22. 32 13. 63 11. 44 8. 39 61. 72 IX. 93. 08 23. 15 13. 83 11. 61 11. 10 61. 74 X. 103. 62 23. 83. 14. 62 11. 76 12. 91 61. 70 XI. 114. 26 24. 40 14. 19 11. 91 14. 19 61. 68 XII. 124. 97 24. 88 14. 34 12. 04 15. 15 61. 66 The numbers in this Table before the points are perches of Rhynland that contain 12 feet, the rest are 10ths. 100ths. of a perch, The Fourth Manner. Is Dogens third, Fritachs' first. Let the Courtine be 36 perches. The face 24 perches. The Angle of the Bulwark 1/● the Angle of the Figure increased with 20 degr. Perches 4 6.72 5 7.84 6 8.96 The Flanque in a 7 Angle is 9.108 8 10.12 9 11.132 10 12. 144 which is kept in all the following Fig. The Fifth Manner Is Fritach's second. Let the Courtine be 36 perches. The Face 24. The Angle of the Bulwark half the Angle of the Figure increased with 15 degr. as in the first manner and the second. Perches 4 8.96 5 9.108 The Flanque in a 6 Angle is 10.12 7 11.132 8 12.144 the same always in the following Fig. Out of these Data, the proportion of the rest of the parts that follows, which the Table underneath will show you. Rad. Capital. Gorge. Flanque 2. Fichant. iv 38.14 20.01 8.97 6.14 little exceeding 60 Rods or Perches. V 48.08 21.03 10.26 10.51 VI 58.19 22.15 11.08 11.86 VII. 68.47 23.31 11.71 12.03 VIII. 78.60 24.48 12.16 11.67 IX. 90.31 24.64 12.89 12.95 X. 101.84 24.66 13.47 13.90 XI. 113.38 24.76 13.95 14.63 XII. 124.77 24.85 14.29 15.22 The numbers before the points are perches, the rest are 10ths. 100ths. of a perch. The Sixth Manner Is Dogen's Fourth. Let the Courtine be 36 perches. The face 24. The Angle forming the Flanque always 40 degr. The Angle of the Bulwark as in the fourth manner. Therefore it will be degr. 4 65. 5 75. 6 80. In a 7 Angle 84. 17.9 8 87. 30 9 90. And so always after. All these several ways of Fortification agree with the Canons delivered in the 3d. and 4th. Chapters. The Fourth seems least in use (so I gather out of Fritach pag. 15.) The Fifth is more used. The Second and Third are much alike. Betwixt these (viz. the second and third) and the fourth, the Sixth is a mean, which according to Dogen is to be preferred before them. The First goes beyond all the rest for the largeness of the second Flanque, and comes short of all the rest in the first Flanque, the neck, the faces, and in the Angle of the Bulwark. Whence it is consequent, he should have his Bulworks less than any of the rest. His Courtine is larger than the others by 48 feet. This seems to be less in use than any of the other. The Data, or things given in the second and fifth, differ about the, Flanque, which in the fifth is bigger: For which reason it hath its Gorge line and second Flanque lesser. The third and fourth in their Datas differ about the Angle of the Bulwark and the Flanque. The Flanque in the fourth is lesser: the Angle of the Bulwark is bigger, except in a Hexagon. Where, etc. But all these ways are approved; let every one take that which pleases him best. And so have we ordered the constitution of each way in Fortification: But by what Art the quantities of the rest of the Angles, and Lines depending on the things given, are found out of each of the things given; that is, by what method the Tables above were made, we must seek for in the following Rules. How to find the Angles. 1. The Angle of the Centre of any Regular Figure is had, Fig. 6. if you divide 360 degr. by the number of its Angles. See the Scholium of the 16 Propos. of the fourth of Euclid. set out by me. The Angle of the IV V VI VII VIII IX X XI XII Centre. 90. 72. 60. 51, 43′, 38″. 45. 40. 36. 32, 43′, 38″. 30. Figure. 90. 108. 120. 128. 34′, 17″. 135. 140. 144. 147, 16′, 22″, 150. 2. The Angle of the Figure, or of the Circumference is found, if you subtract the Angle of the Centre from the right Angles, that is 180 degrees. For the Angle of the Centre P, together with the Angle's P E F, P F E, makes two right ones. 32. 1. but these are half the Angle of the Figure, and so joined together make up the whole Angle of the Figure. Therefore the Angle of the Centre, with the Angle of the Figure, makes two right ones. Therefore, etc. 3. The Angle of the Bulwark is found after this manner: By the foregoing Rule find the Angle of the Figure, and add to its half 15 degr. 4. The Angle G K A or C K A, will be discovered, if you deduct half the Angle of the Bulwark from half the Angle of the Figure. For because G H, E F are parallel, the Angle E G Q is equal to P E F; and G K A equal to C G Q. Therefore, etc. 5. The Angle A C K is had by substracting the Angle last found C K A, from 90 degr. For since C A K is a right Angle; A C K, C K A, must make another right Angle. 6. The Angle G T H will be found after this manner. Double the Angle C K A, which subtract from 180 degr. the remainder is the Angle I T K, or G T H. For the Angles C K A, D I B, are equal by construction; therefore C K A doubled, is equal to them both. Now these two Angles being known in the Triangle I T K, the third also will be known, Euclid. 32. 1. and the Angle I T K is proved equal to G T H, by the 15. 1. 7. The Angle A C G is discovered, if you subtract A C K from 180 degr. for A C K, and A C G, make two right Angles. Eucl. 13. 1. 8. To find the Angle G E A, subtract P E F, half the Angle of the Figure found in the second Rule, from 180 degrees: For P E F, G E A, are equal to two Right Angles. 13. 1. How to find the Lines. 1. The Lines AK, C K. Fig 6. In the Right angled Triangle A C K the Flanque A C is given, and the Angles C & K are found by the fifth and fourth Rules. Therefore the Sides AK, C K, will be found by trigonometry. 2. The Flanque in the Courtine, and the flanquing Line of defence. The Face which is given being added to C K found out last, gives the flanquing Line of defence G K; and A K one of the Lines last found, being deducted from the Courtine that is given, leaves the Flanque in the Courtine B K. 3. The Lines G Q, Q C. In the right angled Triangle G Q C, the Face G C is given; and the Angles are already found in the fourth Rule. For Q G C is equal to G K A; therefore G Q, Q C will be found. 4. The outward side of the Polygon G H. To G Q doubled, add the Courtine which is given. 5. The Line A Q. To the Flanque which is given, add the Line Q C, found out in the third Rule. 6. The Capitals G E, G Z. In the right angled Triangle G Z E, the Angle E G Z is found; for it is equal to P E F, half the angle of the Figure; and the side Z E, or Q A, is found by the fifth Rule; therefore G E, G Z, are found. 7. The Gorge Line A E. Subtract G Z, found in the sixth Rule, from G Q, found in the third Rule, and there remains Z Q, or E A. 8. The side of the inward Polygon E F. Add the Courtine which is given to the Gorge line doubled, found out in the foregoing Rule. 9 The Radius P E, Y P. In the right angled Triangle E Y P, the side E Y is found (for 'tis half the side of the Figure found out in the last Rule) and the Angle P E Y found in the second Rule of Angles, therefore the sides E P, Y P, will be found. 10. The bigger Radius G P. Add the Capital to the lesser Radius. 11. The Fichant line of defence B G. Out of the sum of the Squares of G R, B R, extract the Root, and that shall give G B. The demonstration is from the 47. 1. of Euclid. R B is found out in the fifth Rule. G R is had, if to Z R, or E B, the sum of the Courtine and Gorge line you add G Z, found in the sixth Rule. And so you have the complete constitution of Fortification. Nor will it now be difficult for one that is not altogether unskilful in trigonometry, which I have have taught in the third Chapter of my first Book of Practical Geometry, to find all the Lines and Angles by the like method out of what Data soever. CHAP. VI The delineation of Regular Fortifications, either on Paper, or in the Field. SInce that in the foregoing Chapter the quantities of the Lines and Angles of Fortifications are determined; to delineate the same either on Paper or in the Field, there is nothing more required than what I have taught in my Practical Geometry. Therefore in the tenth Chapter of my Practical Geometry you'll find what you desire digested into ten Problems. CHAP. VII. An Explanation of the Orthographical Terms. HItherto I have delivered the delineation of Regular Fortification: That is, I have described the out-circuit of the Rampar only: But now I pass to the Orthography, in which all the parts of the Fortification, as to their height and thickness, are contained. The beginning, as it uses to be, is drawn from the Explication of Terms. The Horizontal Line is A E S V Z. The Orthography of a Fortification, Fig. 8. is a Section of a Fortification made by a place per pendicular to the Horizon, showing the height, thickness and position of each part in the Fortification: It is shown in the eighth Figure. The Rampar A L I K E is a body of Earth surrounding the whole Fortification, it includes also the Bulworks. The breadth or thickness of the base of the Rampar A E. The thickness of the top of the Rampar L 3. The outward sloping, or rectination of the Rampar 3 E, called in French penchant du Rempar Exterieur. The outward Talu, or Line forming the sloap of the Rampar E F, called in French le Talu Exterieur du Rempar. The inward sloping or rectination of the Rampar A L, Penchant du Rempar Interieur. The height of the Rampar B L, Haulteur du Rempar. The brestwork of the Rampar, in French called Parapett, 4 G I K 3. It is a bulk of earth surrounding the whole Fortification raised upon the Rampar to a man's height. The thickness of the base of the Brestwork D 3. The thickness of the top of the Brestwork O K: You must take no notice of the little line intercepted betwixt I T, I D. The sloap or inclination of the top of the Brestwork I K. The outward sloping or rectination of the Brestwork K 3; 'tis in a direct or straight line with the outward sloap of the Rampar E 3. The outward Talu, or Line forming the slope of the Brestwork 32; Talu Exterieur du Parapett. The inward Sloap or rectination of the Brestwork T D, penchant interieur du parapett. The inward Talu or Line forming the inward Sloap of the Brestwork D T, Talu Interieur du parapett. The Step of the Brestwork D G, called in French Banquet. The plain or Walk upon the Rampar L 4, in french Terreplein. The Fauss Bray, or Parapett des Rondes, 5 N P Q R, it is a Brestwork raised round the Fort at the foot of the Rampar, principally used for the defence of Moats or wet Ditches, and in all things like to the upper Brestwork. The plain or walk of the Fauss Bray E. 5. or Chemin des Rondes. The Bankside of the Ditch R S, Lisier. The Ditch S 87 V, Le Fosse. The inward sloaping descent of the Ditch S 8, Escarpe. The inward Talu or Line forming the inward sloap of the Ditch, S H, Talu interieur du Fosse. The outward sloaping descent of the Ditch V 7, Contrescarpe. The outward Talu, of Line forming the outward Sloap of the Ditch, V 5, Talu exterieur du Fosse. The lower width of the Ditch, 87. The upper width of the Ditch, S V. The depth of the Ditch 8 H, 75. profundeur du Fosse. The Couvertway, N 6, Chemin Couvert Corridor. The Brestwork of the Couvert way 6 X, Y Z, parapett du chemin Couvert. It's Base O Z, peid ou base du parapett de chemin couvert. It's outward sloping, Y Z. Note, that this Orthographical Section is not drawn by the Courtine, but by the Face of the Bulwark; and so the Lines 87, S V, do represent the width of the Ditch or Moat that washes the Bulwark, which you must always understand, when there shall any mention be made of the width of the Ditch. CHAP. VIII. Wherein are determined the Orthographical dimensions or the Profiles of Fortifications, and first, those of the Rampar, and Brestwork raised upon the Rampar. THe sole and main business of the delineation hitherto expounded, was truly to constitute or form the Ramparts circumference, completed with Faces, Flanque and Courtine, which indeed is the fundamental & principal work of all Martial Structures. But now to prescribe the dimensions of the Rampar itself, and the rest of its parts, as to their height and thickness, is the business of Orthography. Every Fortification consists almost of these parts, (viz.) Rampar, Brestwork, Fauss bray, Ditch or Moat, the Couvert way, and an out-Brestwork. Yet if the Ditch be dry, the Fauss-bray both may, and is wont to be omitted. In this Chapter we shall speak of the dimensions of the Rampar and Brestwork. The Spartans' in former times would not defend their City with Walls and Ditches: and King Agesilaus showing his armed citizens to one that asked why Sparta wanted Walls, said, that those were the Walls of Sparta. This was plainly a foolish and empty ostentation of strength, relying on no sound council, but only rashness; which the experience of all nations hath condemned, and which the Spartans' had almost found fatal to themselves in the Theban War. But leaving this we'll come to the purpose. I. For the Stuff or matter to make the Rampar. The Rampar must not be made of wood nor stone, but Earth; this is every where at hand, and ready to come by, and is easily heaped up to such a thickness that the Rampar may be Cannon Proof, besides, Earth by its yielding and giving way does sooner master and break the force of the Shot. Yet I do not prefer a bare Earthen Rampar before one cased with stone, of which I shall speak hereafter. II. The Height of the Rampar. There is hardly any thing so destructive to a Fortification as a high Rampar. This error hath been committed in most of the ancient Fortifications, especially those of the most famous cities in Europe; for these high Ramparts flatter the sight, and make a show of Strength where there is none, when indeed they spoil the whole defence, and betray the Town to the Enemy; and lest so great mischief might be had gratis, the Treasury must be also drained to obtain it. The fault of high Ramparts consists chief in this, that they shelter the enemy when he draws near them from the Shot of the Townsmen. This to its own great loss, Breda hath taught us, when it was last besieged by the Hollanders. Prince Maurice had fortified this Town with great care and expense, so that it might seem to be reckoned one of the compleatest Fortifications of Europe; but the height of the Rampar flattering his sight, as I said, deceived him. The Inhabitants of Breda being afterwards besieged by Frederick, Mauritius his Brother, were not able from their high Rampar with all their Cannon to remove the enemy approaching nearer unto them; nor his Blinds stealing by degrees upon them; whence they were forced to cut holes in several places of their high Rampar that was raised at such great charges, and pull it down, and levelly it, to make a place for lower Batteries, from whence they might surer hit and break the fatal Blinds of the Enemy. But these high Ramparts cannot be so mended, but they'll be marred worse in another point; for while they are cut in many places, the binding together and jointing of the work is loosened, so that 'twill easily fall if battered with the Enemy's Cannon. But a Rampar that rises to an indifferent height hath not this deadly inconvenience, Fig. 9 as is manifest in itself; nay and Musket Shot doth more Execution from a low Station than from a high one; For let there be two heights, A B the bigger, A C the lesser, and let the Line D E at the height of a man stand perpendicular upon the Horizon: Now it is clear the line or Shot which is directed from C to E, shall fall beyond that line or Shot which shall be directed from B to E, and intercepts a larger space on the Earth D F; whereas the other from B passing through E, intercepts only the space D G: Therefore more ground may be scoured from a low place than from a higher. But perhaps those that are the Patrons of high Ramparts will say they cannot be so easily climbed, and that the Enemy's approaches may better be discovered from them. I answer the inconvenience now alleged must prevail, for an ordinary height will sufficiently hinder the ascent of the Enemy; and for discovering his approaches you may raise Cavaliers in the Bulworks. III. The Height is determined. Therefore let not the height of the Rampar exceed 18 Rhynland feet, nor be less than 10 feet, for this would expose the City to the Enemy's Shot; the other suffices, more would make you fall into the error spoken of before in the second number. Engineers by reason of the several magnitudes of Fortifications, prescribe several heights, but merely by guess. In IU. V VI VII. VIII. etc. The height of the Rampar. feet 12. 14. 15. 16. 18 If Hills should hangover the Town, you must not for that reason raise your Rampar above 18 feet, but raise Cavaliers in your Bulworks, or praeoccupate those higher places with Outworks. iv The Talu of the Rampar or Line forming the Slope. The Rampar must be so built that both without and within it may be sloping, for a body of Earth cannot like a Wall rise to a perpendicle. Fig. 8. The inward Talu A B, must be always equal to the height B L, that upon any sudden occasion the Soldiers might easily run up to their Rampar. The outward Talu E F, is most commonly half the height, and it would be requisite to make it less if the Earth be firm: If the ground be very lose, it may be made equal to two thirds of the height; but if the outward Talu be too big, it gives the Enemy an easy ascent, as appeared in the memorable taking of the Fort of Schenkin. V The upper thickness of the Rampar. Fig. 8. The upper thickness of the Rampar L 3, must not be only such is may bear the force of Cannon, but aught to be so big, that after its Brestwork is set on, whose lower thickness must be 24 feet, (else not Cannon Proof,) together with the step or Banquet D 4 three feet broad, yet it may also have remaining a plain or walk called in French Terreplein 4 L, large enough for the traversing great Guns. Therefore 'twill be most an end 51 or 57 Rhynland feet; a thickness much exceeding this will be superfluous, and for no other use than draining the Exchequer. And here also your Engineers for the diversity of the figures prescribe several thicknesses, and merely again by guess. In IU. V VI VII. VIII. IX. The upper thickness of the Rampar. feet 36. 39 44. 48. 51. 57 And because Ramparts and their Brestworks ought to be Cannon proof, I will briefly add, how much ground a Shot can penetrate. A whole Cannon at 400 feet distance, with a Ball of 48 pound, shall strike 20 feet deep into firm Earth. A Demi-canon at the distance of 300 feet with a Ball of 24 l. shall enter 12 feet of firm ground. A Field piece at the distance of 200 feet, with a Ball of 12. l. shall pass through about 7 feet of firm ground. This Goldman reports. But if the ground be lose, it will penetrate far deeper. Dogen denies that 20 feet of any ordinary Earth can be pierced with whole Cannon Shot. VI The lower thickness of the Rampar. Fig. 8. The lower thickness of the Rampar is found, if to the upper thickness L 3 or B F, you add the outward and inward Talu's A B and F E: 'Tis therefore for the most part six or seven perches, that is 72 feet, or 84 feet; but then the outward Talu E F, will be somewhat less than half the height. For the Quality of the Figure Author's order again by guess In IV. V VI VII. VIII. IX. The lower thickness of the Rampar. feet 54. 60. 66. 72. 78. 84. VII. Of a Rampar Cased with Stone. A Rampar cased with Stone is to be preferred before a bare one, 1. because it chief hinders nocturnal invasions, and sudden attempts, since the enemy cannot mount it without Ladders, the providing of which will be very troublesome, and the use as uncertain. 2. Because it hinders an open assault, since it cannot be attempted but by Ladders, which will be to no purpose, or by the ruins of the wall thrown down with Mines. 3. Because it is a stable and everlasting work; whereas a bare Rampar, unless it be continually repaired, falls to the ground. They that disagree, reason after this manner. 1. That Walls battered with Cannon sooner fall than the bare Earth. 2. Their Stones beaten down fill up the Ditch. 3. That the pieces or Splinters of the stones flying about will hurt the defendants. The first I deny, if the Walls be very thick, or if (as I ordered) propped with an earthen Rampar. As to the second, 'twill be the same thing, or rather worse in a bare Rampar. The third is avoided, if you do not raise the wall to the top of the Rampar, which is observed in the Wall of Antwerp. This inconvenience will be much less if you make the walls of Brick. VIII. The Brestwork of the Rampar. Upon the Rampar there is always a Brestwork built 4 G, I K 3, Fig. 8. whose dimensions are these following. 1. The inward height T 4 must be always 6 feet, that it may conveniently shelter the Soldiers, who seldom exceed this measure. 2. The outward height 2 K must be feet, for so not only the field and the out-Brestwork, but also a great part of the Ditch will be defended by the Rampar; and you may know how much, if you can come to the knowledge of C φ, which will be found after this manner; as I O is to O K, so is I C to C φ. The three first terms are known, therefore the fourth C φ must be known. Now from C V known, take C φ known, there will remain φ V also known. 3. The inward Talu D I must be always 1 foot; there is no need of a greater, since it lies from the Enemy, and is propped up sufficiently by the Step or Banquet G 4 D, neither is it exposed to the feet of men always running up it, as the inward side of the Rampar. 4. The outward Talu 2 3. must be always 2 feet; for since the outward side of the Brestwork K 3 lies in a straight Line, with the outward side of the Rampar 3 E, and K 2, 3 F, are parallel. 'Tis evident that the Triangles 2 K 3, F 3 E, are like Triangles. Therefore since in the fourth number we ordered the outward Talu of the Rampar E F, to be half the height of the Rampar F 3, 32 will also be half the height 2 K: But 2 K was appointed to be always 4 feet, therefore 32 will be always 2 feet. 5. The upper thickness O K, must be Cannon proof, therefore since a whole Cannon will scarce strike through 20 feet of Earth, 21 feet may suffice. 6. The lower thickness D 3 is composed of the two Talues D T 32, and the upper thickness O K; the two Talues taken together, make 3 feet, and the upper thickness 21 feet, so that the lower thickness will be 24 feet. And here again our Engineers sport it, and for the variety of the Figures alter the thicknesses after this manner. In IU. V VI VII. VIII. IX. etc. Lat. sup. 9 11. 12. 15. 17 21 feet. Lat. inf. 12 14 15 18 20 24 feet. The Step or Banquet is built at the foot of all Brestworks on the inside, and is 3 feet thick or broad, and 1 ½ feet high. IX. The Terreplein or Walk upon the Rampar. The Walk on the Rampar L 4 is found, if from the upper thickness of the Rampar L 3 you subtract the lower thickness of the Brestwork D 3, and the thickness or breadth of the step D 4; wherefore since D 3 in number 8. was ordered to be 24 feet, and D 4 to be 3 feet, and in the 6 number L 3 was ordered to be 51 feet, or 57 feet, there remains for the Walk 24 feet or 30 feet. But if you have a mind to sport with the Engineers above, it will be In IV. V VI VII. VIII. IX etc. The breadth of the Terreplein. 21. 22. 25 ½. 27. 28. 30. feet X. The Bank of the Ditch. If the Rampar want a Fauss-bray, there will be left a Bankside, or a space of Earth 6 feet broad from the feet of the Rampar to the Brink of the Ditch R S. CHAP. IX. The Orthography of the Fauss-bray. I. The End and necessity of a Fauss-bray. EXperience hath taught us in the taking of many Towns in Holland, that so soon as the Outworks are taken in, the Moat without any great difficulty will be covered with Galleries, and so conquered; for the water in the Moat hindering the sallies of the besieged, the Builders of the Galleries can only be called from the opposite flanques, being safe before by reason of the necessary height of the Rampar which protects the Enemy lying so near under it from the Shot and sight of the besieged. Against so deadly an inconvenience the Brestwork 5 N P Q R is built, at the foot of the Rampar, which is called commonly Fauss-bray, or parapet des Rondes: And in this alone consists the safety of a Moat or wet Ditch. For from this the besiegers are beat off on all sides, with Shot almost quite level or Horizontal; And therefore surer to do Execution, as I shown in the eighth chapter, number the second. Therefore the only End of a Fauss-bray, is the defence of a Moat, which help, a dry ditch doth not stand in need of, as shall be taught hereafter. II. Its height and Structure. Some Architects sharply contend, that such a height ought to be given to the Fauss-bray, as might make it able to command the Outworks. But the defence of the Outworks will better be performed by the Rampar itself; and as much as you shall add to the height of the Fauss-bray, so much will you diminish from the defence of the graft: Therefore let it not exceed humane stature. The rest of its Structure is the same in all things, as that of the Brestwork of the Rampar, delivered in the eighth Chapter, numb. 8. III. The Walk of the Fauss-bray. Chemin des Rondes. Betwixt the Rampar and the Fauss-bray is left a space E 5, fit for the Besiegers to Plant and Traverse their great Guns, which we call the Walk of the Fauss-bray; It's greatest breadth is equal to two Rhynland Perches, and the least is equal to one. When upon occasion a Fauss-bray shall be drawn about the ancient Rampar of Cities, to be defended only by Musquetiers, the breadth of the Walk may be taken somewhat less than a Perch. If you have a mind to proportion it to the Polygons, you may order it after this fashion. In IU. V VI VII. VIII. IX The walk of the Fauss-bray, with its step or banquet. 15. 18. 20. 24. 24. 24. etc. This Width will serve to plant Guns in, but not the biggest. iv The Bankside or Lisier. At the foot of the Fauss-bray towards the Ditch, is left a space of six feet R S, for the strengthening and keeping up of the work, lest any of the Earth should fall into the Ditch. CHAP. X. I. Whether a dry Ditch or Graft be better than a Moat. THere is not a question more frequent amongst Engineers; and many now prefer the dry one. The inconveniences of a Moat are these; it keeps the besieged in like Prisoners, that they cannot sally out upon the Enemy, unless a Covert way and Out-brestwork be raised beyond it at very great expenses: And when the Out-brestwork shall be taken, it cannot defend itself, since there is no going on it but by little boats. Therefore the Galleries are easily brought over the Moat unto the Rampar, as Experience hath often taught the Hollanders, the water hindering the besieged, that they cannot run down into the Ditch, with handy blows to throw down the Fatal Engine. This defect however, is supplied by building a Fauss-bray, Ravelins and Halfmoons, at vast expenses, and the entertainment of a far greater Garrison. Therefore a Moat is both of itself weak, and keeps the Townsmen in like Prisoners, so that they cannot come to beat off the Enemy any other way than by firing at a distance, though they see him spring his Mines, and bring the last destruction to the Town; besides, the Fauss-bray is built only for the security of the Moat, as is the Out-brestwork and the Couvert way, and in fine, all sorts of Outworks; and it requires a far greater number of Soldiers to defend it. A dry Ditch, safe in its own strength, doth not need these chargeable Outworks, especially an Out-brestwork it never wants: For as the Moat keeps in the Soldiers like Prisoners, the dry Ditch conveys them safe and unseen on the Enemy. Neither have these that sally any need of a Couvertway, since the Ditch can hid them in its own bottom; nor have they any need of an Out-brestwork, since the outside of the Ditch itself, viz. if it have steps made to it, is able to supply the place of an Out-brestwork. Nay, there is no sort of Out-work required, since they are raised only to keep the Enemy from the Ditch and Rampar, which will be better performed by Sallies, which may be made safely through the dry Ditch. Again, a dry Ditch makes an easy and safe retreat for those that sally, when they are wholly pursued by the Enemy: But a wet Ditch would either exclude or drown them; for there is no passage from Out-work to Out-work, or from the Outworks to the principal Rampar, but what is made by little narrow wooden bridges, which can receive but few at a time; and if they are crowded too much, as commonly in such cases it happens, they yield to their weight, and are broken: As it fell out when Breda was last besieged, in the taking of Ginekens Horn-work, with the great loss of their stoutest Soldiers perishing in the waters. To conclude, since a dry Ditch can safely be without Halfmoons, Ravelins, Horn-works, and Out-brestworks, and all other Outworks, or at least may neglect them far safer than a wet Ditch can; we must confess that the Town, if it were besieged, would be defended with a far less Garrison. It plainly appeared at the siege of Mastreicht, the sharpest of all the Dutch Sieges, how far a dry Ditch is to be preferred before a wet one. The ditches of the Town being partly wet, partly dry, the Prince of Orange consulted with his Captains which was best to fall upon; who resolved to attempt the dry one; but the taking of it was so slow and so difficult, that the Prince confessed his error, and resolved, after that, never to try the taking of a dry Ditch before a wet one: That I may omit the rest of the action; in this most valiant defence. The Townsmen from the Ditch itself brought forth their Mines, to blow up the lines of Approaches, with such facility and success, that the Enemy was forced to spend five weeks to gain a Line of five Perches: Then with Skirmishes, Works and Countermines, they so tired the Dutch that besieged them, that the Prince despairing to bring his Line over the dry Ditch, was constrained to carry a Mine into the Town, under the bottom of it, which was very near forty feet lower than the level of the Town. Notwithstanding, 'tis to be confessed, the nocturnal attempts and surprises of the Enemy are better kept off by a wet Ditch than by a dry one; yet there is great danger from the water itself being once frozen, unless the Ice be always broke; as appeared in the taking of Wachtendonch by the Dutch, and Philipsbourg by the Emperialists, by a surprise in the dark, over their Moats that were frozen. Whilst these things are controverted on both sides, This is my opinion, that a dry Ditch is best against open Assaults, and the wet one best against Surprises: But because all surprises and sudden attempts may be prevented by the care and vigilancy of the Officers and Soldiers, but open force no other way but by force, it seems to me the dry Ditch is absolutely to be chosen, if the nature of the ground will permit it: Especially since a great deal of money is spared, which otherwise would have been spent in building the Fausse-bray and the Outworks. II. The making of the Ditch. Let the solidity of the Ditch be equal to the solidity of the Works that are to be raised, viz. to the Rampar, the Brestwork on the Rampar, the Fauss-bray, and the Out-brestwork, added together; therefore you must not take more earth out of the Ditch than will serve for making the said Works: For which reason all the dimensions of a Ditch cannot be determined, before the solidity of all the Works to be raised is known. III. The upper Width. The upper Width of the Ditch about the Bulwark S V must at least exceed the tallest trees, otherwise the Enemy would lay bridges over it, 120 132, 144 feet will be large enough; but if you will vary it according to the diversity of the Figures, you may order it after this manner. In IU. V VI VII. VIII. IX. X. 72. 84. 96. 108. 120. 132. 144. feet. iv The Talu of the Ditch SH, V 5, or Lines forming the Sloap. The outward Talu V. 5 of a wet Ditch, and the inward S H, must be equal to the depth of it, which is now to be determined, so consequently the Angle H S 8 will be half a right Angle. V The Depth 8 H 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. For the most part it is ordered to be ten or twelve feet; but it cannot be less than six feet, otherwise a wet Ditch might be waded over, and a dry Ditch would not cover a man standing. But why a Ditch having the Width s above-determined, and its depth ten feet, should supply earth enough to raise the Rampar and its Brestwork, the Fauss-bray and Out-brestwork: Thus I demonstrate. Measure the Orthographical Sections of the Rampar and its Brestwork A LIKE, the Fauss-bray 5 N P Q R; and of the Out-brestwork 6 X Y Z, and multiply their sum into the principal Perimeter of the Fortification, which will be known, if all the Courtines, Faces, Flanques, be added among themselves. But the Orthographical Sections, and the Perimeter of the Fortification must be measured with one and the same measure, and the product shall give a solid almost equal to the aggregate of the Rampar, and its Brestwork, the Fauss-bray and Out-brestwork. In like manner, the Ditch will be almost equal to the solid that shall be produced out of the multiplication of the Orthographical Section of the Ditch S 8 7 V, into the Perimeter that passeth through the middle point of its Width α: Therefore because the Ditch ought to be equal to the aggregate of the Works, 'twill be by the Corrol. of the 34th of the 11th of Euclid. As the Perimeter passing by α, is to the principal Perimeter of the Fortification; so is the sum of the Sections of the Rampar, etc. to the Section of the Ditch S 8 7 V, which is consequently known, because it is a fourth proportional to three quantities known. Now because S V is known, and its half S α, that is α β for since S H is equal to H 8, S α will be equal to α β, by the 4. 6. Euclid. Therefore β α multiplied into S α shall give the Triangle S β V; from which subtract S 8 7 V, already known, and there will remain the Triangle 8 β 7 also known. Then as the Triangle S β V is to the Square of α β, so is the Triangle 8 β 7 to the Square of π β; wherefore since three terms are known, the fourth also will be known, which is the Square of π β, whose root is the Line β π, which substracted from β α (that is S α) shall give α π the depth of the Ditch, which this way is found to be near ten feet. If you need any more Earth to raise batteries for Cannon and Cavaliers, make your Ditch something deeper about the Bulworks: If there be no Faus●-bray, nor Out-brestwork, yet 'twill be requisite to make the Ditch ten feet deep, especially if you intent it a dry one; the Earth that shall be over and above, will serve to raise Cavaliers and other Works, of which there is great use. VI The Width at the bottom of the Ditch 8, 7. This follows from the upper Width, the Angle forming the sloap, and the depth being already determined. In IU. V VI VII. VIII. IX. 52. 64, 76. 84. 96. 108. feet. VII. The Properties of a dry Ditch. 1. It ought to be something deeper than a wet one. 2. It's inward Talu S H must be less than a wet one half the depth, that is six feet, that it may be harder for the Enemy to climb up. 3. But it must not be less than six feet, lest the Rampar fall down. 4. You'll make the Enemy a great deal of work, if in the middle of the great Ditch you dig a less 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 16, 18, 20, feet broad, and 4 or 5. feet deep. 5. The outside of the Ditch 7 V must be made after the fashion of a Brestwork that may cover a man, and have two steps or Banquets for the easier getting up to it. 6. Sally-ports must be made in the Rampar, for the Townsmen to descend into the Ditch. CHAP. XI. The Out-brestwork and Covert-way. I. Its Use. A Dry Ditch may safely be without an Out-brestwork; but a wet one altogether wants it: For since a wet Ditch doth not keep out the Enemy more than it keeps in the Townsmen, when upon occasion they should sally out upon the Besiegers, a Covert-way V 6 was found necessary to be made beyond the Ditch, and a Brestwork to protect it; by which means the Defendants could sally safely out of their City over the Moat; and so the Enemy was kept from the Town, but the Townsmen were not hindered, when they pleased to fall upon the Enemy. II. The breadth of the Covert-way. Most commonly it is made equal to the walk of the Fauss-bray 24 or 21 feet; for so much almost will be required here for traversing great Guns, and performing other Military duties. If you have a fancy to vary it according to the diversity of the Figures, use this Table. In IU. V VI VII. VIII. IX. 12. 15. 15. 17. 21. 24. feet. III. The making of the Out-brestwork. 1. It's height Ψ Y must be six feet. 2. The inward Talu must be one foot, as in the rest of the Brestworks. 3. The outward sloap of it Y Z must be so inclined, that being produced, it may pass through 1. the top of the Brestwork of the Rampar. There are many and great advantages from this form; for so all of it will be scoured from the Brestwork of the Rampar, which would not have been, if the inclination had fallen from Y in 10. for so all the Triangle ΨY 10. is obscured from the sight and shot of the Brestwork of the Rampar. 4. To find this sloap or inclination, the base Ψ Y must first be known; which is after this manner: The Lines I C and C 9 are known; and therefore 9 I is known, and T 3 is also known, or C F and F λ is known; therefore C λ, or 9 Y is known, and so is Y λ known; then by the 4. lib. 6. Euclid. as I 9 is to 9 Y, so is Y λ to λ Z, to which if you add one foot, the whole base λ Z will be known. The Perimeter of this Brestwork, or the Lines of it surrounding the whole Fortification, whether they be inward or outward, must be drawn parallel to the Faces only, so that they meet at a point opposite to the middle points of the Courtine, and make outward Angles; but if Ravelins are built before the Courtines, the Brestwork is drawn about them, but not about the Horn-works, if any should be built. iv Whether it be expedient to make a Ditch about the Out-Brestwork. Some affirm it, and stand to it: But they do not consider, when they think to make this Brestwork stronger, that they quite overthrow the end it was made for; which was, that the besieged might safely sally out upon the Enemy, and in their return enjoy a safe retreat; both which will be hindered by a Ditch made about it: Insomuch that if the Townsmen do not make it, 'twould seem fitter for the Enemy to make. CHAP. XII. An Orthographical Table of Regular Fortifications. This Table is collected out of the doctrine of the four foregoing Chapters. Max. Med Min. Rhynland feet. The breadth of the base of the Rampar A E. 84 72 60 The inward Talu, or line forming the Sloap AB. 18 6 14 The outward Talu E F. 9 8 7 The height of the Rampar B L. 18 16 14 The breadth on the top of the Rampar L 3. 57 48 39 The breadth of the base of the Brestwork 3 D 24 18 14 The inward Talu of the Brestwork D T. 1 1 1 The outward Talu of the Brestwork 32. 2 2 2 The inward height of the Brestwork T I 6 6 6 The outward height of the Brestwork 2 K 4 4 4 The breadth of the top of the Brestwork K O. 21 15 11 The rest of the foregoing Table. Max. Med. Min. Rhynland feet. The breadth of the step or Banquet D 4 3 3 3 The height of the step or Banquet 4 G 1 ½ 1 ⅓ 1 ⅕ The Terrepleine or Walk on the Rampar 4 L 30 27 22 The walk of the Fauss-br., or chemin des Rondes E 5 21 17 15 The Fauss-bray with its Banquet The border or bankside. Lisier R S 6 6 6 The upper width of the Ditch S V 132 108 84 The outward & inward Talu's of the ditch SH V 5 12 12 10 The depth of the Ditch H 8, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 12 12 10 The Width of the bottom of the ditch 87 108 184 64 The Covert way V X 21 17 15 Its step or banquet The base of the out-brestwork λ Z 79 70 69 Its height 6 6 6 For the base of the Out-brestwork, working according to the Rules delivered in the 11. Chap. num. 3. I find it to be Max. Med. Min. 82. 75 ¼ 69. Therefore Dogen and Fritach are out in their account. The first Column shows you the largest and strongest Orthography, which is able to sustain the greatest force of the Besiegers. The second is able to bear an indifferent Siege. The third is made against the least strength which is usually sent against Towns. But here we only treat of the Forts themselves; I shall hereafter give you the Orthography of Castles and Outworks. And again, I had no proportion or respect to the diversity of the Figures or Polygons, as many Engineers have; who for no reason, as I can tell, give to a Pentagon a different Orthography from that which they give to a Hexagon or a Nonagon. For a stronger or weaker Orthography is to be given a Fortification, not as it hath more or less Angles or Bulworks, but as it ought to resist a greater or less strength of an Enemy. Note, If the Fortification be made without a Fauss-bray, the Out-brestwork will have another Base, for it will be a fourth proportional to the three terms I 9, 9 Y, Y λ, but the mean or middle term 9 Y will be less by the space E R, if the Fauss-bray be wanting, and then the base of the Brestwork λ Z will be max. med. 65 50 CHAP. XIII. Of the raising of Outworks. A Fortification form according to its essential parts, is made stronger if it be surrounded with some Outworks. The chief of which is a Raveline, a Halfmoon, a Horn-work, a Crownwork, and Tongues. I shall treat of each of them distinctly in the following propositions. PROP. I. I. The definition and form of a Raveline or Target. A Raveline is a Bulk of Earth almost like a Bulwark cut off, Fig. 10. except that it wants flanques; it is surrounded with water, and separated from the Fortification by the breadth of the whole Ditch. Such an one is F E G H, in the 10th. Figure, its faces are F E, G E. It wants, as I said, for the most part flanques, yet it admits of them when it is built before Gates, which then will be about 8 or 9 perches. Towards the Enemy it is built with a Rampar and Brestwork, and lies open towards the Fortification, lest it might shelter the Enemy when he hath possessed it, it is raised but a little height above the level of the ground, that it may be better defended from the main Fortification, and the plains the better scoured by it. It's Angle must not be less than 60 degr. nor more than a right Angle. The length of the faces is determined in Regular Fortifications, numb. 3. If they are applied to the covering of a Courtine that is above its just length, observe this, that the faces must not be longer than the faces of the Bulworks, therefore they may be about 40, 50, or 60 paces. II. Concerning their place, and how they are defended. For the most part it is raised before Gates and Courtine, but never before the Bulworks. The 10th. Figure shows the Situation of it, as it lies before a Courtine; 'tis best to have it of such a breadth as might cover the Courtine only, and not the flanques, for then 'tis defended by the faces and flanques of the Bulworks that it lies betwixt. III. The making of it Is various; but this is most approved. Fig. 10. Raise an infinite perpendicle from the middle point of the Courtine S, from this Line on the other side of the Ditch cut off H E equal to ¾ or ⅔ or ½ of the Face; then from the point E draw straight Lines either to the ends of the Courtine A, B (and this will be the best form for the Raveline, for the whole Courtine is covered by the Raveline, and the Raveline itself not only scoured and defended by the Faces, but by the flanques of the Bulworks also) or to some other point of the flanque, or to the ends of the flanque C D; those parts of these straight lines F E, G E, cut off from the Bankside of the Ditch towards E, are the Faces of the Bulworks. 1. Another way. On the Centres A B, the extreme points of the Courtine, with the distance of the same Courtine, describe two Arches intersecting one another in E. 2. Produce the marginal lines of the Ditch φ 1, M L till they meet at the point H; then from the ends of the flanques C D draw straight lines to the point E, that may cut the marginal lines of the Ditch in F G, and F E G H shall be the perfect delineation of the Raveline; the faces are F E, G E, the Gorge Lines are F H, G H. 1. Another way, bisect the Gorge Lines of the Bulwark A R, B Q in the points O, P; then draw straight lines from the points O, P, by the ends of the flanques C, D till thewy meet one another in the point E. 2. Then produce the out-lines of the Ditch φ I, M L, till they meet in H, and cut the former lines in F G, so shall F E G H be the Ravelin required. iv The Orthography and ichnography, or the Profile and Plain. This Table following shows the height and breadth of each part. The third column shows the Orthography of the Outworks of Breda; The first and fourth shows the Orthography of the largest; The second and fifth of the middle size; the sixth shows the least; the four last Columns are taken out of Dogen. This Table doth not serve only for Ravelins, but for all manner of Outworks. A Table for the building of Outworks. Rhynland feet. Max. Med. Bred. Stab. Min. saint. Temp. The lower breadth of the Ramp. 40 36 44 36 24 20 The outward Talu of the Ramp. 3 2 6 3 2 2 The inward Talu of the Ramp. 6 4 8 6 4 4 The height of the Rampar. 6 4 8 6 4 4 The upper thickness of the Ram. 31 30 30 27 18 14 The base of the Brestwork. 15 15 16¼ 13 10 8 The outward Talu of the brestw. 2 2 3¼ 2 2 2 The inward Talu of the Brestw. 1 1 1 1 1 1 The outward height of the Breast. 2 2 5 4 4 4 The inward height of the Brestw. 6 6 6 6 6 6 The upper thickness of the Breast. 15 12 12 10 7 5 The height of the step. 1½ 1½ 1½ 1½ 1½ 1½ The breadth of the step. 3 3 3 3 3 3 The Walk on the Ramp. 12 10 10 1/● 11 5 3 The rest of the foregoing Table. Rhynland feet. Max. Med. Bred. Stab. Min. st. Temp. The border at the foot of the Ram. 3 3 6 3 3 2 The width of the Ditch. 48 30 42 30 24 16 The outward Talu of the Ditch. 10 8 7 8 6 4 The inward Talu of the Ditch. 10 8 7 8 6 4 The depth of the Ditch. 10 8 7 8 6 6 The width of the bottom of the D. 18 14 28 14 12 8 PROP. II. Of the Halfmoon or Helmet. I. Its definition and place. Halfmoons for the most part do not differ from Ravelins, unless it be in bigness; perhaps they had this name given them, because those which are built before Bulworks are Arched in the form of a crescent, on that side which lies towards the Bulwark. They are placed upon the Covert-way which is beyond the Ditch, so that their Capital line produced, cuts the Courtine into two equal parts. They are built also before the Angle of Bulworks (as I said) but the greatest use of them is in Irregular Fortification, as I shall show hereafter. II. Their Form. Let not their Angle be less than 60 degr. nor more than 90 degr. Let their height be but indifferent, and not distant from the Rampar above Musquet-Shot, that they may be defended by the Rampar. When they are built on the Covert-way, their faces must be 25 or 30 paces; let the thickness of their Rampar be 15 or 20 feet, and they must be so large as to receive 100 or 150 Soldiers. III. Their Delineation. 1. In the Angle of the Fauss-bray V as in a centre, with the distance of the breadth of the Ditch V M, describe an Arch, and produce the Capital line infinitely, cutting the Arch in α. 2. On the other side of the Ditch cut off α X from the Capital Line produced, which is ⅔ of the Face of the Bulwark, and from the points H and λ where the Gorge lines of the Ravelins intersect one another, draw unto λ the lines H X, λ X. 3. Produce the faces of the Fauss-bray φ V, φ V, till they cut the lines H X λ X, in 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and the Arch in 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or the Fichant lines of the Fauss-bray continued on 2 V, 3 V, may determine these Intersections. So have you a halfmoon delineated, placed before a Bulwark, whose faces are X ζ, X ●, and its flanques (but open) are 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, The delineation of other halfmoons is like that of Ravelins. The Orthography and ichnography, is had out of the foregoing proposition, Chap. XIII. numb. 4. iv Its Use and Conveniency. 'Tis the weakest of all the outworks, since it cannot entertain a good quantity of Soldiers to defend it by reason of its straits, and is also with more difficulty defended from the Fortification. Therefore these halfmoons seem to be hurtful to the Fortification unless they be armed with these cautions; to wit, that Ravelins be built on both sides, and that they consist only of Faces, being altogether without flanques (otherwise being possessed by the Enemy, they cannot be hot from the Ravelins) and at last let them be every where within Musquet-Shot. Yet if all this were performed, 'twill be still doubtful whether they are useful or not: Wherefore they seem not to be built without peculiar necessity. PROP. III. Of the Horn-work. I. Its Definition and Kind's. Fig. 10. THat Outwork that runs farthest into the field with two straight sides objecting to the Enemy two half-Bulworks, is called a Horn-work: The tenth Figure shows an example of it. There are three kinds of Horn-works; the first hath its sides inclining to one another towards the Field; the second towards the Fortification; and the third's are parallel. II. Its Place and Form. They are built opposite to the Courtine, or the Angle of the Bulwark, beyond the Out-brestwork: Yet they are better defended if they cover the Courtine, than if the Bulwark, especially if the sides, are parallel: For when they cover the Bulworks with parallel sides, they receive no other defence than from the Courtine, and that to little purpose, since at so great a distance; besides, after this manner the work would be too narrow: Yet if they are to be placed before Bulworks, 'tis altogether necessary the sides should incline to one another towards the Bulworks, that so they may not take in all the faces, but exclude some part of them from which they may be defended. See the Construction in Dogen, pag. 160, 161. If they are built before the Courtine, let their sides be rather parallel, and perpendicular on the Courtine. If they cover the whole Courtine (as some will have it, and as we have expressed in the Figure) their defence will be from the faces of those Bulworks that the Courtine lies betwixt. If it does not cover the whole Courtine, as others will have it, the defence of the sides will be the greater; to wit, both from the faces of the Bulworks, and from part of the Courtine. Betwixt the Horn-work and the Courtine, there is commonly raised a Raveline; nay, before the work itself, betwixt each of its Horns, a Raveline, or rather an Halfmoon may be built. To conclude, you will add a great deal of strength to this work, if you make some Retrenchments: But of that afterwards. III. Its Delineation. 1. Let there be drawn two parallels E I, F K, for the sides of the Horn-work, from the Out-brestwork towards the field, at such a distance, that if they were produced towards the main Work, they might fall in a straight Line with the flanques of the Bulworks; or if you desire a less breadth for the Horn-work, let them fall within the flanques on the Courtine itself. But the ends of these sides must not be above Musquet-shot from the Rampar, wherefore they must not run beyond the Rampar above sixty Rhynland Perches: Yet these sixty Rhynland Perches use to be counted from the Out-brestwork, that so the approaches of the Enemy might be the more infested. Join E F, on which make the Angles F E G, E F H twenty five degrees each; then bisect one of these F E G; with the right Line E L meeting with F H in C; then from E G cut off E D equal to F C, so will F C, E D, be the faces of the half Bulworks. 3. From the point D and C draw D A and C B, equal and parallel to E I and F K, for the flanques of the Horns, and join the Courtine A B, the proportion of the flanques D A and C B, to the faces, will be almost the same as uses to be in Regular Fortifications. Also after this manner following, the Capital and Gorge lines, the Flanques and Courtine will be with more ease determined: For ⅓ of E F gives the Capitals E N and F M; also ⅓ of M N or E F gives the Gorge lines N A, M B, and there remains for the Courtine A B also ⅓; the right Lines M E, N F, will determine the length of the Flanques raised from A and B; and so also the faces E D, F C will be found. These things being done, a Horn-work is delineated, such as uses to be stretched before the Courtines in a Regular Fortification; the delineation of the rest will be performed almost by the like method, having always a respect to the place. Note. That here is a twofold Practice in building Horn-works; 1. That the Courtine might be determined by the Faces. 2. The faces by the Courtine. iv Its use. If Ravelins, Halfmoons and Horn-works, are built about a fortified place, the Fortification is accounted most complete and perfect, whose use consists most in this; 1. They keep off the Enemy far from the Fortification. 2. They are taken with a great deal of difficulty; for they are defended from the Courtine, from the Bulworks, and from the adjacent Works, and some Lines from the Out-brestwork itself. 3. Being taken and possessed, they can hardly be kept, because they lie open towards the Fortification. 4. Horn-works are most destructive to the approaches of the Enemy, and under their shelter the besieged may work counter, as occasion shall offer, etc. PROP. IU. Of the tongues, in French Tenailes. I. Their Definition and Kind's. THey are Outworks that differ from Horn-works almost only in this, that instead of two half Bulworks they have only an external Angle; and this sort is called the single one: It it called the double one, when it hath two outward Angles with one Inward. The twelfth Figure shows the single one; the thirteenth the double one. Now this outward Angle is that which is without the Figure, and whose sides incline inwards. The inward is that which is within the Figure, with its sides running outward. II. Their Place. The same as that of the Horn-works: Yet it will hardly be expedient to lay them before Bulworks, by reason of their weakness. Of which Num. 4. III. Its Delineation. Fig. 12. You must describe a single one after this manner. Draw the sides A C, B D after the same manner as in the delineation of Horn-works, which is already prescribed, unless these are wont to be shorter, viz. than forty or fifty Perches. 2. Join C D, which bisect in F; and from F let fall the perpendicular F E equal to ¼ of C D, and join C E and D E; so have you the simple external Angle. Fig. 13. Draw the double one after this manner: Having drawn the sides A C, B D, as above, join C D; which being bisected in G, from G raise the perpendicular G E equal to ¼ of C D, and join C E and D E. 2. Produce E G to F, till G F be the half of G E; and the right Lines C E, D E being bisected in K and H, join F K and F H; so will A C K F H D B be the double tongues, or double external Angle. iv Its strength and use. They are much inferior to the Horn-works, insomuch that they seem only then to be made use of, when some sudden occasion urges. Moreover, the defect of these tongues, and of all external Angles, is this; that about its very Angle it affords the Enemy a certain Quadrangular space, within which he need not be exposed to the shot of the Defendants; this space is determined, if the outward sloaping surface of the Brestwork be conceived to be produced till it cut the field; its capacity is almost equal to twenty three Rhynland Perches, which will be easily computed. Since then this sort of building is so much against the first Laws of Architecture, 'twill be almost necessary to raise a Raveline before it. The Double tongues, since they have a double external Angle K and H, will likewise double the defect already spoken of; wherefore they are less used. PROP. V Of the Crownwork. I. Its Definition. THat work is called a Crownwork, that hath on both sides two half Bulworks, Fig. 14. and in the middle one or more whole ones. Therefore it is the part of some Regular Fortification; and seems to have this name given it, because it doth, as it were, encompass part of the Fortification. II. Its Place Is the same as that of Horn-works; though the Crownwork can cover more of the Fortification than the Horn-work, and sometimes they are drawn about Horn-works. Their chiefest use is to enclose neighbouring places, that might infest the Town, as Hills, etc. and so prevent the Enemy. III. Its Delineation. Since 'tis most an end the part of some Regular Fortification, let the Engineer look, what Fortification is fittest for the place of the Polygon that is to be encompassed; which when he hath found, let him delineate so many Bulworks of that Fortification which is built on the observed Polygon, as the place requires; only this let him observe, that the Angles of the half Bulwark be not less than sixty, nor more than ninety degrees. Its Bulworks are wont sometimes to be less than those of the main Work. But let us expound more especially the construction of a Crownwork having one whole Bulwark. The whole description is made after this manner. Let the Capital of the Bulwark be produced infinitely; or if the Crown is to be set before the Courtine, from the middle point of the Courtine raise an Infinite perpendicular; on the Capital produced set off from B to D forty Rhynland Perches; on the perpendicular of the Courtine you may reckon sixty or seventy; for so the sides of the Crownwork will be yet within the shot of a Musket coming from the Bulworks of the main Fort. Then at the point of D, of the right line B D, make the Angle B D I, half of some Multangle or Polygon, and on the other side the Angle B D K; then in the sides of these Angles from D to I and K, reckon 40 or 50 perches, at most 60; and laying a Ruler by the point I, to the flanque of the Bulwark F, as also from the point K to the other flanque E, draw straight lines till they meet with the Out-brestwork in M and L, so will the sides of the Crownwork be determined by the Out-brestwork. But if the sides M I, L K, exceed 60 perches, that is, a Musquet-Shot, the Angles B D I, B D K, must be made less, (Yet so that the whole I D K may remain bigger than a right Angle) or certainly (which is thought best) the Line B D must be shortened. Then see what Regular Figure's Angle is equal, or comes near to the Angle K D I: say for Example an Heptagon or seven-angled figure; therefore make within K D I one whole Bulwark and two half Bulworks of an Heptagon, by the help of your Tables. If you would place more whole Bulworks in the middle, let the sides of the Horn-work be drawn forth, so that they do not exceed Musquet-Shot, and within these build part of a Regular Fortification, as hath been said above. General Rules concerning Outworks. 1. Let them be within Musquet-shot of the main work. 2. Let not their height be more than what may conveniently serve to scour the ground possessed by the Enemy. 3. Let the Remotest be lower than the nearest. 4. Let a dry graft have no outworks, unless Horn-works, if you see occasion; let the wet one have Ravelins and Horn-works, but it will hardly admit of Halfmoons without Damage. THE SECOND PART OF Irregular Fortifications. SInce most Cities are of an Irregular figure, 'tis evident what great use or rather necessity there is like to be of this Part; I shall comprehend all the matter briefly in the following Chapters. CHAP. XIV. The Parts of Irregular Fortification. THese works following serve for the fortifying Irregular places, Ordinary Bulworks, double and Triple Bulworks, Forked Bulworks, Plain Bulworks, Half Bulworks, Ravelins, Half moons, Horn-works, Crown-works, tongues, External Angles, Angular tongues, Plain Moles, half plain Moles, the middle Defence or toothed, Retrenchments. Some of these (viz.) those that are wont to be used in strengthening Regular Fortifications, we have already expounded. And although their manner of building there delivered, be proper to Regular Fortifications, yet out of this 'tis easily understood how they are to be fitted to an Irregular place. Now these that are over and above, are to be explained in this Chapter. 1. The Double or Triple Bulwark, is a Moat or Bulk of Earth composed of several Bulworks placed one above another; 'tis shown in the 15th. figure, and is built commonly in steep places, such as the sides of Hills, that when the Enemy coming up can be no longer touched from the lowest, he might be hot from the second, and lastly from the third; these are seldom used. 2. Forked or cut Bulworks, I call those whose Angle E is cut off, and changed into an external Angle F K G, after this manner in the 16th figure is the Mole or Bulk A C FK G D B; they are of use when the Angle of the Bulwark is too acute. 3. Half-Bulworks, you have in the Horn-work, fig. 10. and in the Crownwork, fig. 14. They are not only to be used in Horn-works and Crown-works. but also in many other places, as we shall say afterwards. Observe that the Angle of these be not too acute, and take care that their plain side be not destitute of defence. 4. The external Angle, Fig. 17. is that which is made by two lines running inwards towards the Centre of the place called in French angle retire; on the contrary, the Inward Angle is that which is made by the sides running forth towards the field from the Centre of the place, called in French angle Avance. In the 17th. figure the outward Angles are, A, L, C, E, G, etc. The inward B, D, F, etc. The outward Angle, if it be not too obtuse, seems strong enough, since its sides do mutually scour one another; and from this is had the defence of the tongues and Forked Bulworks. We have above showed its defect. Some people extol this so, as to think a place surrounded with outward and inward Angles, to be equal in strength to one that is fortified with Bulworks, but they are not to be heard. 1. For first, it always happens, that when a place is enclosed with External and internal Angles set alternately, some of the outward will be too blunt or obtuse; as A L, and some of the inward too acute, either of which is very hurtful. The last in this, that its Angle is liable to be cut off by the Enemy's Canon. The other, in that it loses so much the more of its scouring defence the nearer it comes to a straight line. 2. The outward Angles likewise have this Essential inconvenience, that the Enemy drawing near the Angle itself, cannot be hot within a notable space, as we have shown above, which fault the Bulworks are without. 3. These External Angles do lessen the Area of the place, and increase the circumference, both which is faulty. 5. Angular tongues, are wont to be used in fortifying an acute external Angle, Fig. 18, 19 or a right one; but not so conveniently an obtuse one: with help of these you may mend the second fault spoken of above; you must build it after this manner. Produce A B, E B, the sides of the Angle, 8 or 10 paces to K and N, and join K N; then draw K E, N G parallel to B A, B E, likewise C E, D G parallel to B E and B A, which may meet with the former in E and G. If all the space contained within the Lines C E K N G D be emptied and cleared, you have the tongues sought for. Some build it after this manner, omitting the Line K N, Fig. 19 and slighting the Triangle F B N, they empty only the spaces C E F B, B N G D; yet the first seems to be preferred, because in it the defence is not only had from the flanques E K, G N, but also from K N, which is as it were a little Courtine; but the other wants this defence, and its sides B F, B N are almost useleless for defence. But if they are to be built with a wall, (as for the most part they ought to be) the labour is doubled and without profit, because F B and B N are bigger than F N, and as I said unuseful. On the ends of the sides of the Angle which is strengthened with the tongues, half-Bulworks, X, Z, are always wont to be made. 6. Plain Moles, serve for the strengthening obtuse outward Angles, Fig. 20. less fit for acute and right ones: you shall build them after this manner. From the sides of the outward Angle E B D cut off the right lines B A, B C 25 or 30 paces, and raise the Perpendicles A H, C I equal unto them, and join H I; so will A H I C be the Plain Mole, whose flanques A H and C I, will scour the sides of the Angle A E, C D, and these will be scoured by them. But the Front H I will be scoured by N E, M D the segments of the sides which the Front produced cuts off on both sides. Therefore the sides of the Angle ought to be so long that they may cut the Front prolonged on both sides, and the parts N E, M D, must be of a considerable quantity, lest otherwise the Front want its defence. This work is better than the tongues, because it enlarges the places, and is capable of great Retrenchments. If you desire orillon's to it, or Ears, take H K, I L 1/● of the flanques, and on these you must build them. The rest of the parts A K, L C, being each ●/3 of the flanques, will give the Covert flanques. 7. The 21 figure shows, The half plain Mole; Fig. 21. 'tis of use when one side B E of the External Angle is longer than the other, and so much longer that it exceeds Musquet-shot. Fig. 22. 8. Inward Angles, angel's avance's, may be taken in stead of Angular tongues or the plain Mole, for the defence of External Angles, whether they are acute or obtuse. In the example let there be the outward Angle B A C: here it will be conveniently fortified by building the inward Angle D F E, where observe this, that the parts of the sides intercepted A D, A E must be always of such a bigness, that the remaining segments of the sides may not exceed Musquet-shot. Fig. 23. 24. 9 The middle or simple defences, are shown in the 23, 24. figures They are of use when any side of a Fortification will not admit any other defence. Also in some people's judgements, they may be used to purpose, about the out-Brestwork. Others had rather be without these middle or simple defences, because C D, E F, etc. are each of them scoured but by one flanque, C B or E D, etc. far otherwise then it is in Courtines, which are placed between two Bulworks. Fig. 25. 10. Retrenchment is a part cut off from the whole work, which can be no longer defended, and it is like the whole. The 25 figure shows the Retrenchment of Horn-works and Bulworks, after whose Idea the rest may be perfected. Fig. 26. 11. Now there remains that we should expound the construction of plain Bulworks. Those are said to be plain Bulworks, that are not made upon Angles, but upon a right Line, and are used in the strengthening River-sides, and Courtines that are over long etc. Though when they are applied to the fortifying of Courtines, their construction will be somewhat different from the rest, as will be said afterwards. This Table serves for their construction to be made three several ways, the first is due to an Hexagon, the second to an Octogon, the third to an Enneagon, or those bigger than an Enneagon. Courtine. Gorge. Flanque. Manner 1. 480.0.0.0. 169.7.0.6. 90.0.0.0. Manner 2. 480.0.0.0. 169.7.0.6. 110.0.0.0. Manner 3. 480.0.0.0. 169.7.0.6. 120.0.0.0. The construction will be after this manner. Let there be given the right line A Z to be fortified after the second manner. 1. First look in the Table for the Courtine, you'll find it 480 Rhynland feet, which cut off from A Z, and let them be A B. In like manner look in the Table for the Neck line, you'll find it to be 169, 706. feet, which cut off twice from B Z, and let them be B C, C D; and mark the point C. Then again cut off the Courtine D E, and the Necklines E F, F G, and so proceed for the number of Bulworks you shall want. 2. In the Table seek the flanques, you I find them 110 feet, which raise perpendicularly from B to D, and let them be B K, D L, and join K L, which bisect in N, and from N raise the perpendicular N I equal to the Neck line C B; at last join K I, L I, and you'll have the plain Bulwark B K I L D, whose Angle at I is a right one. In like manner the rest will be made, the proportion of the rest of the parts will arise from this construction, which the Table underneath showeth. The Face. The flanque of the Courtine. The flanquing line of defence. The fichant line of defence. The angle of the Bulwark. 1. Manner. 240 390 367. 2.7.9. 699. 6.8.9. 90 d. 2. Manner. 240 370 795. 5.6.3. 707. 3.5.3. 90 d. 3. Manner. 240 360 409. 7.0.5. 711. 3.7.0. 90 d. CHAP. XV. How an Irregular place may be regularly Fortified. IRregular places may be strengthened two ways, viz. Regularly and Irregularly. An Irregular place is said to be Regularly fortified, when it is so changed, as that it may become Regular; or if it cannot be produced to Regularity, a Regular Figure is circumscribed about it. But an Irregular place is fortified irregularly when the Figure of the place is not reduced to a Regular one. PROBLEM I. Let it be proposed to fortify an Irregular place Regularly. 1. Describe the plain of the place to be fortified, and observe what Regular Figure it comes nearest to, and reduce it to that you find nearest. The Reduction must be so, that all those parts of the old circumference that can be used, must be retained: The restare to be excluded with a new circumference, if the place be large; or included rather, if the place be only of a mean capacity. Now a place reduced after this manner, will be fortified according to the laws of Regular Fortifications. 2. But if the Figure of the place be so Irregular, as not to be reduced to a Regular, 'twill behoove you to circumscribe about it a Regular Figure. But that you may know how many sides the Figure circumscribed is to have, measure the largest Radius of the place you intent to enclose, then turn to the Tables of Regular Fortifications, and observe what Figures Radius, your Radius is equal to, or nearest; and what Figures Radius you find it to be, that Figure you must circumscribe. CHAP. XVI. How an Irregular Place having fit Sides and Angles, is to be Irregularly fortified. SOme Angles of Irregular Place are said to be fit, others unfit; as likewise some of the sides are fit, and some unfit. That is a fit Angle that is not less than ninety degrees; that which is less is unfit; for the Angle of the Bulwark set upon it would be less than sixty degrees, if a due proportion were kept of the rest for the parts. The external Angles also are reckoned among the unfit. That side is fit, that leaves for the Courtine not less than three hundred feet, nor more than five hundred feet, when the two Gorge lines belonging to a Square shall be cut off on both sides. That side is unfit that leaves more than five hundred, or less than three hundred feet. Dogen pronounces one side to be unfit, that is less than the side of a square Regular Figure: Therefore look in the Tables for the Necklines of a square Fortification, and cut them off at each end from every particular side; and if the remainder be no less than three hundred feet, or more than five hundred feet, the side are fit. PROB. I. Let there be given an Irregular place Z, having fit Sides and Angles, Fig. 27. which were required to be Irregularly fortified. 1. Found out by help of an Instrument the least Angle of the Place, which let be A; then observe what Regular Figure's Angle of the Circumference is equal to this least angled, or next less. Let us order it to be the Angle of a Square. 2. Seek therefore in your Tables (Chap 5.) the Necklines that serve for a Square, which let be A H, A H, cut off from the sides: Seek also the flanques of a Square, which being raised perpendicularly from H, H let be H G, H G. Then bisecting the Angle A, with an infinite Right line A Q, cut off from it the Capital line of a Square A F, likewise found in the Table, and join F G, FG: so you have H G F G H the Bulwark of a square Fortification. Where note, that if the least Angle be 100 degrees, or betwixt 110 or 108, you must give to the Flanques seventy feet. 3. If on the rest of the Angles you make Bulworks belonging to a Square, the Fortification will be complete and perfect. 4. If the Courtine, and flanques in the Courtine, be in some places too little, there make the Bulwark of a Regular Figure next less, till your Courtine be long enough; you may also lessen the Angle of the Bulwark if the Flanques are too short, still preserving its just bigness spoke of in the Maxims, On the contrary, you may increase the Angle of the Bulwark, if the flanque of the Courtine be very big. 5. Very great Angles, to wit, such as are bigger than 150 degrees, shall be fortified as right sides; that is, you shall so fortify each side of the Angle, as if it were one Courtine: The manner will be delivered afterwards. 6. The Bulworks being built after this form, by help of the least Angle; if the Courtine, and flanques of the Courtine, be of that length, that that they may be shortened, still preserving their due quantity, than 'twill be lawful to increase the Angle of the Bulwark by increasing either the Flanques or Necklines, or both together; and so will you take, away any inconvenience that might be in this way; neither will there be any thing that Dogen can condemn; nor such need of that troublesome new invention of Lines, found by the Rule of Proportion. PROB. II. To do the same thing another way. 1. ME sure each Angle of the place, and see what Regular Figure's, angel's each angle is equal to, or next bigger. 2. On each Angle of the given place build Bulworks, with their Necklines, Flanques, Capital, taken from those Figures, unto whose Angles of circumference, the Angles of the given place shall come nearest. The business shall be illustrated with an Example. Suppose the Angle A to be found next less than the Angle of a Square, on this build the Bulwark of a Square; then let the Angle B, be next bigger than the Angle of an Hexagon; therefore you must build on B the Bulwark of an Hexagon; and so for the rest. 3. But if, when the Bulworks shall be built after this manner, that is to say, Fig. 27. on B that of an Hexagon, on C that of a Pentagon, it happens that the Courtine L K is notably less than 300 feet, you must build on B the Bulwark of a Pentagon, and on C the Bulwark of a Square. If the Courtine be not yet 300 feet, you must also make on B the Bulwark of a Square; but if yet the Courtine be less than 300 feet, the side C B will be unfit. PROB. III. To do the same yet another way. 1. THe third manner is this; Fig. 27. if the Angle of the Place differ notably from the Angle of the next Regular Figure, then with the same Data as are in any of the six manners of the fifth Chapter, find for each of the Angles A, B all the Angles and Lines as we did there in Regular Fortifications. Dogen, in pag. 204. seems to prefer for this purpose the third manner delivered in the fifth Chapter. 2. On the Angle A, make a Bulwark with his Necklines, Capital, Flanques, which you found for the Angle A; in the like manner on the Angle B make a Bulwark, taking the Necklines, Capital and Flanques, which you found for the Angle B, and so in the rest of the Angles C D E. 3, If, after the Bulworks are thus ordered, the Courtine be found too short, you must help that fault almost after the same manner, as in num. 3. Prob. II. 4. At last, the Figure being fortified after this manner, according us the several circumstances may require, the proportion of the Flanques, Faces, and of the Angle of Bulwark, may be freely changed and altered, etc. provided you do not transgress the Canons established in the third Chapter: Dogen hath Tables of this after pag. 200. This way is taken out of Dogen. CHAP. XVII. How an Irregular place, having unfit Sides and Angles, aught to be fortified. PROB. I. To fortify the unfit Angles of the Irregular Place A. Fig. 28. 1. IF the Angle S I B be only little less than a right one, build on it the Bulwark of a Square, and cut off its Angle Q, for it is less than it should be, and make a pair of tongues, or the outward Angle N O P. Others, when the Angle is betwixt eighty and ninety degrees, had rather build before it a Horn-work. I judge it best to do both. 2. If the Angle B C H were less than eighty degrees, but bigger than sixty, surround it with a Crownwork. Others cut away the Angle itself, if it be near sixty degrees, and turn it to a pair of tongues D F E: He doth best for a Fortification that joins both. 3. If any Angle, as S G H, be less than sixty degrees, let the Figure of the place be changed, by drawing a new side G R C, that may make Angles of a just quantity with both the sides S G and B C. 4. 'Twill be lawful also to change an unfit Angle, provided not less than sixty degrees, into a whole Bulwark or half Bulwark, or into a Raveline, or Half-moon; or else to cut it off, and change it into tongues or a Horn-work. PROB. II. To fortify the external Angles of an Irregular Place. Fig. 29. LEt there be given the outward Angle of an Irregular Place A B C, to be fortified. 1. If the ends of the Sides A and C are not distant from one another, neither less than 518 feet, nor more than 826, build whole Bulworks on A and C; as we taught in Chap 16. Prob. 1, 2. etc. 2. If the distance of the ends A and C be more than 826 feet, you must build before the outward Angle either a Raveline, or Hornwork, or else both. Likewise you may make in the sides middle or toothed defences (of which see Chap. 14. num. 9) building over and above a Raveline. Fig. 30. 3. If the distance of the ends A and C be less than 518 feet, make two half Bulworks for the defence of the sides A S and C R: But before the outward Angle you must build a larger sort of Raveline. 4. The best way of all to fortify external Angles, Fig. 28. is to enclose them within the Figure, by drawing a new side G C; and then the Angles B C G, S G C, and the side G C, may be fortified after the manner delivered in Chap. 16. if they are fit; if unfit, according to the method, partly already delivered in this Chapter, and partly to be delivered. PROB. III. To fortify the sides of an Irregular Fortification. 1. LEt the side that is too long be A B, measure the least Angle of the place A, Fig. 31. and observe as above what Regular figures Angle of the circumference it comes nearest to; Let us suppose it comes nearest to the Angle of a Pentagon, and bisect the side A B in G; also cut off the Necklines of the Pentagon A O and B N, because we supposed the least Angle at A to be nearest that of a Pentagon. This being done, if the remainder G O, G N, be not less than 300 feet, or more than 500, you shall build on the middle point of the Courtine G, a plain Bulwark, according to the Method delivered Chap. 14. numb. 11. In which altar only this, that the Necklines G I, G H be taken equal to the Necklines A O, B N of the Bulworks set on the neighbouring Angles. 2. If any side as A L be of so great a length, that being itself divided into equal parts L 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 A, and having its Necklines cut off, A 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, L 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, does leave its Courtines 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, not less than 300 feet, nor more than 500, you shall build more plain Bulworks on the side A L. 3. That side for which two Bulworks are too little, and three are too much, must be rather fortified with two great ones, than three little ones. 4. If the side too long will not admit of one plain Bulwark, the Courtine must be fortified with Ravelins and other works, but their Profile must be longer than ordinary. Note, That universally sides either too long or too short, may be corrected or not; they may be corrected when the sides that are too long, can be cut shorter; or when those that are too short can be produced. Besides you may make a new Angle on the side that is too long, that shall yield two sides of a fit quantity. PROB. iv To fortify the sides of an Irregular place that is too short. 1. IF several sides are less than 300 feet, you must change the figure and fortify it after some manner already delivered. 2. If the figure of the place will not admit of a change, either the Courtines must be fortified with Ravelins built before them, whose profile must be more than ordinary, or the Angles must be surrounded with Crown-works; they may be also changed into tongues or Hornworks, or else they may be sheltered with one whole Bulwark. 3. If the side to be fortified, having on each end the Necklines belonging to a square cut off, be less than 300 feet, Bulworks must not be built on the Angel's adjacent to the second side, although they be fit, but shall be fortified with other Outworks; and if the Angles are betwixt 90 and 120 degrees, you must build before them Horn-works; or if more than 120 degr. you must object before the angles in the Ditch itself either Ravelins, or Retrenched Bulworks. 4. The side that is too short, and those too long may be also mended; if you make Irregular Bulworks, whose Necklines are almost all set off on the longest side. PROB. V. How Ancient Cities are to be Fortified. 1. AN ancient Rampar if it be strong and surrounded with a Wall and Towers, must not be demolished; therefore you must enclose it with a new fortification, which must be Regular, if possible, or as near a Regular as might be. Betwixt the New Fortification and the old Ditch there must be left a large Po●●rium fit for Military uses. 2. If the ancient Fortifications be of Earth, or can be mended without much cost and labour, then proceed according to the Rules of Irregular Fortification already delivered. Many French and Dutch Cities are fortified with Ravelins, Halfmoons, Hornworks, and other sort of works: which sort of building since 'tis to supply the place of Bulworks ought to be stronger than usual. They are likewise frequently fortified with a Fauss-bray, and the Brestwork of the Covert-way, and sometimes with a Ditch about this Out-brestwork, and with Stakadoes. Corollary. Out of these three foregoing Chapters, 'tis understood by what Method all Irregular places are to be fortified, whether they labour with all the defects above mentioned, or not with all. Moreover, this is to be observed in the Fortification of every Irregular place, that you have the Plane of the place described on paper, that so you may the better see, what form of Fortification, and what works may best agree with the given place; and as the figure that is to be fortified proves Irregular, so commonly its Bulworks, Hornworks, Ravelins, etc. will have an Irregular figure, the place so requiring. CHAP. XVIII. SOmething of what is now to be said is also common to Regular places, but we shall conveniently dispatch them all together in this place. 1. Those places o'er which rising Hills or neighbouring Mountains domineer, are unfit to be fortified. Either therefore the Hill is to be enclosed within the circuit of the walls, or if it cannot be enclosed, all care must be taken that the Enemy do not possess it: Which, will be done by setting a new and strong Fortification upon it; or when this cannot be done, it must be by raising of Cavaliers or batteries in the Bulwark or Courtine, o'er which the Hill seems to hang. If Castles or Cities are built upon Mountains where there may be danger of Mining, you must fortify the foot of the Mountain with works. 2. The most convenient and safest place for the Gates, is betwixt the two Bulworks in the middle of the Courtine, for they can be defended in no other place with so much security and facility. For the same reason Rivers cutting through a City, are received betwixt the two Bulworks. 3. To keep great Cities in their duty and obedience, there is nothing fit than to join a Citadel to that place which may most command the Town. Concerning their building and situation observe this, 1. Let them possess the strongest part of the City; wherefore if there be a Rock or Hill within the Town, there let them be built. So they have done at Namur, Cambray, Naples, and other places. 2. Let them be set against the chiefest avenues of the Towns, and let the gates be liable to their command. 3. Let them be Pentagons, for this figure is fittest; for the square is weaker, and not so capacious: The rest of the figures above a Pentagon, are larger than needs, and are too costly. Antwerp, Turin, Amiens, Vitri, Phallzbourg, Stenay, and many other Towns, have Pentagonal Citadels; Milan, Perpignan, and casal, have Hexagons; Manheim, Verdun, Blavett have septangular ones. 4. They are so to be placed that they turn two of their Bulworks towards the Town, three to the field; And so that one of the Count tines of the City A B, meet with the Courtine of the Citadel T, betwixt the two Bulworks C and G, one of which looks towards the City, the other towards the Enemy, Fig. 32. as you have it expressed in the 32 Figure. This last is not of little moment, for so the Bulwark G is stoutly defended from the Courtine of the Town; and the Courtine itself of the Town is scoured and defended by the Citadel. From whence it appears, they very much err, who remove the Citadels far from the Towns. 5. Let them have at least two gates, one towards the Town, another towards the field, to receive in succours upon occasion. 6. Betwixt the Citadel and the houses of the Town let there be a plane of a sufficient bigness. Antwerp shows you an example of a Citadel complete and perfect with all its numbers; for this commands the City with two Bulworks, with two more scowrs the Scald that flows by it; and with three, proudly domineers o'er the field, and it is furnished with all the rest that my either appertain to its form or situation. 4. The sides of Cities that are washed with Rivers, may be fortified with slight works, to wit, with a single External or internal Angles, or with middle defences, terminated with half-Bulworks. You shall fortify the sides with Hornworks fitted for the place, vid. fig. 33. Not only the mouths of Havens, Fig. 33. but the sides that are longer than ordinary, are to be strengthened with Fortifications. If the city be distant from the River a Musquet-shot, it must be joined to it by building a Citadel. 5. The Bank opposite to the Town, if it be within Musquet-shot, and in a friend's Country, may be fortified with less Works; To wit, with an half sexangular Star, or with a plain Bulwark. But if it be in an enemy's Country, or in a friends, out of Musquet-shot, you shall fortify it with half a Regular Hexagon, whose sides must be protected with Hornworks and other works. You have an example in Fig. 34. The neglect of this was the loss of Nimmeghen on the Vahal. Of all this you may see farther in Dogen Lib. 2. These few Rules following shall put an end to Irregular Fortification, of which there is great use in this Business. I. Let the Irregular Fortification be reduced altogether to a Regular one, or as near it as can be. II. Let it be round about as equal as possible can be, or equally firm. III. A Fortification that is larger with the same circumference, is to be preferred before a less. iv Sides that bend inwards, that is, those that contain an External Angle, must be avoided, because they lessen the place, and are built at greater expense. V The Bulworks may be Irregular, and unlike; for that sort of Fortification is counted handsomest that is strongest. VI The least distance of the Bulworks (according to Dogen pag. 188.) must be 60 Rhynland perches, the greatest 80. VII. The Angle of defence on the Angle of the Tenailles, must be as oft as can be, opposite to the middle point of the Courtine. VIII. Against Hills that hang over the Town, or against Rivers that flow into the Moat, rather object the Courtine than the Bulwark, for that is stronger than this. THE THIRD PART. Of besieging Towns, and how to defend them. THere are five Acts proper to the Siege; Circumvallation, The Lines of approach and Batteries for Cannons, The Sappes, or the cutting through the out-brestwork, The Gallery, and the breaking of the Bulwark by a Mine. 1. First, therefore the place that is to be besieged is to be so enclosed round about with a Rampar, fortified with all sorts of works, that no going out, nor coming in, may lie open to it. 2. You come to the out-brestwork under the favour of trenches depressed beneath the Horizon, and drawn with various wind, so that they cannot be scoured from any part of the place besieged. 3. The out-brestwork in cutting through, you must no longer use trenches drawn obliquely, but it must be done by the shortest cut, that is by a Line drawn directly. 4. The Graft must be filled with a bank made of earth and stones and Faggots, carried on through it to the Rampar, on which at last the Gallery is laid. If the Ditch be dry, sometimes the Gallery is carried under ground to the place appointed for the Mine. 5. Through the Gallery that is now finished, the Pioners advance without any danger to the Rampar, where they dig a hole, and put in such a quantity of Gunpowder as may serve to break the great Bulk of earth that stands over it; which at last being set on fire, and the Rampar broken, the Soldiers are led on through the Gallery to the breach, to enter the City that lies open before them. This is the Sum of the Siege, whose parts I shall briefly expound, and every one distinctly by itself. CHAP. XIX. Of Circumvallation. CIrcumvallation consists in Camps, Trenches, and works of all sorts. The very Camps also being a lesser kind of Circumvallaiion, do comprehend the two last, to wit, Trenches, and variety of Works. PROP. I. The disposing of the Camp or Quarters. 1. THe Camp is to be formed in those places that seem most convenient to let in an External Enemy. 2. It must not be made in a place that may be drowned. 3. Let there be so many, that relief may be readily sent from them, to all parts of the Circumvallation. 4. Let them be above Cannon shot from the Town, or at least so far off, as that they may fear little damage from their Guns. 5. Let them be placed, if you can, by a River side. 6. The Camp, as likewise all the rest of the Circumvallation, must be fortified with Trenches, that is, with a Rampar round about it, and several other works. PROP. II. Of the Lines commonly called Trenches. THese Lines of the Siege are a continual kind of Rampar, which surround as well the Camp, as all the rest of the places about the Town besieged. Concerning these, Observe this. 1. Let them be twofold, one inward, built against the besieged, to keep them in, least with their Sallies they hurt the Besiegers; the other outward, to keep off any enemy that should attack the Camp from without. Let the outward be stronger than the inward; nay, when there is but a small Garrison in the Town, these inward ones may be spared, or at least very slightly built. 2. These Trenches, especially the outward one, must not be extended above 750 feet upon a right Line: After every 750 feet, they must be fortified with several works cast before and betwixt them. These are wont to be used, Redoubts or little Turrets, Middle or toothed defences, outward and inward Angles, Little tongues, Stars, square Forts with whole Bulworks, various Forts with half Bulworks, whole plain Bulworks, and half ones, Ravelins, half moons, Hornworks, Crownworks. All this Trade of Works so various and so manifold, was used in no time more than in our age, nor in no place oftener than in Holland, at the Siege of Hartogen Bosch, at both the Sieges of Breda, Mastricht, and many others; most of those are already delivered in the foregoing propositions: we will expound those that remain in the following. 3. The Profiles and Ichnography of these Trenches is various, in respect of their place and danger; I'll give you three sorts of them used at the siege of Hartogen Bosch. The Base of the Brestwork. 7½. 7. The outward Sloap or Talu. 2½. 3. The inward Sloap. 1. 1. The inward height. 6. 6. The outward height. 5. 5. The upper part. 4. 3. The width of the Step. 3. 3. The height of the Step. ½. ½. The Border or footing on the outside. 3. 3. The width of the Ditch. 12. 8. The outward Talu or Sloap of the Ditch. 4. 2. The inward Sloap of the Ditch. 4. 2. The depth of the Ditch. 5. 2. The width at the bottom of the Ditch. 4. 4. At the coming of the Royal Army, the Dutch made their Circumvallation stronger, they increased the Base of their Brestwork to 9 feet, making three Steps, whose widths added together made 9 feet; the height of the brestwork was likewise 9 feet, the width of the Ditch was 15 feet. PROP. III. To build a Redoubt or Turret. IT is a most easy thing, since their form is simply square. Therefore describe on the earth a Line of 48 feet, and on it delineate a square; and what you require is done. The ichnography and Profile is after this manner. It's Base. 14. or 20. It's width a top. 4. or 6. It's height. 8. or 10. It's border or footing. 2. or 3. The width of its Ditch. 15. or 24. The depth of the Ditch. 5. or 6. There is usually added to the Brestwork two or three Steps gradually placed over one another. PROP. iv To delineate a Star. Fig. 35. To delineate a quadrangular one, work after this manner. 1. DEscribe on the field a Line of 48 or 50 feet, and on it describe a square. 2. Bisect the side A B in C, and from C raise the perpendicular C D equal to ¼ of A C, or 1/● of the whole A B. 3. Join A D, D B, if this construction be made round all the sides, you'll have a quadrangular Star. Fig. 36. To have a Pentagonal Star, work after this manner. Describe a Regular Pentagon; and from the side A B bisected in C raise the perpendicle C D equal to ⅓ of A C or ⅙ of A B. Join A D, D B, and if you do the same round the figure, you will have a Pentagonal Star. For a Sexangular one. Describe A C E etc. a Regular Hexagon, Fig. X. let each of its sides A C etc. be equal to about 104 paces, at the ends of C H etc. make the Angles D A C, D C A, etc. 30 degrees each; And D A, D C will be each about 60 paces. Their ichnography and Profiles are the same as that of Redoubts. Your larger Stars are not in use. PROP. V To delineate a square Fort with half-Bulworks. 1. DEscribe the square A B C D, whose sides must not be less than 120 feet, Fig. 37. nor more than 180. 2. Trisect the sides in E, F, L, M, Q, S, T, V. 3. To each of the sides add ⅓ B I, DN, C O, A H; but for the Necklines take ⅓ in the sides themselves, to wit, BL, D Q, C T, A E. 4. From the ends of the Necklines raise the perpendicular LK, QR, TX, EGLANTINE, each of which must be ⅙ of the side. 5. Draw the right lines I K, N R, O X, H G. So have you a Fort with four half-Bulworks. PROP. VI To delineate a Fort on a Rectangular Paralellogram with half-Bulworks. 1. TRisect one of the lesser sides A B, Fig. 38. and cut off 1/● of it from all the sides for the Necklines A F, BG, C O, D Q. 2. Add also to each of the sides A K, B L, CP, DS, equal to 1/● of A B. 3. On the ends of the Necklines raise the perpendicles F I, G M, O N, Q R, equal to ⅙ of the same A B. 4. Join K I, LM, PN, SIR. I say 'tis done. PROP. VII. To delineate another sort of Quadrilateral Fort, with half Bulworks and double tongues. 1. TAke the third part of the sides of the square A B C D, Fig. 39 for the Necklines CP, A M, BN, RD. 2. Add to the side C D on both sides ⅓ C I, D K, but to the sides C A, D B likewise add ⅓ A S, B T. 3. From the ends of the Necklines raise perpendicles equal to ⅙ P X, M L, N V, R Z, and join I X, S L. T V, K Z. 4. Bisect the side C D in E, and thence cut off E G, E H equal to ⅓ of the side; and thence again raise the perpendicle E F equal also to 1/●. 5. Join G F, H F, you have your purpose. Fig. 40. There are built also square Forts with two whole Bulworks, and on the opposite side the double tongues. See Fig. 40. PROP. VIII. To delineate a threesided Fort with half Bulworks. Fig. 41. 1. DEscribe an equilateral Triangle A B C, whose sides must be less than those of a Square. 2. Cut off from the sides the third part A I, B L, C K, for the Necklines. 3. From the end of the Necklines raise perpendicularly the sixth part of the sides I H, L M, K G. 4. Add to the sides of the third part B D, C E, A F, and join F H, D M, E G. you have your purpose, The four Forts described in the foregoing Propositions, are not to be built promiscuously, and for variety's sake, but with choice, and with respect to the place: And although they are much weaker than Forts with whole Bulworks, nevertheless they are conveniently made use of. As to their Profile and Ichnography, you may give them the same as to Redoubts and Stars; or if they require a greater, you may give them that which was used in the siege of Hartogen Bosch; in which the base of the Rampar was 27 feet, the height 6, the upper breadth of the Rampar 18, the base of the Brestwork 8, the upper breadth of the Brest-work 4, the height of the Brest-work 6, the width of the Ditch 30 feet. CHAP. XX. Of Batteries for great Guns, and of the Approaches. THe Circumvallation being finished, which is the first act of the Siege, delivered in the foregoing Chapter, you raise batteries for great Guns in certain places, and go towards the Out-brestwork, covered in obliqne Trenches. Of these therefore in this present Chapter. PROP. I. To build an Offensive and Defensive Battery. THere is a twofold Battery, offensive and defensive; Fig. 42. the last is directed towards the enemy without; the first towards the besieged. You shall build an Offensive one after this manner. 1. Multiply the number of Guns that are to be mounted by 12; the product shall give in feet the length of the Battery, for each Gun is distant from another 12. feet, and the two at the ends are distant from the Brestwork 6 feet each. 2. You'll have the, breadth A D, if, to the length of a Gun mounted in his carriage, you add the space A F, ten or twelve feet for the recoiling of the piece; and the space F D, for traversing and passage. 3. Let the platform of the Battery be made sloping downwards towards the Enemy, that when the Guns are recoiled they may with more ease be brought back to their places: Let its entry behind be I, K; the way leading to it must not be very steep, but gently rising, that the Guns may with more ease be got in. 4. That part of the Battery that faces the Enemy, must be fortified with a Brest-work, whose Base you may make 12, 15, or 18 feet, its height 6; for the sides A D, B E a less width will suffice. 5. Let there be so many Ports in the Brestwork as there are Guns; let their height be three feet, their outward width four, their inward two; the outward width is more than the inward, that the Guns may scour more of the field. 6. Behind the Battery you must describe a space D S N E equal and like the Battery; in it make a square hole, as M, whose side must be ten or twelve feet; in which the powder must be kept, and you must cover the mouth with leather, lest any sparks should fall in. To conclude, as well about the Battery itself A E, as the space D N, you must make a Ditch eight or ten feet wide, six feet deep. 7. The first Batteries are wont to be raised at a Musquet-shot from the Town, afterwads near the very ditches; the general rule may be this, that the nearer they are the place, they do the greater execution. 8. The Defensive Batteries are not so full of work; their Brestwork, if it be made of earth, may be six or seven feet thick; the height is sufficient, if it cover a Gun in its carriage; instead of an earthen Brestwork they use commonly great wicker Baskets filled with earth. PROP. II. To direct the Lines of Approaches to a place Besieged. 1. ABout the distance of a thousand feet from the Town open the Trench 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, Fig. 43. which you must carry on obliquely towards the place besieged, so that it may not be scoured from any part of it; which being continued some space you must dig a new one the other way, as 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, with the same obliqueness; and so by several turn you proceed to the Out-brestwork itself, where at length the Approaches are finished, drawing two Trenches 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 longer than ordinary, and parallel to the place besieged. These two last Lines cover the Besiegers like a Brest-work, so that being so near at hand they frighten away the Defendants from guarding their Graft and Rampar. 2. Although the Approaches ought so to be carried on, that they may never be scoured from the Enemy's Rampar, yet the Engineer shall take good heed he make them no more obliquer than needs, to the loss of time and expenses. I think with two turn you may always come to the out-brestwork, a far shorter way than if more obliqne lines had been made: For let there be drawn from the point where you began your Approaches, the right line 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, which continued may fall a little without the Angle of the brestwork, and if another line be produced from β, which goes without the Angles of the out-brestwork, you will arrive at the out-brestwork in two turn 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉: but why this way of Approaches is less used, I think this to be the reason: That your long lines of Approach, if attempted, may be sooner carried and demolished by the Enemy, than those that are cut in and out with several wind. 3. At the end of every Line you must build Redoubts, after such a manner, that two may be flanqued by one; for this is the best situation of Redoubts: If one of the Lines be drawn longer than ordinary, you may also build Redoubts in the middle for its defence, all which the 43 Figure sufficiently expresses. 4. The earth which is cast out is thrown towards the Enemy, that it may be instead of a Brestwork to the Pioners. Let its Tower width be six feet, its upper twelve or fifteen, it's least depth must be such, that may cover a standing man, with the height of its Brestwork joined to it. The nearer they advance to the Town deeper they must be: The width also must be increased, if there is occasion to bring stuff for the Gallery through the Trenches: They use frequently to make three steps to the Brestwork. 6. For the security of the Approaches, Batteries are to be built in convenient places. CHAP. XXI. The Sapp, or the cutting through the Out-brestwork. Fig. 43. 1. THe Approaches being advanced to the out-brestwork, two longer Trenches, as I said before, aught to be drawn parallel to the place that is besieged, the Brestwork being built towards the Enemy; in these Musqueteers are to be placed, that they may hinder the Enemy from showing his head above the Rampar. 2. These things being done, when you can no longer draw your Lines obliquely, 'tis necessary that from that longer Trench, which is parallel to the place you intent to attaque, you cut a straight Channel L H, commonly called a Sappe, through the out-brestwork, to the very ditch of the Fortification. Without doubt this work is full of dangerous chances: But the danger seems to be lessened by these means. 1. The Soldiers being placed in the Trenches 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, by their continual firing hindering the Defendants. 2. The Brestwork and flanques of the Rampar are now so battered by the Cannon, that the Defendants can scarce stand upon their Rampar. 3. This Channel is made deeper than the rest of the Approaches, and is covered above with boughs, straw, hides, and other things necessary; that if a man cannot be protected by it from the shot, yet at least the Pioners may be by this means withdrawn from the sight of the besieged. 4. This Channel is to be directed to that part of the Fortification which is designed for the Mine; wherefore, if you besiege a Regular Fortification, you must not direct it towards the Courtine, or the Angle of the Bulwark, but to either of the faces of the Bulwark; For whosoever attaques the Courtine, is liable to shot from both the Bulworks, and they very near; and whosoever attempts the Angle of the Bulwark, is also liable to the shot of two Bulworks, though they lie farther off: Whilst he that attaques the face can be hurt but from one only. But if the Courtine hath not on both sides its full defence, as it often happens in Irregular places not perfectly fortified, the Sappe and the attaque may be carried on to the middle point of the Courtine. CHAP. XXII. Concerning filling the Ditch, and carrying over the Gallery advanced. THe Sappe L H being advanced through the out-brestwork and covert way unto the Ditch, Fig. 43. all that remains is that you fill the Ditch with a solid bank of earth carried on quite over it, and that the Gallery be built upon this bank. 1. The Ditch whether it be wet or dry is filled with stones, boughs, faggots, logs, and with sacks full of earth; but this Rubbish that is cast in must be so ordered, that the bank may rise quite over, the Ditch as high as the foot of the Rampar, and have such a breadth that the Gallery may conveniently be set upon it. 2. The bank being now finished, there is commonly so much earth brought through the Sappe and cast down on the bank, as may serve to make a kind of little hill betwixt the face of the Bulwark and the besiegers; then casting, with shovels longer than ordinary, the lower part of this heap of earth over the upper, this hill is turned over and over, and is rolled on by degrees to the face of the Bulwark. 3. This hill being rolled on some space, there are two gates erected at a little distance from one another; which are so joined together with planks, as well on each side as at top, that no part of them lies open. On that side which regards the Enemy's Bulwark so much earth is cast up, as may make it Cannon-proof: The other side doth not need so much covering. Also the upper part will be sufficiently fortified against fire, if it be covered with a foot or a foot and half of Earth. In like manner the rest of the parts of this Gallery shall be continued till they come to the Rampar. The width of these gates is either 9 or 10 feet, the height 10 feet, the thickness of its beams or timbers 6 or 7 inches, half a foot. 4. This is the Theory of Galleries, which you'll hardly describe easier than build. In the universal affair of the Siege there is nothing more dangerous than this enterprise: Nevertheless the danger seems to be lessened by these means. 1. That rolling hill of earth betwixt the face of the Bulwark and the Workmen, keeps their front safe. 2. The opposite flanque, as well that of the Bulwark as that of the Courtine, is so battered with Cannon, that the side of the Gallery cannot be broken from thence by the Guns of the besieged. Also from the Trenches of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, the Musqueteers that guard the bvilders of the Gallery, are continually firing on every part of the Rampar. 3. They work most commonly in the night. 4. They secure their sides with faggot which they set upon cleftwood, commonly called candlesticks, by which means they escape many shots, and hid themselves from the sight of the Enemy. CHAP. XXIII. Of the Mine. Fig. 43. THe Ancients also used Mines, but to a different end, and after a different manner. In this Age now that this Art may seem to have attained its perfection, the business is done almost after this manner. 1. The Gallery A A being brought over to the face of the enemy's Bulwark, you design the place where you intent to put the powder. Then digging two or three turn C E, E F, you come to the place appointed K by the conduct of a needle; the channel C E F G is made winding, that the powder might not so easily get out toward C. It is 4 feet or 4 1/● feet deep, 4 feet or 3 1/● feet wide, yet it is made narrower the nearer you come to the place appointed. 2. When you come to the place appointed K, there you dig a place to lodge the powder, whose height is commonly 6 or 7 feet, the side of its base 4 or 5 feet; here you put your Barrels of powder so as to set them close together in the place, for so the powder will be all lighted in a shorter time; and therefore does it effect the stronger. This also experience hath taught us, that the earth of the broken Bulwark will fall towards that part, toward which the greatest space was left between the Barrels and the Superficies of the place where they are put; therefore if you would have the Earth fall towards the Enemy, you shall put the powder nearer the side φ N, if towards etc. 3. One Barrel of powder will blow up 12 feet of earth; hence gather how many Barrels are to be put in. The powder must not be long carried in before you intent to put fire to it, otherwise it would grow moist, and be spoilt. 4. The mouth of the Mine C must be diligently stopped, only leaving in it a Trunk or hollow pipe full of powder for the Train, reaching the powder in K, that putting a match to it you may blow up the Mine at the time appointed. As for the Attacque itself, which is ordered when the Mine is sprung and the breach made, I leave that to the Officers and Soldiers, to whom these things belong. CHAP. XXIV. Of defending Towns. 1. THe first beginning is to keep the enemy from the Town as far off and as long as you can. Therefore whatsoever without the works can put a stop to the Enemy, the Besiegers must possess and defend as long as they can. 2. They must use all their endeavour to hinder the approaches of the Enemy; therefore let them sally frequently (but warily, lest they fall into snares to the irreparable loss of the Town) and rout and kill the Pioners and Soldiers; Let them throw down the Lines that are finished, and if they cannot carry away their Guns, they must spike them up, by driving Nails in their Touch-holes. 3. Those outward works which they can keep no longer must be retrenched, (see what we said before of Retrenchments) but if they are utterly like to be lost, they must be blown up together with those that possess them. 4. The sapping of the out-brestwork must be intercepted by a counter and transverse Sappe. 5. The filling of the Ditch and the building of the Gallery must be hindered at a distance by the continual firing of Muskets, great Guns, hand Granades, and other fireworks; nor is there any other way if the Ditch be full of water. But if the Ditch be dry, than they must fall upon the bvilders of the Gallery with handy-strokes, as well as with all that which I declared above. And the Gallery itself must either be destroyed by fire, or blown up with a Mine. 6. But if notwithstanding all this, the force of the Enemy prevailing, the Gallery is brought over to the Bulwark, and the Bulwark itself be undermined. Against this plague no remedy remains, but to find out the place of the Mine. To do this they use several practices. Some by the motion of Pease leaping on a Drum-head well braced, do conjecture at the place of their digging; others boaring a very long Augur into the ground suspected, and applying their ear to it, think to hear the strokes of their digging; others use other ways to discover it. The most certain way is by countermining to search the foundation of the Bulwark. The Mine being found, the powder must be carried out; but if the straightness of time will not permit, it must be wetted, and a passage opened for the fire. 7. The Bulworks being blown up, if the Besieged have no inward works remaining, the last refuge is, that since they can no longer resist the Enemy with wall and Rampar, that they stop his passage with arms and hands as he is breaking in at the breach. Which since they are rather the parts of Captains and Soldiers than the Engineers, I leave the rest to them, and put an end to this treatise. FINIS. A New, Exact, and most Expeditious METHOD Of Delineating all manner of FORTIFICATIONS (Regular and Irregular) As well from the INTERIOR, as from the EXTERIOR POLIGONE; Being comprehended within the Two Faces or Superficies of a MEDAL. LONDON, Printed in the Year 1672. A New, Exact, and most Expeditious METHOD Of Delineating all manner of FORTIFICATIONS Regular and Irregular, (as well from the Interior, as from the Exterior Poligon;) being comprehended within the Two Faces or Superficies of a MEDAL. The use of the First Face or Superficies of the MEDAL as represented in Fig. A. THe first Face or Superficies of the Medal serves to delineate all manner of Fortifications from the Base or Exterior Poligon; And that 1. From a Pentagon to a Right Line, as being the more perfect 2. From a Square to a Pentagon, as being the less perfect Figures. 1. From a Pentagon to a Right Line. Having divided the given Base or Exterior Poligon A A (as in Fig. C,) into two equal parts in the point D; from that point D erect a Perpendicular D E of a sufficient length. Then take any measure whatsoever, (be it a Chain, Pole, Staff, or Stake out of a Hedge) and mark out 3, or 6, or 9, or 12, or 15, or 18, or 21, or 24, or 27, or 30 Lengths upon the Line A D in the point B; from which raise a Perpendicular B C equal to ⅓ of A B, so is C a visual point, through which is to be drawn the Line A F, cutting the Perpendicular D E in the point E; And E a visual point, through which is to be drawn the Line A N. Which done, divide the Perpendicular D E into eight equal parts, and make either of the Lines E N and E F equal to nine of those parts. And then from the points N, and F, of the Lines A N and A F, let fall the Perpendicular N O, till it cut the Line A F in the point O. And so likewise the Perpendicular E P, till it cut the Line A N in the point P. Lastly, join the points A O N F P A, and so you have A O, and A P for the two Faces; N O, and F P for the two Flanks, and N F for the Curtain of that Fortification. And observing the same Method from all the Bases, the Fortification becomes entire, as in Fig. C. 2. From a Square to a Pentagon. The Method of delineating from a Square to a Pentagon, is the very same with that from a Pentagon to a Right Line; Only instead of marking out three Lengths upon the Half-Base, you are to mark out 15 for the Line G H. And instead of (1) you are to allow (4) for the Perpendicular H I. And lastly, instead of dividing the Perpendicular K L into eight parts, you are to divide it into five; and of those parts you are to set off seven both upon the Line L M, and upon the Line L R. And this is all the difference, as may be clearly seen in Fig. D. The use of the Second Face or Superficies of the MEDAL, as represented in Fig. B. THe second Face or Superficies of this Medal directs how to delineate any Fortification by the Interior Poligon; And that from a Square to a Right Line: For Example. The Interior Poligon D F O being given (as in Fig. E) first draw the Capital Lines A G, K T, and M Q of a sufficient length. Then by the foregoing Directions, describe a Fortification inward upon this Interior Poligon (as though it were an Exterior;) Which done, continue the Curtains, and so you have given you the two Lines A C, and K M, which you are to divide equally in the points B, and L. And from those 2 Points to draw the four Lines B D, B F, L F, and L O: As likewise from the two points, E and N, you are to draw the four Lines E G, E H, N T, and N Q; so as E G, may be parallel to B D, E H to B F, N T to L F, and N Q to L O; Or (which is the very same thing) make the Angle D E G, equal to the Angle A B D; the Angle F E H, to the Angle C B F; the Angle F N T, to the Angle K L F; and the Angle O N Q, to the Angle M L O. Lastly, from the four points of Intersection, viz. G, H, T, and Q, draw the Lines G H, and T Q, which are the two Bases sought; upon which, by the foregoing Method, describe a Fortification Inward, and the Work is done. Only whensoever the Bases (and consequently the two Faces of a Bastion) do not meet in a point, (as very rarely they will) the Face of the less Half-Bastion cuts off the Face of the greater Half-Bastion; which hath this good property among many other, that it often opens or enlarges the Angle of the Bastion very considerably. Thus in Fig. E, the Face R H cuts off the Face P T in the point S. There is one thing observable in the Method both of the first and second Face of this Medal, which is this, That instead of taking three Lengths of any Measure for the Line A D, in Fig. C, and then setting off (1) for the Perpendicular B C, I might divide the Half-Base A D into 3 or 6, or 9 equal parts, and take ⅓ thereof for the Perpendicular D E, because the Line D E bears the same proportion to the Line A D, as the Line B C doth too the Line A B. So likewise, instead of taking 15 or 30 Lengths upon the Half-Base G K in Fig. D, for the Line G H, and setting off 4 or 8 of those parts in the Perpendicular H I, I might as well have divided the Half-Base G K into 15 or 30, and set off 4 or 8 for K L. For as K L is to G K; so is H I to G H. But forasmuch as this last way is more difficult and tedious than the other before mentioned, That was made use of, and This laid aside. FINIS. A A PENTAGONO AS LINEAM RECTAM INTROSUM. PRO QVADRATO B A QVADRATO AD LINEAM RECTAM. EXTRORSUM. C A PENTAGONO, ad Lineam Rectam, Introrsum. D Pro QUADRATO, Introrsum. E A QUADRATO, ad Lineam Rectam, Extrorsum. A SECOND METHOD (Not inferior to the former) Of Delineating any FORTIFICATION, By the INTERIOR POLIGONE given. LEt the Interior Poligone given be (A C) in the opposite superficies of a Medal or (D F N V) in the adjoining Figure. Having delineated a Fortification inwards, and thereby gotten the second Interior Poligone according to the foregoing Direction, Page 2. continue the Distance B E to a sufficient length: For as the length of A C in any number of Parts, is to the Distance B E, so is the length of D F (being divided into the same number of Parts to the Distance E G. Then draw a Line X Y through the Point G parallel to D F, which Line X Y is the true Base, upon which is to be erected a Fortification by the Directions of Pag. 1. And this Method being continued from each respective Poligone given, the Fortification becomes perfectly delineated. For as H K, is to I L; so is F N, to M O. And so likewise as P R, to Q S; so is N V, to T W. Than which nothing can be more evident, as to the matter of truth and demonstration; or more expeditious, as to the real practice and performance. A Caveat to the Reader. BUt to prevent any mistake, which some persons, either out of ignorance, or inadvertency, may run into, it will be convenient, to let the Reader understand, That although in Fig. C, Pag. 3. the middle Base (or Poligone) A A, is much longer than that on the left hand, and almost double to that on the right, that so it might appear to the eye to be sufficiently Irregular, and also that it might resemble the Fortification in Fig. E, where, without such an inequality of Bases, the Method of one Face cutting another, could not be so plainly expressed, or so clearly discerned. (Otherwise it had been more easy to have made all the Bases equal within that very same Figure C, than it was to make them so in this opposite Figure F.) Yet notwithstanding this new Method takes it for granted, That all who pretend to make use of it, be so far instructed in the first Principles of Fortification, as to know, That when ever an Exterior Poligone, or rather a Ground-Plot, is given them, they are so to design and contrive it, That, if possible, all the Bases, (if not the Angles) may be equal, That so there may be a perfect Harmony and Symmetry in all the parts thereof. This new Rule does likewise suppose, that he already knows, That, if it be practicable, each of his respective Bases, (or Exterior Poligones) ought to be about 1150 Feet; but never less than 1024. nor yet more than 1280. That so the Lines of Defence may not be too short on the one hand, nor exceed the Port of a Musket on the other. As likewise, that the Angle of his Bastions be in no case whatsoever less than 60 Degrees. But now, where either the situation of a Place, or the old Walls or Ramparts of a Town, or City, admit not any such equality, either of Bases, or Angles, there the Hercotectonick Laws do permit the Engineer, either to open, or sharpen his Angles, or else to lengthen, or shorten his Lines, as he shall find it necessary. A QVADRATO AD LINEAM RECTAM EXTRORSUM THE COUNT of PAGAN'S METHOD Of Delineating all manner of FORTIFICATIONS (Regular and Irregular) FROM THE Exterior Poligone. REDUCED TO English Measure, And converted into HERCOTECTONICK-LINES, By S. M. LONDON, Printed in the Year 1672. ICHNOGRAPHICK Terms: OR Words of Art for Lines in Fortification, necessary to be known. Lines English. Latin. French. German. B D Side of the Exterior Poligone. Latus Multanguli Exterioris. Poligone Exterieur. Beite der Bollwercks' puncten. K N Side of the Interior Poligone. Latus Multanguli Interioris. Poligone Interieur. Die Seite der Burgh. S B or S E Radius of the Exterior Poligone. Radius Multanguli Exterioris. Le grand demidiameter. Des eussersten Bieleks halbe Mittellinie. S K or S P Radius of the Interior Poligone. Radius Multanguli Interioris. Le petit demidiameter. Der Bestung halbe Mittellinie. K B Capital Line. Capitalis. Ligne Capital. Haupt-linie. B F Face. Fancies Propugnaculi. La Face. Gesicht-linie. F L Flanck. Ala Propugnaculi. Flancq. Die Streich. L Q Curtain. Cortina, & Chorda. La Courtine. Ball. B Q Line of Defence. Linea Defensionis. Ligne de Defence. Behrlinie. C M Distance between the Ext. & Int. Polig. Distantia Multangulorum. Distance des Poligones. Die weyts der beyden Biel-eck. K L Shoulder. Collum. La Gorge. Hals Keel-linie. B C Half-Base. Semi-Basis. Demi-Base. H Q Compliment. Complimentum. Compliment. ICHNOGRAPHICK Terms: OR Words of Art for Angles in Fortification, necessary to be known: Angles English. Latin. French. German. K S N Angle of the Centre. Angulus Centri. Angle du Centre. Mittelpunets' eck. O K N Angle of the Figure. Angulus Figurae. Angle du Poligone. Keelpunct. R B F Angle of the Bastion. Angulus Prepugnaculi. Angle Flancque Bolwercks' eck. B H D Angle Flancking. Angulus Defendens. Angle Flanquant. Der Schutzwinckel. B F L Angle of the Face and Flanck. Angulus Faciti & Alae. Angle du Flancq & de la Face. Der winckel der Streichen und Gesich-linie. 1. From a Pentagone, to a Right-line. HAving divided the given Base (or Exterior Poligone C D in Fig. I. which suppose to be 575 English Feet) into two equal parts, in E; From the Point E raise a Perpendicular E L of a sufficient length. This done, enter the Number of the Half-Base (viz. 575) in the first Column of the Hercotectonick Table, (over which is D. Base, and look what number answers to it in the second Column, (over which is Perp.) and finding it to be 192. take from off your Sector or Scale 192, and set it on the Perpendicular E L, where it will terminate in the Point F. And then from either Point D and C of the given Base C D through the Point F, draw the Lines C G and D H of a sufficient length. In the next place, enter the number of the same Half-Base, (viz. 575) in the third Column of the Table, (at the head whereof is D. Base) to which you will find the Number 351½ answers in the fourth Column (over which is the word Face). This likewise you must find upon your Sector or Scale, and by it, determine the two Lines C I, and D K. Lastly, enter the aforesaid Number 575 in the fifth Column of the Table, which you will find answered by 204½ for the Compliment; which Compliment (or 204 1/●) must determine the two Lines F G and F H. Which done, join the Points C I H G K D; so have you C I and K D for the two Faces; H I and G K for the two Flanks; and H G for the Curtain of that Fortification. And observing the very same method from each Base, the Fortification becomes perfectly delineated; as in Fig. I. 2. For a Square. THE Method for delineating a Fortification upon a Square, is the very same with that from a Pentagone to a Right-line; only the Proportions, and consequently the Numbers expressing those Proportions are different, as may be better seen in the second Part of the Hercotectonick Table, compared with Fig. II. I. II. But now forasmuch as in Fortifying Cities, and other Irregular places, it often happens that the Engineer is constrained to make use of the old Walls and Ramparts, and consequently the Courtines must be the same with those Walls: Therefore the Count de Pagan thought it would be some help, to give a Rule to find the Distance between the two Poligones; which Distance is also found in the 8th. and 16th. Columns of the Table. For example, in Fig. I. E L (or the Distance between H G and C D) is 257 Feet, and four Inches; And in Fig. II. M N (or the Distance between O P and Q R) is 207 Feet, and eight Inches: But as to this last particular, namely of Fortifying from the Interior Poligone, the New Method comprised in a MEDAL, is much more exact and expeditious. Hercotectonick Table LINEAE HERCOTECTONICAE NOVAE, Augustisimo Principi CAROLO TWO Magnae BRITANNIAE, etc. REGI; humillimè oblatae à Samuele Morlando equity Aurato et Baronetto, nec non Camerae Regis Privatae Adjuncto. Anno Salutis MDCLXVI Of the Dimensions of the Bastions, Ramparts, Ditches, Halfmoons, Counterscarps, etc. AS concerning the Measures and Dimensions of the Count de Pagan's Bastions, Ramparts, Ditches, Halfmoons, Counterscarps, etc. it would require more time than I can at this present afford, and a larger Volumn than I have designed for this Treatise; forasmuch as the Count has given Names to many things, quite different from those in other Authors. I shall therefore leave the comparing those differences to those who are more at leisure, and only content myself to have set down some few of his Proportions, which are adjoined to the opposite Table of Plain-Angles, which Table is of Excellent and Universal use. The use of the Table of Plain-Angles. WHen you would measure an Angle of any Field or Plot of ground; As for example, let the Angle to be measured be C A B in Fig. C. Take a Chain and measure 30 Links (it matters not of what length those Links be, so they be equal one to another) from A to C, and so from A to B. And at B and C stick up two sticks: And then measure with the same Chain, the distance between C and B, and finding it to be 20, seek 20 in the Table in one of the Columns over which is the word (Bases) and the Number of the next Column answering to it, is the true Number of Degrees and Minutes of the Angle sought, viz. 40° 00′. After the same manner, because the distance between I and K is 55 Links, the opposite Angle is 132° 55′. Again, suppose you desire to lay out an Angle of 100° 05′. I first stick down two sticks at the two ends or Terms of any given Line F E, (divided into 30 equal parts) in the Points F and E. Then fastening a Chain of 30 Links (equal to those 30 equal parts) at F, and one of 60 Links at E, I enter the Table of Angles with 100° 05′; and finding 46 to answer to it, wherever the Chain of 30 Links, and 46 of the Chain of 60 meet, (as in G.) thence draw the Line F G, and you have what you desire. And after the same manner may any Angle be laid out most exactly and expeditiously from 10 Minutes to 180 Degrees. ●ES BASTIONS, DES RAMPARTS, ET DES FOSSEZ Largeur des Ramparts 45 Largeur des Parapets 19 Hauteur de la 3 casematte, du fond du sossé 38+ Hauteur des Parapets au dedans 6+ Hauteur des Parapets au dehors 5+ Largeur de Grand Fossé 102 Profondeur du Grand Fossé 19 La largeur du Fossé, compris entre le premier et 2 Rampart du Bastion est diverse selon la Fortification, & le Poligone, et sa profondeur 13 Reds, ou plus. Et la largeur du Flanc retiré, 77 Pieds DES DEMI: LUNES, ET DES CONTRESCARPES 1 Method Pieds d'Angl: Demiegorge de la Demi-Lune 192 Face de la Demi-Lune 320 Largeur de la Grande Contrescarpe 320 Largeur de son Fossé 77 Largeur de la Petite Contrescarpe 26 Lafoy Demi-Lune se form tousiours sur l'Angle Rentrant de la Contrescarpe. 2. Method Pieds d'Angl: Largeur de la Grande Contrescarpe 161 Largeur de son Fossé 77 Largeur de la Petite Contrescarpe 26 Demi-gorge de la Demi-Lune 128+ Face de la Demi-Lune 217+ ●es Flanes de la Grande Contrescarpe comprennet Parapets, et pewent ainsi contenir 9 Pieces de Canon. LIGNE DES ANGLES PLANS' tousiours compris par deux costez de trente Pieds. Angel's Bases 1 2 3 4 10 5 6 7 8 9 20 10 11 12 13 14 30 15 16 17 18 19 40 20 21 22 23 24 50 25 26 26 28 29 60 30 31 32 33 70 34 35 36 37 38 80 39 40 41 90 42 43 44 45 100 46 47 48 110 49 50 51 120 52 53 130 54 55 140 56 57 150 58 160 59 170 180 60 The Figure of a most useful Instrument, by the help whereof any Poligone, from a Square to a Dodecagone, (which is as much as is required in any Fortification) may be described, not only with greater expedition, but likewise much more exactly than by any Sector, Scale, or other Instrument or Method whatsoever. THE use of this Instrument, is only to lay it upon your Paper, and holding it fast with your left hand, to mark out any Poligone therein contained with the point of a Needle, by its respective Figures, and so join the Points. And if you desire to describe a Poligone larger than the Instrument, (as is the Dodecagone in this Figure) it is easy to continue the Lines from the said Pricks to the Circumference: And if it be desired to have a Poligone less than the Instrument, the reason is the same. ARCHITEC: MILIT. 1 2 3 4 5 ARCHITEC. MILIT. 6 7 8 9 ARCHITEC. MILIT. 10 ARCHITEC. MILIT. 11 12 13 14 15 16 ARCHITEC. MILIT. 17 18 19 20 21 22 23 24 ARCHITEC. MILIT. 25 26 27 28 ARCHITEC MILIT. 29 30 31 32 33 34 ARCHITEC. MILIT. 35 36 X 37 38 39 40 ARCHITEC. MILIT. 41 42 43 THE Complete Gunner, IN THREE PARTS. PART I. Showing the Art of Founding and Casting Pieces of Ordnance, with the composition of Metal thereunto necessary. The Composition and Matters of Gunpowders, the Several Sorts, Colours, and Operation. PART II. Discovers the necessary Instruments, and variety of Instructions to the completing of a Gunner, with a Table of Squares and Cubes serving for the Resolution of Questions of Gunnery and other Arts. AS ALSO The way of taking Heights, Distances and Profundities, either with or without Instruments. PART III. Shows the Nature of Fireworks, the manner of Composing many that are Excellent and Useful both for Sea and Land, for the defence of ourselves as well as the offence of our Enemies. Translated out of Casimir, Diego, Vffano, Hexam, and other Authors. To which is added the Doctrine of Projects applied to Gunnery by those late famous Authors Galilaeus and Torricellio, now rendered into English. TOGETHER WITH Some Excellent Observations out of Mersennus and other famous Authors. LONDON, Printed for Rob. Pawlet, Tho. Passenger, and Benj. Hurlock. 1672. TO THE READER. Courteous Reader, AMong Arts and Sciences Mathematical Gunnery will not deserve the least respect which has been practised for many years (as you may read in the first Chapter of this Book where we treat of its Original) and from time to time Necessity and Art together have produced many new Invention: so that some may judge it almost impossible to add more unto this Art; and are ready to say of this as of other Studies, Nil dictum quod non dictum prius. But we have not only endeavoured the inquisition into the most knowing Professors of these Arts both Germane, Italian, Frenchmen, Netherlander, etc. from whence we have drawn the more Excellent and useful parts which were never before in our English Tongue; but may boldly adventure to call some things in it new: And finding the great Occasion which these present times do require in the knowledge of these things made me the readier to compose this Work, adjudging it a very great injury to our Countrymen to be deprived of the knowledge of such things which are of so great importance in this very juncture of time. I did therefore encourage myself in this Work, hoping my endeavours in the same will show my willingness to serve my Countrymen: And as it is the part of wise men not to censure any thing, without a good consideration and a perfect knowledge of the subject upon which they ought to ground their judgement: So also I hope you will not blame my Endeavours, when you have judiciously examined the same. I have divided it into three Parts, endeavouring that it might be imperfect in nothing that is necessary to this Art, or useful for a Gunner to know. I will assure you that I have no other end in publishing this Treatise, than what I have mentioned before. I shall only crave your pardon for the faults that may be committed in the Printing, as being not there present at the Correction of any part of it, my occasions calling me other ways: yet I hope their care was so much that the faults are not material, or at most not so much but your Courtesy may supply that defect. So I recommend this Work to your good reception, and bid you farewell. W.T. THE Complete Gunner. CHAP. I. Treating of the Earth necessary in making of Moulds for the Casting of Pieces of Ordnance, with the manner of Casting, etc. WE will not dispute of the first Invention of Guns, that is, whether it came from Archimedes, as the Italians do report, or from an Englishman, or from a Monk, for this knowledge matters not much to the Art, nor is it of any profitable signification to the Artist; especially considering, that Authors do not really consent in this thing. Our intent is therefore not to trouble the ingenious Students with vain uncertain repetitions, but to compose a complete Piece of Gunnery, and therein to discourse from the beginning to the end, all that is necessary to be known or learned (after the knowledge of common Arithmetic) by one that intends to be a perfect Proficient in the said Art. We do suppose it therefore necessary for a Master Gunner to know first the making of Moulds and casting of Pieces. Therefore I shall first begin to discourse of the property and Nature of the Earth fit for casting, or making Moulds; for this is of great moment, considering that many, or indeed most Earth's are not for this purpose; for the Earth fit for the casting of Pieces of Ordnance must be such as will not be melted or fuse, although it be put into a very great fire, but must remain firm and hard: and these Earth's are generally of a Reddish, or Iron-like colour, which is well known to many Potters, especially such as make Chemical Vessels. The Earth being obtained, it must be sifted and cast up after the usual manner, as men do in the making of Mortar; then let it be moistened with an Alchalated Water (especially such as is made of Niter) for that purpose, and make it like paste; then, as is usual, let it be beaten up strongly with an Iron Bar; the more 'tis beaten the better it is: in the beating add one sixth part of Horse dung, and a proportionable part of Flox or Hair, and let it again be well beaten and incorporated, always keeping a Moiety of this Earth, without Hair or Flox, which is for Groundwork; and these Compositions or Earth thus incorporated, you must reserve for the making your Moulds for Pieces of Ordnance, according to the Rules prescribed in the next Chapter. CHAP. II. Of making Moulds, and Casting Pieces of Ordnance, with the mixture of Metals, and allowance of Powder for proof. AS a Master Builder when he intends the Building a Ship, makes first a Mould or Moddel of the same; so the Master Gunner, or he that takes in hand the business of Casting Guns, must have a form or Model of his Piece intended made of wood, or such other matter he may think most convenient, which then being brought to the Founder with an intent to be Cast, must first be smeered all over with Palm Oil, or instead of that, our Lard or Hogs-grease, than first cover it over with the said earth thinly, and let it dry leisurely, then lay on more, increasing it to such a thickness, as you may judge convenient for your purpose; and it must be so made that it may be taken into several parts, so that the pattern may be taken out, and the Mould again exactly closed, and the outside strengthened with Iron plates as long as the Chase of the Piece is, and hooped together with Iron hoops to knock on and off. Then must there be made (with the same earth upon a square Bar of Iron, bound round with a Cord that the clay may stick well) a form exactly round, of the fashion of the concave of your Piece (whether you intent it a Cylender or a Chamber-board Piece) proportioned both in length and diameter, and it must be placed exactly in the middle of the concave; and when all is well joined together, be sure it be well polished and smoothed, that the Metal may run the better, and be the clearer from flaws, holes, or clefts. In the beginning of your work take care that your Mould be exactly proportionable as to height and substantialness of Metal, according to the nature of the Piece you intent. That is, the Canon double-fortified must be so cast that the Diameter at Muzzle be but 7/18 of the Diameter at Britch. The lesser Cannon at Britch to be ¾ so big as the greater Cannon 9/18 at Trunions, and 1/18 at Muzzle, whereas ordinary fortified Cannons have at the Touchhole 7/8 at the Trunions 5/8 and at the Muzzle 1/8, all lesser Pieces in that kind have 18/18 at the Touchhole 25/●8 at Trunions, and 9/18 at Muzzle; and the ordinary fortified Culverins are fortified every way like the double fortified Cannon, and the lesser Culverin like the ordinary fortified Cannon in all respects. Great care must be taken in the Casting of Pieces of Ordnance, that they be equal every way in proportion of Metals, that is, that the Cylender be in the very middle of the Metal, that it may be truly bored, otherwise your Piece will fail the Artist that shall use it, until the error be known. In the next place let the Trunions be exactly placed in a Diagonal line with the Axis of the Piece; and they may be placed in their proper distance from the Muzzle and Britch, if you observe these Rules. Take the length of the bore of the Piece from Muzzle to Britch, divide that measure by seven, and multiply that sum that cometh of the Quotient by three, the Product will show you how many inches the Trunions must stand from the lowest part of the concavity of the Piece. And farther note, that the Trunions ought to be placed so, as ⅔ of the Circumference of the Piece, may be seen in that place where the Trunions are set. When all additional Patterns, as Britch, etc. be made and Luted in their proper place, all things at pleasure being neatly added to the pattern, let the Mould then be fixed or placed so as is most convenient for the pouring in the Metal; so when the Metal is cast, the perfect impression will be made upon the superficial part of the Piece, and the Cylender will keep the bore proposed according to what you have prescribed, the length of the Piece and its Diameter of the bore may be found by the following Table in the next Chapter. For the Metals generally used for those Guns, generally called brass Guns, they are mixtures, and many times varied as experience will give leave. Some of the chiefest do approve of this mixture, that is, to every hundred Weight of Copper 24 pounds of Tin, and 6 pounds of Latin. Others to 100 l. of Copper, add 8 l. of Tin, and 10 l. of Latin. Others to ever 100 l. add 20 l. of Bell-Metal, which is 25 l. of Lead and Tin to every 100 l. of of Copper. Some add Tin, Led, Copper, and Lapis Calaminaris together; so every one follows such ways of Composition as doth most please his own Experience. The Copper and other better Metals being once melted, the Tin and Lead is added for the better and quicker fusion; and the higher the Metal is in fusion, the more solid and compact your Metal will run and settle. The Latin doth incorporate and cause the Piece to be of a good colour, and the Tin doth strengthen and bind the other matters together. Now a Piece of Ordnance being Cast, before it comes to Service, it must be put to trial; for which purpose there is used for proof, according to the weight of the shot, about two thirds, or four fifths of that weight in Powder, and for smaller Pieces more. CHAP. III. The Names of the principal Pieces of Ordnance used in England, their Weight, Length, Diameter of the Boar, Height and Weight of the Shot, allowance of Powder. THe greatest in use is the Cannon Royal, which is in weight of Metal about 8000 l. in length about 12 foot, carries a Shot of 7 ½ inch. Diameter, and its weight is 58 l. of Iron, its bore is 8 inches, requireth for her charge in Powder, 32 l. 8 z. Demi-Cannon of the greater size, called by some Cannon of Seven, whose weight of Metal is 7000 l. in length about 12 foot, carrying a Shot of 6 ¾ inch. Diameter, and its weight of Iron is 42 l. 10 z. the Diameter at bore is 7 inches, requireth for her charge in Powder 20 l. Demi-Cannon great size, it's weight of Metal is 6000 l. in length about 12 foot, carrying a Shot of 6 ¼ inch. Diameter, and its weight in Iron is 34 l. the Diameter at bore is 6 ½ inch. requireth for her charge of Cannon Powder 18 l. Demi-Cannon ordinary, its weight of Metal is 5600 l. in length 11 foot, carrying a Shot of 6 1/● inch. Diameter, its weight in Iron is 32 l. the Diameter at bore is 6 ½ inch. requireth for her charge in Powder 17 ½ pounds. The lowest Demi-Cannon, whose weight of Metal is 5400 l. being in length sometime 10 and sometimes 12 foot, it carries a Shot of 6 inches, the weight of that Shot in Iron is 30 l. the Diameter of the bore is 6 ¼ inch. it requireth for charge in Powder 14 l. Culverin of the largest size, weighs about 4800 l. being in length 10 or 12. foot, it carries a Shot of 5 ●/● inch. Diameter, the weight of that Shot in Iron is 20 l. the Diameter of the bore is 6 ¼ inch, it requireth for charge in Powder 12 l. 8 z. Ordinary whole Culverin weighs about 4500 l. being in length about 12 foot, it carries a Shot of 5 inches Diameter, the weight of that Shot of Iron is about 17 l. Diameter at bore is 5 ¼ inch. it requireth for charge in Powder 11 l. 6 z. Culverin of the least size, weighs about 4000 l. being in length about 12 foot, it carries a Shot of 4 ¾ inch. Diameter, the weight of that Shot of Iron is 15 l. Diameter, at bore is 5 inch. charge of Powder is 10 l. Demi-Culverin of the greatest size weighs about 3000 l. being in length 10 or 12 foot, carries a Shot of 4 ½ inch. Diameter, the weight of that Shot of Iron is 12 l. 11 z. Diameter of the bore 4 ¾ inch. charge of Powder is 8 l. 12 z. Demi-Culverin ordinary, weighs about 2700 l. being in length 10 or 12 foot, carries a Shot of 4 ¼ inch. Diameter, weight of that Shot of Iron is 10 l. 12 z. Diameter of the bore 4 ½ inch. charge of Powder is 7 l. 4 z. Demi-Culverin lower than ordinary, weighs about 2000 l. being in length 9 or 10 foot, carries a Shot of 4 inches Diameter, weight of that Shot 9 l. Diameter of the bore 4 ¼ inch. charge of Powder is 6 l. 4 z. Saker of the oldest sort, of 1800 l. weight, being in length 9 or 10 foot, carries a Shot of 3 ¾ inch. weight of that Shot 7 l. 5 z. Diameter at the bore 4 inches, charge of Powder 5 l. Saker ordinary, of 1500 l. weight, in length about 9 foot, carries a Shot of 3 1/8 inch. Diameter, weight of that Shot 6 l. 0 z. Diameter at the bore 3 ¾ inches, charge of Powder 4 l. Saker of the lowest size, of 1400 l. weight, in length about 8 foot, carries a Shot of 3 ¼ inch. weight of that Shot 4 l. 12 z. Diameter at the bore 3 inches and a half, charge of Powder 3 l. 6 z. Minion of the largest size, of 800 or 1000 l. length 8 foot, height of the Shot 3 inches, weight of the Shot 3 l. 2 z. height of the bore 3 inches, and one quarter, the charge of Powder, if of 800 l. two pounds and a half, if of 1000 l. three pounds and a quarter. The ordinary Minion of 750 l. in length 7 foot, height of the Shot 3 ¼ inch. weight of the Shot 3 l. 4 z. height of the bore 3 inches, charge of Powder 2 ½ pounds. Faucons of 750 l. length 7 foot, height of the Shot 2 ½ inch. weight 2 ½ pounds, height of the bore 2 ¾ inch. charge in Powder 2 ½ pounds. Fauconet of 400 l. in length 6 foot, height of the Shot 2 1/8 inch. weight 1 l. 5 z. height of the bore 2 ¼ inch. charge 1 l. 4 z. of Powder. Rabnet of 300 l. length 5 foot, height of the Shot 1 1/3 inch. weight 8 ounces of Iron, height of the bore 1 ½ inch. charge of Powder 12 ounces. Base of 200 l. length 4 foot, height of Shot 1 ½ inch, weight 5 ounces, height of the bore 1 ¼ inch. charge of Powder 8 ounces. There are other Pieces in use in our Nation, which are called Bastard Pieces; of which you shall have a particular account in its proper place. CHAP. IU. The Names of the Principal parts of a piece of Ordnance. IT is necessary for him that intends to be a Gunner to understand, after the knowledge of the Piece in general, to know and learn every part and member of a Piece of Ordnance; for well understanding the same take these Instructions following. All the outside of the Piece round about is called the superficial part of the same, or Surface of the Piece; the Inner part is called the concave Cylinder, and Soul of the Piece. The full length is called the Chase of the Piece; so much of the Cylinder or concave of the Piece as contains the powder and Shot is called the Chamber or charged Cylinder, the remaining part to the small end of the Gun is called the vacant Cylinder. The Spindle standing out, or Ears by which the Piece must hang in the Carriage, is called the Trunions; the space between the Trunions, the gravity of the Centre. The Pumel or Button at her coil or Britchend is called the Casacabel or her Deck, the little hole the Touchhole, all the metal behind the touchhole the Breach or coil, the greatest ring at her touchhole the Base Ring, the next ring or circled the reinforced Ring, the next the Trunion Rings, the next before the Trunions is called the Cornish Ring, the foremost next the Muzzle is called the Muzzle Ring, Lastly, all the rings, Circles, Eminencies, at her Muzzle, and so those behind the base Ring, are Prizes. Let the Piece with its several names be placed by this Chapter. Fig. 1. CHAP. V The Mounting of a Piece of Ordnance in its Carriage. THe Gunners upon Land-Service, for the conveniency of mounting a piece of Ordnance, that is by any means whatsoever dismounted, have for their principal Services, a Screw, and a Ghynne, and their appurtenances (which you will find in their proper place) by whose help they are able to mount a Piece, and place him in his Carriage, whereby he may be able to perform the work intended. Which to perform artificially, observe these Rules. Before you endeavour to mount your Piece, above all things have a great and diligent care that the Ghynne be very firmly set, so that it may not slip any way; but so placed, that the Poultry or Truckle coming down from the head, fall just between the Trunions, or gravity of the Piece, whereof to be assured you may let fall down from the head of the Ghynne a Plummet with a Line, or for want of a Plummet any stone made fast to a Line, and so moving the Ghynne until the said Plummet fall just upon the Centre of Gravity, which is between the Ears of the Piece, that the metal may fall near equal, or that an easy hand may poise it; and this care must be the more, if the Ground whereon the Ghynne stands be sandy or lose Ground, or the Earth be boggy soft, so that the feet may fail or sink in or give way, according to the greatness of the weight. For sometimes it may be necessary to put planks or some solid thing under the Ghynne and Pins to stay them; but this as necessity shall require. Now the Ghynne firmly placed and settled, the Gunner must get up by the Ladder, or some Steps, to the head or top of it, having the Rope in his hand, shall put it through the uppermost truckle of the head, and let it fall down to another man again, that he may catch it, that he may put it through one side of the Piece to fasten it into the Ears of the Piece, and so having put it through them he may draw it up, until he can give it him that is above, and then put it through the other hole of the Truckle, and give it to him that is under him, who must reach it again to him that is above, and so fasten it to the head of the Ghynne, giving it some turns until it come under the uppermost Truckle. This done, he must fasten it with great diligence to the lower Truckle, by putting the Ears as through the Ring which is under the said Truckle; after this begin to Hoist your Peice, and in the Hoisting put a spar or some such thing into the mouth of the Peice, so that thereby it may be governed, and may not sway from one side to the other, which would be dangerous; for if it should strike against the Rouler or any one of the feet of the Gynne, it may break all, and so spoil both the work and the men tending upon it. Therefore I say, be sure that those who stand by the Spar be careful in guiding the Piece and keeping it steady and right, until the weight of the Piece is well settled, a diligent Eye being had all this while, that neither the feet of the Gynne, nor Rope give way; and be sure every part of the Rope draw equal, and that there be no Knicks, or that they be not tangled one amongst another; and for that purpose, when they begin to hoist the Piece, blows must be given upon the Tackling until it be set tort, and all bear equal. But if you should perceive that the Ghynne or any part give way, presently let your Piece sink, and underlay and settle well the feet of the Ghynne, and that as gently as may be, to the end the Cross beam or Rouler may not be disjoined or broken. Then wind it up carefully and very gently by the help of two men only, and in such a manner, as when one of the Levers is brought down, it must be held there fast until the other has got purchase, and then must this other also be brought down; this must be reiterated so often until it be so high that the Carriage may be placed under it, so that the Trunions may fall into the Sockets, or holes of the Carriage, and then Guide the Piece by the Spar, so that it fall easily in, and so rest itself in the Carriage, and then let it be well clasped over, and then locked in and fastened with Forelocks, and so you may draw away your Piece where you please. On board Ships this Ghynne is not of use, it being the Boatswains business to fix a Tackle that may be able to hoist up any Piece into its Carriage, the Slings one part must come about the Casacabel, and the other part about a Billet, so made that it may fit in at the Muzzle, and by strength of hands, or by help of a Windless, or Capstain, it may be hoist up so that the Carriage may be brought under; so that the Gun being Loared, its Trunions may fall into the holes of the Carriage, which then clasp over with its Iron Clasps; let them be Forelocked, and then with Hand-Tackles be brought where you please. See the Figure of the Gynne, and the Field, and Ship-Pieces mounted in the Figure 11. CHAP. VI The way to draw a Piece of Ordnance, with the necessary things thereunto belonging both for Land and Sea. SEeing we have discovered the way of Casting a Piece, and Mounting it in its Carriage, it follows in the next place that in this Chapter we treat of, and show the manner of drawing them from place to place, for Service; where care must be taken what the way is that you are to pass, for if the way be foul, moorish, and dirty, there is then required as many more Horses as in good ways. That is, For a whole Cannon of 8000 l. you may use 15 couple of Horses, besides the tiller. For a Demi-Cannon of about 6000 l. you may use 11 couple of Horses, besides the tiller. For a Piece of 4000 l. weight, you may use 8 couple of Horses, besides the tiller. For a Field Piece of about 3000 l. use 6 couple of Horses, besides the tiller. For a Saker of 1800 l. weight, you may use 4 couple of Horses, besides the tiller. For a Piece of 1500 l. weight, you may use 3 couple of Horses, besides the tiller. For a Falcon, two couple of Horses, besides the tiller. For a small Drake of about 250 l. one Horse will serve: and by the same Rule you may find how many Horses will draw any weight whatsoever. Many times when Horses are wanting, men are made use of: Upon such occasions, you must divide your men into three drawing files, according to the greatness of the Piece; now to the end the Ranks may spread, and every man may draw equally alike, fasten to the end of the Carriage a Cross beam or bar, to which you must fasten the drawing Ropes, equally at such distance, that one may not impead the other, and let there be besure one to steer the Piece when you come to any winding or turning. If the drawing Ropes be long, 'tis necessary to cross it with Ropes, or some light pieces of wood like a Ladder, with two or more cross pieces; let them be made fast for the better and more steady drawing, and to every there must be a Neck-line fastened to the Ropes, and so to cast over every man's Shoulders, in manner as is used to draw our Western Barges: And you must know your proportion of men fit to draw any Piece of Ordnance, and that must be regulated according to the goodness or badness of the way, and so more or less men, allowing every man to draw about 50, 60, or 80 pounds; for 'tis supposed a man may draw in ordinary way 50 or 60 pounds, but in very good way more than 80 pounds; however 'tis good to have men enough. Let the Sponge, Ladle, etc. be made fast along the Piece to the Ring and Britch end. Sometimes by reason of the unevenness, steepness, or other defects of the way, it sometimes happens, that you may be forced to dismount your Piece, and remount it again; there 'tis necessary every Gunner have with him a Ghynne, a winch, and all appurtenances necessary thereunto. As to the Sea Gunner on board Ship, their occasions require no more than the Wynch; and their Piece being mounted according to the directions given in the former Chapter, then with one or two Tackles he bring the Piece to the place desired, where it ought to be well fastened in its place; for which purpose there is thereunto required Tackles and Britchins; and in case of foul weather, or that any of the Gear or Tackling be suspected, or by my much tumbling every thing hanging upon the Nail, for fear any Bolts should give way or draw, it is usual to nail down to the Deck with Spikes, one Coin behind each Truck, or at least the after Trucks, which to great Pieces are commonly dead Trucks; so that each Piece may have little or no play. But in case any thing should give way in foul weather, then with all speed dismount the Piece as soon as possible you can, for fear of further mischief; for which purpose put in his way as he runs from side to side, Rugs, Pillows, Beds, &c, and stand ready with Crows and Handspikes, and with Tackles, to hitch or catch him close and fast to any Ring by the Ship side, or such other place as best presents. As for the length of the Tackles useful, it is usually known thus; see how long the Piece is, and make the Tackles four times as long, and let the Britchin be twice the length of the Piece, and something more. The manner of drawing of Pieces by Man and Horse, you will see in the third Figure. CHAP. VII. To Grove or Examine the goodness of a Piece of Ordnance, whether it be Flawed, Honycombed, Cracked, Chamber-bored, etc. With the difference of Common, Legitimate, and Bastard Pieces. IT remains necessary for this Chapter to treat, or show the way to know, whether a Piece be serviceable or no, which is usually done in the first proof by Powder, which we intent not to Write of here, having mentioned it before, and more will be said, when we have showed the composition of Powder. That knowledge of a Piece we here intent, is to examine a Piece, bought, or to be taken into Service, whether good or serviceable, or out of many Pieces to make choice of the best, or such as are freed from holes, flaws, cracks, honycombs, etc. And first to know if a Piece be free from crack, or have holes through, take a long stick, longer than the Piece, made of a Hoopstick or otherwise, slit it at one end, so that you may put a short piece of Candle in it, then light the Candle, and put it into the Piece, and so putting it along easily, whilst another laying his Eye close to the Piece, do go along equally with the Candle, until the whole Piece be viewed, and so by help of the Light within side, the Eye without side will perceive whether there be any Flaws, Cracks, etc. This may be done by the reflection of the Sun beams in at the Muzzle of a Piece, by help of a Looking-glass, or polished Steel; but many times a Piece may be Flawed or Honycombed, and cannot be discerned through the Piece, and then the best way to find them out is thus; make the usual search with two or three Springs, or in case you have them not, bend the Iron point of a Half Pike, than put it into the Piece up to the Britch end or bottom of the Cylinder, turning it round carefully and gradually, as you pluck it out, and if there be any Honey-combs, Cracks or Flaws, the end or bended point of the Half Pike will stick or catch at them. To know whether the Piece be Chamber-bored, take a priming Iron that is small, or a piece of Wire, bend it a little at the end, but so that it may go down at the Touchhole, and put it down so far as it will go; Then at the Touchhole close by the Metal of the Piece, make a mark upon the Wire; then gently pluck it up upon one side of the Touchhole, until the bended point stop upon the Metal or upper side of the Chamber; and then make another mark upon the Wire, just by the Touchhole; then draw out the Wire, and the distance between these two marks, is the height of the Chamber or bore of the Piece at Britch: take the height of the bore at Muzzle, and if this height at Muzzle agree with that taken at the Britch of the Piece, then is the Piece full bored; but if they differ, so much as the difference is, sheweth the tapering of the Piece, and according to this must your former be made for your Cartredges. There is another way to know whether a Piece be Chamber-bored, or Tapering, by the disparting of a Piece; which way we shall show in its proper place, where we treat of disparting a Piece of Ordnance. Now although we have mentioned in the former Chapters the most usual Pieces of Ordnance; yet, as I have said, there are other Pieces which are longer, or shorter, which are used, and are generally called by the name of Bastard Pieces, and they are distinguished from the common Legitimate Pieces thus; The Legitimate Pieces have their due length of Chase, and are proportioned according to the true height of their bore. Bastard Pieces are shorter Chases, such as the proportion of their bore doth require, and are therefore called Cuts of the same nature of the Piece they agree with in the bore; as those of Demi-Culverin bore, are called Demi-Culverin Cuts, etc. There are also Pieces called Extraordinary, which are such whose Chases are longer than is usually for that bore. Now we have well and duly understood how, not only to make, but also to examine and prove a Piece of Ordnance; in the next place shall follow their use, set down in due order: Wherein first 'tis necessary for us to treat of the nature of Gunpowder, and its various Compositions, with the Materials necessary thereunto, and afterward show its use. CHAP. VIII. Of the Materials used in the Composition of Gunpowder; and first we will treat of the Original of Salt-Peter. IT is believed by many in these latter times, that the Salt-Peter now in use, is not the Niter of the Ancients, but a new Invention used or found our for the Composition of Powder; And that theirs was only a Niter generated by nature, or that Salt that is coagulated of itself, without any humane Artifice, in the Caverns of the Earth, from whence they took it which nevertheless they divide into four different Species, to wit, Armenian, African, Roman, and Egyptian; and this Egyptian holds its name by a certain Region in Egypt, in which is found great abundance. Serapian delivers to us, that the places from whence they drew their Niter were all one and the same, like them where common Salt is form, in which the water running doth congeal, and condenseth like a vulgar Stone, from hence came it to be called stonified Salt, or Sal-Peter. The same Author doth affirm, that Niter was found of divers colours, viz. White, Reddish, Livid, or Lead-like, and all other colours it was able to take; he saith likewise that it was found in different forms; for some was found full of holes or caverns like a Sponge; others on the contrary were firm, close, solid, shining, and Diaphanous as Glass, which being let fall easily will split in thin leaves, and is fryable in beating; and from its various appearances is judged its manifold virtues, in one more powerful than another, which is known by its operation. From hence we see that which is to be found from the testimony of the best received Authors about the Mineral Niter, and in none is any mention made of Artificial Salt-Peter, or such as we at present make use of generally, which is called properly Salt-Peter, Sal Nitre, or Halinitre; yet is there very little difference between the Natural that useth to be brought to us, and the Artificial, for if we compare the virtues and operations of the one, we shall find them in our uses no way d ffering, as Scaliger testifies, saying that the ancient Niter is not much different from ours, particularly if we consider its tenuity and subtle part. There is of the ancient Niter found upon the superficies of old Walls, exposed to the humidity; but particularly in Cellars and deep Caves, and in covered Vaults; it resembles perfectly a certain Brine, or white Jelly, or fine Meal, or in more proper speaking, fine Sugar, and is many times white as Snow; and this thus had, the virtues are to be commended, which I myself have taken the pains to collect, in the imitation of many others which I have often seen; which if now it be desired to prepare this Salt according to the method, of our Art; It will be congealed into small little long Crystals like Icicles, and it will be like that of the Ancients. But as 'tis impossible to find so great a quantity, as the continual use doth consume, and necessity doth excite to this day for the supply of all Wars, which have been great, and in few years consumed many great and vast places of the Universe: We are therefore constrained to this new subject, and are forced even to study and invent in these latter ages a new way to supply the want of the former, which being made with much labour and industry from the bowels of the Earth, and then purified and washed divers times to separate it from its more gross and Terrestrial parts, and taken from its first crudity, that its may show its likeness of its Mother, it is in the end perfectly purified and brought to such a height, that it differs nothing to he of the same form and virtue of the ancient Salt-Peter. Wherefore if I may be admitted to speak my thoughts upon it, I shall say openly and plainly, leaving none in doubt, the Ancients did indeed find natural growing Niter, which came out of itself at the tops of Rocks, filling the clefts and holes, and there condensing into small Icicles, it hardens and petrefies. This Niter is natural; but since Art is the Imitator of Nature, as 'tis allowed by all, than you may not think it strange, if we can by a little of her aid, and by force of industry, attain to the perfection of her productions; nay, (if I may be bold to say it) such as shall surpass by far, the more perfect of her works. Do we not daily see an infinite of very principal Works brought to light, after a long and painful travel, which is not permitted nature to imitate, although she did employ at the best all her secret and full strength to come to perfection. It may from hence herefore be concluded that our Salt made by the Art of Fire, is such as is every way agreeing with that of the Ancients, not any way differing one from the other; especially as to those uses we intent here. For if according to our method given in the next Chapter, I dare affirm, in all our uses it will truly imitate the natural, but the more, if it be purified and purged many times: So that at last it will come to be more excellent than the Ancient and natural Salt-Peter; which is plainly seen in the ordinary way of purifying Common Salt or Sugar, which by Art is so purged, that it comes to be far purer and whiter than 'twas before, in its first natural dress. And this we do suppose to be a sufficient argument, or reason, for us to judge that our Artificial Salt-Peter is not only as good, but far more excellent than the natural: Which being thus allowed, we will add only a few words of the properties of Niter, and so pass to its Artificial preparation. And first of the spitting quality and noise it makes in the fire, which Scaliger would have to be caused by its terrestrity that it holds in itself, which we cannot allow of, but rather judge otherwise; for if the Earthy part were the subject that made it make such noise, than the Earth itself might be adjudged to make a far greater noise, seeing it is also mixed with this Element, and yet we find it cracks not at all, being put in the fire; therefore by consequence this reason is void. Well then, is it of its rarity, which Aristotle calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. This cannot pass for a truth, since daily experience doth let us see that the Mushrooms, or Toad-stools, and many other things which are of a most rare thin nature, yet make no noise when put upon burning coals. Neither is the hardness that is joined to these more subtle parts, the cause of the cracking; For we see that the Pumicestone will not spit nor crack, nor make any noise in the fire, although it be of a substance sufficiently spongy and hard. There must therefore be another thing that must be the cause of this spitting, and all the noise that is made by Nitre, when it is embraced by the fire. The Divine Praeceptor, in the 11 Section of his Questions saith, that the Salt cracks in the fire, because it contains in it much moisture, which being attenuated by the fire, and rarified in a high degree, converts all into Spirits, and an Airy nature; For in it there is contained more of a Spirit, than watery matter, which being brought to the fire, the two fiery Spirits mutually attract each other, and joining together, do become Master of the lesser part the Water; for the fire of the Niter being fortified and put into action by the common fire, the Water is constrained from its bonds, and can stay no longer there, but must of a sudden depart, and in its way, by the violency of its departure, overthroweth all such obstacles as come in its way: And in this action the external air being strongly and violently agitated, by their refraction, it breaks with impetuosity or great violence, and from thence by consequence follows that hideous and fearful noise which commonly and ordinarily happens, in the combustion of Salt-Peter, and other Compositions mixed with it, whereof Salt-Peter is the greatest part. CHAP. IX. The way of Preparing Salt-Peter from a Nitrous Earth. THe Earth and matter of Salt-Peter is found commonly in great abundance, in obscure shadowed places, where no Rain nor any fresh water doth penetrate, nor likewise where the Sun by his rays can communicate his heat; it is likewise drawn from Horse dung under Stables, and from covered places where great and small Cattle are shut up; likewise in such places as men use to piss in, or Jaqueses, or the like places; or in places where has been made great Fights, or where has been laid up together many dead Bodies, and earth thrown upon them: For from thence in few years may much Salt-Peter be drawn. I shall declare three several ways whereby to ground your judgement with more certainty, concerning the goodness of the place from whence one would draw the Salt-Peter, which is most necessary to be known by all Salt-Peter men, or such as intent to manage these Affairs. The first is, that such Earth as you suspect to hold Salt-Peter, be put upon the Tongue, and if it prick a little sharply, it is a most certain sign you will not lose your labour in taking it to task; but on the contrary if it be not biting, or a little corrosive, it will not well answer your money and labour in preparing of it. The second way to know a good Nitrous Earth is this: make a hole in the Earth with a sharp pointed thing, either of Wood or Iron, and in it put a piece of Iron red hot; after having stopped the hole, let it stand until it be quite cold, then draw it out, and if you find a little after about this Iron some Citrine marks, inclining a little after to a whiteness, you need not doubt that earth; but further assure yourself 'tis very good to put to work. The third way is, throw a little of that Earth upon burning Coals, and if you perceive it make any noise, and that it spits in the fire, or that clear and shining sparks come from it, you may from thence judge that that Earth holds a forcible matter of that nature. After you have found a proper Earth to draw Salt-Peter from, and that by some of these proofs you have testimony of its goodness and worth, let be taken of it a great quantity, or as much as you please; let it be carried to a place appointed for this purpose, then prepare to burn a good quantity of Wood, either of Oak, Ash, Elm, Maple, or other sorts of hard Wood, that you may have Ashes; then take two parts of these Ashes, one part of quick Lime, mix them well, and put this mixture by itself, for such uses as I shall show you anon. Take then Vessels of Wood, or Pipes, or Hogsheads cut in two parts, for they must be able to hold a good quantity of Water, make a hole at the bottom about one or two fingers breadth, put into the hole a small wicker thing, or you may whelm over it an Earthen Dish, after put Rushes all over the bottom (not excepting the hole) or in its place clean straw; this Vessel being thus fitted, dispose of it in this manner; Set it so, that under may stand a lesser Vessel of Wood to receive the Liquor that shall distil down from the upper Vessel; after put into the upper Vessel about the height of a hand of this Salt-Peter Earth, which has been before for some time dried in the Air; upon this Earth put the height of three or four fingers of the mixture made of Ashes and quick Lime, and then again of the Salt-Peter Earth, after of the Ashes about the same height as before; and continue this fashion, putting Earth upon Ashes, and Ashes upon Earth, until the Vessel be full within a hands breadth at the top, to hold the Water that is put in; this done put upon it fresh Water as much as shall be necessary, viz. so much as must surmount the Earth two or three fingers breadth, and look that it pass through all the Earth, and run drop by drop through the hole at bottom of the Vessel into the Tub standing under, and you shall have a Nitrous Lixivium, according to the quantity of Water as you poured into the Vessel; which if you judge is too little, you must reiterate the infusion, and the second time also the water passing through the Earth will carry with it a substance; And so the third time. This done, put all the Lixivium into a Kettle of a sufficient bigness, and let it be boiled upon the fire very easily, and moderately at first; after increase the fire to the consumption of the Liquor, or a little more, keeping continually skimming it all the time it boils. And when 'tis thus consumed, pour it into wooden Vessels that are broad, and cover them over with , and let them stand until the pure part Christalize into white Salt, and the feculent or more terrestrial part settle to the bottom. In the mean time continue pouring in of the Lixivium again into the Kettle, boiling and skimming it as before; and this do until all your Lixivium be boiled up and poured into wooden Vessels to Christalize. Then from the wooden Vessels, inclining them gently, pour all the Lixivium (leaving the settling at bottom by itself) into your Copper as before, and boil it up again with a good fire until half be consumed, or until it begin to thicken, or until by putting a little upon a stone or piece of board, it do immediately congeal. Then take it from the fire, and when 'tis a little cooled, pour it as before into wooden Vessels or Bowls, and put into each about a hand in height; then cover each Vessel with course , put it into a cool place, and two or three days after you will find your Salt-Peter congealed and thrust together in small Crystals, like transparent Ice, sticking to the sides of the Vessel, and likewise upon some sticks for that purpose, provided the rinds being taken off and placed in the wooden Vessels before the pouring in of the Liquor; get diligently together the Peter, as well that which sticks to the sides of the Vessel, as that to the sticks, in a Vessel of wood proper to receive it, and cover it, and keep it dry. The remaining water you must boil up, as before, not forgetting to separate it from its residence. Whilst 'tis boiling, it happens sometimes that the Liquor may rise and boil over the Cauldron; to prevent that danger, have in readiness other Lixivium, made of three parts of Ashes, and one part of quick Lyme, as we spoke before, in which is dissolved Roch Alum, allowing to every hundred weight of Lixivium, four pounds of Alum; and when it gins to rise, pour in a little of this from time to time; And by this means you will see that the water that was hastening to come over, will fall down; and that the common Salt and more terrestrial part will settle to the bottom. The Earth remaining in the Wooden Tubs from whence the salt was drawn, must be put in some covered place made for that purpose, where neither Sun, Rain, nor any other water may come; and there it must be spread all abroad about a foot high: Then you must have in readiness Horse dung or the Excrements of all sorts of Beasts, great and small, and put off this upon the other, about the height of three or four foot; then take all that was skumed from the Lixivium in boiling, and the water that is left and will not shoot, and the bottoms that are left in the wooden Vessel, where the Salt-Peter did shoot, and throw them away, as hurtful and useless, upon the Dunghill; throw likewise every day, or as often as you can, the Urine of men, and let it lie two years, and you shall have your Earth filled with Salt-Peter as before, with a greater abundance: You may likewise throw upon your Dunghill, the Horns, Claws, and Hooss of Beast, and then from this Earth it will be very easy to draw good Salt-Peter by the method we have prescribed. CHAP. X. To Clarify and Refine Salt-Peter. TAke as much Salt-Peter as you please, and being put in a Copper, pour upon it so much fair water as will dissolve it, that is about eight of Water, and three of Salt; and pour upon the same of the former Lixivium, prepared of Ashes, Quick-lyme, and Roch Alum; boil it upon the fire until all the Salt-Peter be dissolved; that being done, have in readiness a Vessel of Wood sufficiently big, and so disposed, that another may stand under the same: which must, before it be so set, be pierced in the middle, and the hole covered over with an Earthen Dish: Let the uppermost Tub be filled five or six inches with fine clean sand; then let the Tub be covered over with a course cloth, and pour through the same into your Sand-Tub your dissolved Salt-Peter, and so it will distil by little and little into the Vessel which stands under; and so passing through the Sand, it will be discharged of all its superfluities, and will leave the most terrestrial part, and such as is useless, in the Sand, which water again put into the Cauldron, and boil it up as formerly, until it may be fit to congeal, and in the end pour it into wooden long flat Vessels as before, and in two or three days 'twill be shot into Crystals as formerly; which if you would have purer, you must reiterate this work once more, or you may put upon this Peter, Lyme-water, filter it and boil it up according to Art, and it will be pure. Salt-Peter may be purified thus; put your Salt-Peter in a Vessel of Copper, Iron, or Vernished Earth (I like a Crucible best) which being put to a small fire, augment it gradually until all the Salt be melted and boiled; then take common Sulphur finely pulverised, and throw it upon the liquified Salt-Peter, which will quickly take fire and burn, and by the same means consume all the gross and viscous humours, with the terrestrial Salt remaining useless amongst the Salt-Peter, before the rectification; besides you may reiterate this work by putting on fresh Sulphur many times, until such time all the strange humours be quite consumed; in the end, the Salt-Peter being well melted and well purified, pour it upon well polished Marble or Plates of Iron, or Copper, or glazed Earth, and let it cool, and you will have a Salt-Peter congealed, almost resembling in colour and hardness the true Alabaster. CHAP. XI. How Salt-Peter Meal is made without any beating, for the making of Gunpowder. SAlt-Peter well purified, must be put in a Kettle, upon a furnace over a fire, then moderately increase the fire with Bellows to such a degree of heat, until it begin to smoke and evaporate, until the Salt begin to lose its humidity, and obtain a whiteness, and so keep continually stirring it with a wooden or Iron Ladle, for fear it should return into its pristine form, and hereby will be taken away all its fatty greasiness that may be commixed. This being done, pour so much water into the Kettle as will cover the Salt-Peter, and when it shall be dissolved, and it has obtained the consistence of a thick Liquor; then with a wooden stick or Ladle keep continually stirring it without any intermission, until all its humidity be evaporated, and all be reduced into most dry white Meal. CHAP. XII. To make Salt-Peter with the flower of Old Walls, of Caves, Cellars, Vaults, etc. GAther together a good quantity of this Flower, which you may find upon the Surface of Old Walls, which are in moist places under the Earth; you may also make provision with a certain Salt which sticks to Lyme, or upon ruinated Walls; which Peter, one Sardi a Roman took notice of, was always well practised at Brussels in Brabant, as he confesseth in his fifth Book of Artillery, Chap. 49. First, see how much Salt-Peter matter you have; then take one fourth part so much of quick Lyme, pour upon it warm water, boil it well, and clarify it according to custom, than put your Salt-Peter matter into a Tub with a tap in it, and a little Earthen Dish before the hole of the tap within, pour into this Tub the Lie, and stir it well with a stick until all the Salt Peter be dissolved in the Water; then let it distil leisurely into a Vessel that stands under the tap; and at last being all dissolved and run out, put this water into a Kettle, and boil it over the fire, until so much be consumed, that the remainder being dropped upon a Tyle-stone or Board, do congeal, and be of hardness, but not too hard; for if it be very hard, the water is burnt; but if too soft, not enough. When 'tis well boiled and scummed, take it from the fire, and proceed with it as in the tenth and eleventh Chapters. CHAP. XIII. How to examine the goodness of Salt-Peter. PUt upon a Wooden Table, or any clean and smooth Board, a little Salt-Peter; then give fire to it with a live coal, and observe these Rules following, viz. If it make the same noise in burning as the common Salt doth when it is thrown upon live coals, it is a sign it holds yet much common Salt. If it hold a thick and fat scum, it is a sign 'tis fatty and viscous. If after the Salt be consumed, there resteth yet crass and filthy matter upon the board, it is an infallible sign that the Salt contains yet a quantity of earthy matter, and so much the more, if you see much dregs after the combustion of the Salt-Peter is passed; and therefore the less powerful and active. But by contraries, if it render a clear long flame divided into many streams, and that the superficies of the board remain neat without any filth; or that it be consumed so that nothing is left, but a white clean ash, without making much noise, or great trembling, you may then conclude that the Salt-Peter is good, and well cleansed, and in its perfect preparation. CHAP. XIV. The true way to purify Salt-Peter, and separating it from all offending and superfluous matter; as common Salt, Vitriol, Alum, and all fatty and viscous humours. TAke Two pound of Quick-Lyme, Two pound of common Salt, One pound of Verdigrease, One pound of Roman Vitriol, One pound of Sal-Armoniack, beat them all together; after put them into an Iron Vessel, and pour upon them a good quantity of Vinegar, or in default of them, good clear water; and make a Lixivium, which you shall let rarify and clarify of itself, standing the space of three days; after put your Salt-Peter in a Kettle, and pour upon the same as much of this Lixivium as will well cover the Salt-Peter; put it upon a fire sufficiently moderate at first, increasing it until it boil to the consumption of half; take it then away from the fire, and pour it by gentle inclination into a wooden Vessel, and throw away all the dregs and Salt which remaineth in the bottom of the Kettle: That done, let the Salt-Peter water cool, and continue your preparation as we have given before, where we treated of refining Salt-Peter. CHAP. XV. How to clarify common Sulphur, and to know its goodness. WE experience often, and without contradiction, that not only Salt-Peter is filled with terrestrial qualities, but Brimstone also, which is not only of a fatty & certain oleganious humour, but likewise a noisome quality which is in the compound, common to one and the other of its matters; from hence (if we desire to be curious in our work) we judge it may be necessary to purify Sulphur, and to procure to it by power of clarification, a nature most sublime, subtle, fiery and volatile. The order and method that ought to be used in this, is thus; in Vessels of Iron or Copper, melt your Sulphur with a very gentle fire over Coals, well lighted, and not flaming; and when it is melted with a Ladle, skim neatly off all that riseth on the top and swimmeth upon the Sulphur; than not long after, let it be taken from the fire, and strained through a double Linen Cloth into another Vessel, pouring it through at leisure; thus all the Oily matter and crassy substance remains in the Cloth; but under in the Vessel will be a pure Sulphur, such as we have before spoken of. To know the goodness of Sulphur you must do thus: Press it between two Iron plates, that are hot, and if in the running it appear yellow, without any bad odour, and that which remains be of a reddish colour, one may believe 'tis natural and excellent; so likewise 'tis a good sign, if when 'tis set on fire, it do freely burn all away, leaving little or no resident matter. For if Sulphur be pure and good, we do find that there is such a sympathy between it and fire, that the fire is desirous of the Sulphur for its nutriment, and that reciprocally the Sulphur is pleased likewise to be thus devoured and consumed by the Element of fire; so that if some fragment of it be put about some pieces of Wood, if this shall feel the fire at some distance, it seems as if it did attract it to itself, and doth sometimes unawares at a distance catch or take fire, if great care be not taken. There is a certain kind of Sulphur which will not burn so freely as other Sulphur, nor send forth any ill scent, but being put upon the fire, melts not otherwise than common Wax; and this Sulphur is found abundantly near Mount Aetna, as Carniola of Libavius reports, in his first Book of the Apocap. Hermel. but this Sulphur is commonly red, as also is that which is found in the Heil des Heim (as Agricola mentions in his first Book, Chap. 22.) And upon the testimony of John Johnson, Adm. Nat. Clas. 4. Chap. 13. Sulphur is found likewise of divers other colours, as pale, Yellow, Green, as is many times to be seen and found sticking about Stones and Rocks: So, that a man may, without any great difficulty, take it from thence, and make it into a Mass. That which is clear, perfectly yellow, not very hard, nor too much shining, is the very best. Yet there is another Sulphur which looks greenish, and hath never passed the fire; and this is called Sulphur Vivum, and by some Virgin Sulphur, by reason Women and Maids had a custom to compose with it a certain fucus or Paint, with which they used to adorn their faces. CHAP. XVI. Of the third Principal in Composition of Gunpowder, viz. Coal, and its Preparation. IN the Month of May or June, when all sorts of Trees are easy to peel, by reason in that time there comes out a sap, and they are fuller of humours than at any other time of the year, Cut then a great quantity of Hazle or Ash, the length of two or three foot, of the bigness of half your fist, taking away from them with a Bill all that is Superfluous, then take away the rind likewise; and of these make little bundles, and make them very dry in a warm Oven; then in a place chosen for that purpose, that is plain and even, set them upright one by another, and set them on fire; and after you see the fire well lighted, and that the fire hath reduced them all into burning Coals, cover them closely and diligently with watered earth, so that it may have no respiration, or that no Air may pass in; then, the flame being thus stifled upon the Coals, they will remain pure and whole, without being charged with much Ashes; then 24 hours after, you may take them away and keep them for to serve you in your business, and put them to such uses as we shall write of hereafter. But if you have occasion for a small quantity only, take then of the Arms and Limbs of such Trees aforesaid, that is of Teil wood, of Juniper, of Ash, etc. Cut them in small pieces, and dry them well; then shut them in an Earthen Vessel, and lute the Cover on the top with Clay; then place Coals round about the Pot, and let it be all covered with Coals, leaving them so the space of a good hour, continuing the fire all this while in the same degree of heat; at last let it cool of itself, and when 'tis cold, open the pot, and take out the Coals for your use. CHAP. XVII. The ways of Compounding or Making Gunpowder. THe ways of Compounding of Gunpowder have been so commonly known, that not only such as are conversant in fireworks do understand the same, but others also; so that it is made a particular Trade: nay, that which is more strange, the Country people in Polonia have learned to prepare it with their own hands, without the use of any Artificial Engine, or Chemical Vessel. For I have seen many of the People of Podolie, and the Vkrains, which we call now the Cossaques, who prepare their Powder quite contrary to the common way, or that which is used by Fire-Masters. For they put Sulphur, Salt-Peter, Charcoal, all together in an Earthen Pot, a certain proportion of each; (which proportion one to the other they have learned by experimental practice) upon which they pour fair fresh water, which they boil upon the fire until all the water is evaporated, and the matter become thick; then they take it from the fire, and dry it in the Sun, or in some warm place, as a Stove, or the like; then they pass it through a Hair Sieve, and reduce it into small Grains. There are others that take these Materials, and grind them upon a smooth flat Stone, or a smooth Earthen Dish, and then having moistened it, by their Skill they bring it into Grains; which powder brought to this degree of perfection, they serve their occasions with as much utility and profit, as if it had been made by the hand of one of the most knowing or skilful Powder-makers in the world. It is in my judgement, labour lost to speak more of these superficial ways; but come to the order and method which is necessary and usually observed in the preparing of Gunpowder: It shall likewise suffice me to propose in this Chapter some Compositions most excellent and best approved; which are these, Compositions for Cannon Powder. Compositions for Musquet-Powder. Compositions for Pistol-powder. The first. The first. The first. Salt Peter 100 l. Salt-Peter 100 l. Salt-Peter 100 l. Sulphur 25 Sulphur 18 Sulphur 12 Coals 25 Coals 20 Coals 15 The Second. The Second. The Second. Salt-Peter 100 l. Salt-Peter 100 l. Salt-Peter 100 l. Sulphur 20 Sulphur 15 Sulphur 10 Coals 24 Coals 18 Coals 8 You must first finely powder these compositions or mixtures, for Cannon or Musket Powder, and after moisten them with fair fresh water or Vinegar, or with Aquavitae; but if you will have your Pistol Powder stronger and more violent, you ought to stir it up several times whilst 'tis in the Mortar, with this following liquor; that is, a water distilled from Rinds of Oranges, Citrons, or Lemons, by an Alymbeck, or any other Chemical Vessel; then let all be beaten and well brayed 24. hours, and then in the end reduce it into very fine small grains. A Liquor for this purpose may likewise be made of twenty parts of Aquavitae, and 12 parts of distilled Vinegar made of Whitewine, and four parts of Spirit of Salt-Peter, and two parts of water of Salarmoniac, and one part of Camphire dissolved in Brandywine, or reduced into Powder with powdered Sulphur, or reduced with Oil of sweet Almonds. To Corn Powder well, you must prepare a Sieve with a bottom of thick Parchment, made full of round holes; then moisten the Powder that must be corned with its water, and make it up in Balls as big as Eggs; which put into the Sieve, and with it put a wooden Bowl, and when you have so done, sift the Powder so, as the Bowl rolling about the Sieve, may break the Clods of Powder, and make it pass through those little holes into Corns. It is observed by Fire-Masters and Gunners, that Powder when it is Corned, is of much greater force and power, than in Meal; from hence 'tis concluded, that powder when 'tis put into a Piece of Ordnance, ought not to be pressed or beaten home too hard in the Piece; for thereby it will lose its form of grains, and thereby looseth a great part of its strength that it had, and is therefore not able to throw out the Bullet with so great a violence, as if the Powder had been gently thrust home to the Britch end. CHAP. XVIII. Of the several Colours which are to be given to Powder. KNow first that all the blackness which you see in Gunpowder comes from the Coal; not that this colour is absolutely necessary to be conjoined to its nature, or that it is absolutely necessary to be given to it, for its meliorating or making it more vigorous; this is not so; but by contraries you may be permitted to give unto it any such colours as you shall think fit, without prejudice or hindrance of the Powder and virtue of it. For if instead of Coal you take rotten dried wood, or Sawdust well dried, or white paper moistened and dried in a Stove and powdered, or indeed any other thing of a combustible nature, or that is well disposed to take fire (such as you read hereunder) and to this you may add a colour according to your fancy and pleasure; and you will infallibly have a Powder that will make the same Effect as the black powder. And for this purpose I shall lay down in this Chapter certain mictions, with which I served myself many times, and therefore known to be experimental truths. White Powder. Take Salt-Peter six pounds, Sulphur one pound, of Sawdust of the Elder Tree well dried and powdered one pound, these mixed according to the directions in the former Chapter, there will be made a Powder of a white colour. Or thus, Take Salt-Peter ten pounds, of Sulphur one pound, of the woody part when the Hemp is taken away, one pound, etc. Or thus, Salt-Peter six pounds, Sulphur one pound, of Tartar calcined until it be brought to a whiteness, and the Salt extracted for use, one Ounce. Red Powder. Take of Salt-Peter twelve Parts, of Sulphur two parts, of Amber one part, of Red two parts, etc. Or, Take Salt-Peter eight pounds, of Sulphur one pound, of dried powdered Paper boiled up in a Water, wherein is Cinaber or Brazil Wood, and then again dried, one pound. Yellow Powder. Take Salt-Peter eight pounds, Sulphur one pound, Wild or Bastard Saffron boiled in Aqua Vitae, after dried and powdered, two pounds, etc. Green Powder. Salt-Peter ten pounds, of Sulphur one pound, dried Wood or Sawdust boiled in Aqua Vitae with some Verditer, then dried and powdered, of this two pounds. Blue Powder. Salt-Peter eight pounds, of Sulphur one pound, of the Sawdust of the Teil Wood boiled in Brandy Wine with Indigo, and after dried and powdered, one pound. CHAP. XIX. Still Powder, or Powder without Noise. THere are several that do Writ many strange things concerning this Still Powder, or Powder, without noise, or as some do give it the name, Deaf Powder, whereof they have treated prolixly; the which I think not convenient to do, by reason I am loath to tyre the Reader with any such Discourse, as tends not much to Edification: I shall therefore put down certain mixtures, which I have known to be more excellent and best approved. First way, Take Common Powder two pounds, Venus Borax one pound; these being well powdered, mingled and incorporated together, must be made up into Corn Powder. Second way, Take common Powder two pounds, Venus Borax one pound, of Lapis Calaminaris half a pound, of Sal-armoniack half a pound; powder and mix them well, and make them up into Grains. Third way, Take common Powder six pounds, of Live Moles burnt in an Earthen Pot, of Venus Borax half a pound, mix them as before, etc. Fourth way, Take Salt-Peter six pounds, Sulphur eight pounds and a half, powder of the Second Bark of Elder Tree half a pound, common decripitated Salt two pounds; make Corn Powder of these according to the precedent order, or accustomed method. To these known things, I shall add here a thing whereof you may make experience if you please; it being only taken from the Books of Authors, without any trial made by me; which you may also find written in the natural Magic of John Baptista Porta, which is in our English Tongue, where he saith, that if you add burnt Paper in the Composition of Gunpowder, or the double quantity of Hay seed well beaten; these will take away a great part of the strength, and will hinder it from making so great flame and noise. Some do say that the Gall of a Pike doth the same effect, if it be mixed and mingled with the same; but we shall leave the belief of these things to the faith of such Authors as have experimented the same. There are some wise and knowing men in this Art, attribute the cause of this noise, or as some do express it, this horrible noise, produced by a Cannon after the firing, not to the Powder, but to the beating and contusion of the Air which is enraged, or in a passion, by being so furiously endeavoured to be stifled or choked by a strange and extraordinary movement, of which we have spoken more at large in the former Chapter, where we treated of Salt-Peter. Yet in favour of the Sons of Art, we shall nevertheless give you the opinion of Scaliger, taken out of his his fifteenth Book, in his Exer. Exoter. against Cardan of Subtle. Exer. 25. Long pejus illud cum sonitus causam a bellicis machinis editi, attribuis Sal Petrae; nam tenuissimum in pulverem comminutum cavernulas amisit. CHAP. XX. The Proof or Trial of Gunpowder. IT is accustomary for men skilled in these Arts, to try Powder three several ways; that is, by sight, by touch, and by fire: And first, for the trial by sight; it is thus, If the Powder be too black, it is a manifest sign of too much humidity, or too much coal; now if it contain too much, as you suppose, rub it upon white Paper; if it black the Paper more than other good Powder use to do, it is a sign there is more coal in it than aught: for such Gunpowder as is of a fair azure colour, or a little obscure, something bordering upon red, is the best sign, and the most assured testimony of good Powder. Secondly, Gunpowder its goodness is known by the touch, in this manner, crush some Corns under your finger's ends, and if they easily break and return to Meal without resisting the touch, or without feeling hard, you may assure yourself from thence, that your Powder hath in it too much Coal. If by pressing it a little hard under your fingers upon a smooth hard board, or upon a stone, you feel amongst it small grains harder or more solid than the rest, which do in a manner prick the ends of the fingers, and do not yield to the finger but very difficultly, or hardly, you may infer from hence that the Sulphur is not well incorporated with the Salt-Peter, and by consequence the Powder is not well and duly prepared. You may draw infallible proofs or conjectures of the goodness of Powder by its burning, if after you have made little heaps of Powder upon a clean and even Table, distant one from another about a hands breadth, you then put fire to one of them only; and if it take fire alone, and burn all away without lighting the others, and make a small thundering noise, or make a white clear smoke, and that it rise with a quickness, suddenly, almost imperceptible, and if it rise in the Air like a circle of smoke, or like a small Crown; this is an infallible sign the Powder is good, and perfectly well prepared. If after the burning of the Powder there remain some black marks upon the Table, this then signifies that the Powder contains too much Coal, which has not been enough burnt. If the board looks greasy, than the Sulphur and Salt-Peter is not enough cleansed, and by consequence it retains much of their terrestrial matter and oily natures which were naturally conjoined to their matters. If you find small grains, white and Citrine, it is a testimony that the Salt-Peter is not enough cleansed, and by consequence it retains much of its terrestrial matter, and of common Salt, and besides, the Sulphur hath not been well powdered, nor sufficiently incorporated with the two other matters of its Composition. If two or three Corns of Gunpowder be laid upon a Paper, distant about a finger's breadth one from the other, and you put fire to them, if the fire be good and strong, they will fire at once, and there will remain no grossness of Brimstone, or of Salt-Peter, nor any thing but a white smoky colour in the place where they were burnt, nor will the Paper be touched. If small black knots, which will burn downward in the place where proof is made, remain after firing, they do show that the Gunpowder hath not enough of Peter, and that it is of little force or strength. Good Gunpowder will not burn your hand, if it be set on fire there. Gunpowder that is very sharp or eager in taste, is not well purified, and will turn moist. Amongst many sorts of Powder, to know the best, make a little heap of every sort at a distance one from another; observing well when you fire each heap, which of them doth soon take fire, for that which soon takes fire, smokes least and clearest, and riseth quickly up close and round, and leaves little or no sign behind it, is the best Powder. There are Instruments likewise invented for the trial or proof of Powder, which the most part of Fire-Masters and Gunners are accustomed to use, which are described at large by other Authors; therefore we shall not here repeat the same; considering likewise, that we have found by experience a great fallacy in the same, for that one and the same Powder, in the same measure and quantities, hath raised the cover to different degrees of height. CHAP. XXI. To fortify weak Powder, and amend that which is spoiled, and bring it to its full strength again; and to preserve good Powder from decaying. WE call such Gunpowder weak, which hath much degenerated from its first strength, and the force which it did acquire in its first preparation; as such as hath taken wind, wet, or air; for these do diminish the quantity of Salt-Peter, and actually separate the Sulphur and Coal. There are two different ways that these accidents do happen; that is, by being many years made, or lying in a moist place long; for in time the Salt-Peter altars and separates itself, being naturally subject to alter, and return into its first matter; for Salt-Peter in its beginning or original being engendered of water, or of a certain Saline humour, no otherwise than other Salts are produced of their own proper Brines, doth at last, or in a long time, separate itself from the Coal and Sulphur, and so return to a Brine water again, as it was in the original, and so abandons the other two matters that adhered to it, the Sulphur and Coals losing nothing of their weight, seeing that no humidity that is attracted, can be able to dissolve them; but rather by the contrary, the Coal doth attract greedily, and becomes more ponderous. If for the reasons aforesaid you desire to repair and restore the strength of Gunpowder that gins to alter, or that hath quite lost its force, its defects may be amended three several ways, etc. viz. The first is thus, make a Lie of two parts of Aqua vitae, and one part of clarified Salt-Peter made into fine Powder, of good Vinegar made of good Wine half a part, of Oil of Sulphur one eighth part, and as much Camphire dissolved in Brandy; these put together, do make a Lixivium, which must be strained through a large Strainer, and then with it you may amend your powder that is decayed, by moistening it with the same, very often, and drying it by the Sun in Wooden Vessels, and then putting it up in a dry place, free from any humidity or air, and then it will not in a long time again be damnified. The second way to repair Powder is thus, examine how much your Powder weighed when it was first put into the Cask or Barrel, then see how much it doth now weigh after 'tis damnified (it being first dried if it chance to be wet) then see the difference between these two weights, and add so much Salt-Peter to your decayed powder, mix it well, and make it up into Corns again, and preserve it as before. The third way to restore the strength of Gunpowder, is such as is most plain and commonly used amongst the Powder-men; they put upon a Sale-cloath or smooth place or board, a portion of damnified Powder, to which they add an equal weight of that which is new made, and then with their hand or wooden Shovel they mingle it well together; then they dry it in the Sun, and put it up into a Barrel again, and keep it in a dry and proper place. Yet there is another way may be allowed, but this is almost the same with making new Powder, and it is thus; Take what quantity of decayed Powder you please, put it into Earthen or Wooden Vessels, pour upon the same three times so much hot water, stir it well about, and when it gins to be cold, or hath stood one hour or two, strain the water away, and to the feces put more water, stirring it well about, then let it stand and settle as before, and strain it from the feces, this do a third time, and you will have drawn out all the Salt-Peter; put these waters in a clean Kettle, and boil it away until so much be consumed, as that a drop dropped upon a Stone or Iron do congeal, then pour it into some wooden Vessel that it may congeal into Salt-Peter; and that water as remains, you must boil up again as before; and if need be, you must in the boiling scum what riseth on the top of the water. Having by this Art obtained the Salt-Peter out of the decayed Gunpowder, you may according to the proportions given in the Composition of Powder, mix it with its remaining Sulphur and Coal, or fresh Sulphur and Coal, which is better; and after 'tis well mixed, Corn it according to the given Rules; then let it be well dried, and put up into dry Powder Barrels, and let it be conserved in a dry place from Air or any Moisture. Some do mend their Powder in this nature, they moisten it with Vinegar or fair water, beat it fine, and sift it and dry it, and to every pound of Powder they put one Ounce of Mealed Salt-Peter; then moisten and mix them well, so that neither may be discerned one from the other, but that they be perfectly incorporated, which you may know by cutting the Mass with a Knife, or breaking it: When it is well compounded, let it be Corned in manner as we have before prescribed. If your Composition of Powder be made up with Aqua vitae, and so made up into great Balls, and well dried in a Stove, or in the Sun, and put into glazed earthen Pots, and close covered, you may keep it as long as you please, for age will not decay it. There ought always a care to be taken by Gunners or Fire-Masters, or such as have the charge of Gunpowder, to choose if they can such places as are dry, and stand upon the best ground, free from dampness of the Air or any water possibly coming near. Every Gunner, etc. aught to take care that his Barrel be turned upside down, or any Carthredge ready filled; for if the Powder attract air, the Peter with the moisture it hath attracted, will in time separate from the other matters, and sink to the bottom; so that the Powder in the upper part will lose its strength, which is prevented by turning and shaking them every fourteen days, and airing them at the Sun at convenient times. And as 'tis necessary a Gunner should have Carthredges filled for present Service, those aught also to be turned out and filled again every fourteen days more or less, as the Gunner in his judgement shall allow of. CHAP. XXII. Of the property and particular office of every Material in the Composition of Gunpowder. WE ought infallibly to believe that Gunpowder was not found out casually, or by fortune; but invented by a true knowledge, and by reasonable speculation in Natural Philosophy; considering that to this day no man hath opposed (notwithstanding many persons have made it their endeavour) or could find any other Materials like unto these, or of such a nature, which being well united and incorporated together, they are able to produce a fire so vigorous, fearful, powerful, and above all, so inextinguishable that the whole Universal matter is consumed in a moment; which is the more to be believed, since we make not much difficulty, particularly in this our Age wherein we live, to add many things to the invention of others, and that (as the Physicians say) all that had a beginning doth pass from imperfection to perfection. We desire therefore it may be permitted (since the Inventors have left us nothing in Writing) to propose here some Observations of Speculative truths, drawn from Experiment, which have been made about the strength, nature, effects, and Office of all the matters comprehended in the Composition of Gunpowder, as well of the particulars, as all made up into one body. For I believe, that having insinuated into a perfect knowledge of the properties, and the affections, as well specificated as general, of all its Ingredients, no body more will fall into those Errors which are too often committed in the Art of Pyrotechny. We must therefore know, that Gunpowder was not without reason composed of these three materials, to wit, Salt-Peter, Sulphur, and Coal, but to the end that one might remedy or supply the defaults of the others. And this is it which is easy to be comprehended in the effect of Sulphur; for this is naturally the very aliment of the fire, seeing it joins with it so willingly and freely, and having once taken fire, is most difficult to put out, being no otherwise rightly than a flaming fire, or, to express it better, a pure flame; and therefore hath an aptitude to inflame the Salt-Peter, by its activity, more than any other kind of fire. But as the Salt-Peter lighted doth go promptly into certain windy exhalations, it hath thereby such a strength in it, that it would by its ventosity put out the flame which the Sulphur hath conceived, and by consequence deny itself of that which the Sulphur communicateth to it; hereby you may see, if one had made a simple composition of these two things only, that is, of Sulphur and Salt-Peter compounded well together, if fire were then applied, they would in truth be suddenly inflamed, but they would soon after go out, that is, the fire will not continue to the Conflagration and Consumption of the whole matter, the reason whereof we have given a little before. It was therefore by good reason adjudged, that Coal well dried and powdered, being adjoined to these two materials in a certain proportion, was an excellent remedy for the supplying of this defect, seeing that Coal is of such a property and of such a nature, that if it be held to the fire, it will soon light and be reduced to a fire without any flame; And from hence it comes to pass, that the more it is agitated by the Air, or by wind, the more the fire augments, and will not go out, but conserve itself until the matter that nourisheth it is totally consumed, a little ashes only excepted. From hence it was concluded that a Composition made of these three Ingredients, such as is our Gunpowder, will conceive fire, and will be conserved, inflamed and consumed unto the last Atom. For it is most certain, that if we approach fire with it, the Sulphur which the fire extremely loves is soon taken with it, and holdeth the same and introduceth it, not only into the Salt-Peter, but the coal also at the same moment, without producing any flame. Now this fire (as we have said before) cannot be suffocated by wind, but on the contrary is inflamed the more, and takes new strength by the agitation of the Air. And as this Sulphur is a great neighbour of the fire either with or without flame, so it cannot hinder it from taking fire; and 'tis the flame of the Brimstone embraces the Salt-Peter, and the Coal continues it. And by consequence these three materials joined together, and well incorporated, and then lighted, produceth a fire, until all its aliment and substance be universally consumed and annihilated: Yet there must care be taken that none of these substances have any accidental defaults, either in humidity or disproportion, either more or less. We will conclude then all that we have said, that the true office of Sulphur in the Powder is to conceive the flame or receive the fire, and having received it, to communicate it to the other matters; and that the Coal hath a particular care to retain and consume it, and to hinder the fire (after it is once introduced by the Sulphur) from suffocating or going out by any windy Exhalation and great violence caused by the Salt-Peter; and lastly, that the most notable and particular office of the Salt-Peter is to produce and cause a most vehement and powerful ventosity or windy Exhalation. And in this which I have said, lieth all the truth of the strength, power and expulsive motion and activity of the Gunpowder; and by consequence Salt-Peter alone is the first and principal cause of all the admirable and astonishing Effects produced by Gunpowder; and consequently, the two other materials are alliated with the Salt-Peter for no other end than to make it break forth into fire and wind. For proof of this, if any one will make a Composition of Sulphur and Coal only, and with it charge a Piece of Ordnance, he will find that this will not move or thrust out a Shot of Iron or any other metal; the reason of this weakness is easy to be understood by our foregoing discourse, because the violent expulsion depends absolutely in the Salt-Peter, and in this only expulsive faculty, and not in any of the other matters. Yea I believe that one may prepare Gunpowder without Brimstone or Coal, rather than without Salt-Peter; or that a man may without much difficulty prepare other matters, that the one may do the office of Sulphur in kindling the matter, and the other that of Coal in Conserving it and keeping it without flame. But any other thing that hath such hidden natural properties to cause such a ventous Exhalation, so violent and capable to produce such prodigious Effects, as Salt-Peter, may not be produced. CHAP. XXIII. How to prepare Eommon Match and Extraordinary Match, that is such as will render no Smoke nor bad scent. FIrst there must be made Cords of corpse hemp, or rather of Tow, about the bigness of half your thumb, or a good finger in Diameter; then take the ashes of Oak, Ash, Elm, or Maple, three parts, of quick Lyme one part, and make thereof a Lie after the usual manner; which being done, add to it of the Liquor drawn from Horse-dung neatly strained and leisurely exprimed through a strainer, or linen Cloth, two parts, of Salt-Peter one part, and being all well mixed, put into a Copper your Match Cords, and pour upon them your Lixivium, and make a small fire under the same, augmenting it gradually, until it be great, which you must keep boiling two or three days continually; not boiling it dry, as some of our Writers prescribe, but supplying it continually with fresh Lixivium, for fear both Match and Kettle burn for want of Liquor; in the end having taken out the fire, take the Cords out of the Liquor, and wring them hard in your hands, rubbing off the moisture from them with a piece of Cloth, that comes forth in the wring; then hang them in the Air or Sun upon long Poles to dry, and when they are well dried, make them up in bundles, and carry them into a commodious place to keep for use. But to make Match that will never have bad scent nor smoke, you must get a certain quantity of red Sand, or Gravel well washed, and purged from all its filth; put it into an Earthen pot that is not varnished, then put into the pot upon the Sand, your common Match, or any other made of Cotton, or the like matter, and coil it in such manner, that there be half a finger's breadth of interval between every coil of the Match, to the end they may not touch each other, but that the Match in its turning or coils have its sides equally distant one from the other; then throw again upon that a good quantity of Sand, and coil in the Cord again as before: Continue thus your work until your pot be full, then cover the pot with a cover of the same earth, and close well the joints with Lute made of fat Earth that no Air may enter; This being well and surely done, put lighted coals round about the pot, and let it stand in this posture some time, then take it away and let it stand until it be quite cold before you open it; When 'tis perfectly cold, take off the Cover, pour out the Sand, and draw out the match, for 'tis prepared, and will burn as we have said. CHAP. XXIV. Of the Square and Cube Roots. WE have already in the Second Chapter of this Book shown the way of moulding and casting pieces of Ordnance; if well understood, you cannot be ignorant in the way of Casting Shot. Therefore to avoid any thing that might be tedious or unnecessary to the Students of this art, we will come to the most necessary things concerning Shot, that is, such as every Gunner ought to know. But because most of the propositions depend upon the knowledge of the Square and Cube Roots, which many (though otherwise knowing in most common Arithmetic) do not understand, I thought it good therefore to show the Extraction of the Square and Cube Roots after a very easy way; with the necessary propositions in Gunnery, thereunto belonging. A Table of Squares and Cubes. 1. 2. 3. 4. 5. 6. 7. 8. 9— Roots. 1. 4. 9 16. 25. 36. 49. 64. 81.— Squares. 1. 8. 27. 64. 125. 216. 343. 512. 729.— Cubes. The Extraction of the Square Root. Set down any number of figures as you shall think good, as, 2735716, then begin at your first right hand figure that is at 6, and make a prick under it, and so along every other figure as you may see here already done; and seeing the first prick to the left hand falls to be under 2, therefore seek in the Table above in the rank of Squares for this number 2, or the nearest number less, which here we find to be 1, and over it we find the Root to be 1, which must be placed in the quotient, and likewise under the first prick to the left hand, then having 1 for a Divisor, and 1 for the quotient, say but the common Rule of Division, 1 times 1 is one, 1 from 2 and there remains 1; which sent over the 2, then double the quotient and it makes 2, which place between the two first pricks to the left hand that is under 7; then say how many times 2 in 17, (here you must be very cautious not to take too many) which here may be six times, place the 6 in the quotient as before, and under the second prick that is under 3, and divide as before, then double the quotient which is now 16 and it makes 32, place the 2 between the second and third prick, viz. under 5, and the 3 before it under the 6, so the 32 will stand under the 175 which is above; then say how many times 3 in 17, which you will find to be 5, place it in the quotient and under the third prick, and divide as before, always setting the Remainder over the head of its proper figures; then double the quotient again, which is now 165 and it makes 330, place the 0 between the two pricks as before, and place the figures before it to the left hand, as you see above, and the first figure to the left will be 3 which stands under 13; then say how many times 3 in 13, which will be 4, which place in the quotient, and under the fourth or last prick, and divide as before; so you will find no Remainder, which assures the number given to be a square number. The proof of these is known by multiplying the square Root found in itself (taking in the remains if any be) and it must produce that given number, otherwise it is false. Note how many pricks you have, and so many numbers must the quotient consist of. If the number given be not a true Square, than a fraction will remain, which fraction you may find out the value thereof to a tenth, hundredth, or a thousandth part; etc. Doing thus set next to the right hand after the Sum proposed, two, four, or six cyphers, or more (for the more cyphers you put, the less is your Error) and every two cyphers will produce a fractional figure more than the Integers belonging to the proper quotient, which are tenths, hundredths, or thousand parts of a Unite, according to the number of cyphers added; that is, if you add two cyphers, than you find the tenths of a Unite etc. But the Square Root being not of so much use in Gunnery, as the Cube Root, we shall proceed no farther to Exemplify the same, supposing it to be done already in the Treatise of Military Discipline. The Extraction of the Cube Root. Begin at your right hand, (as you did in Extracting the Square Root) and set pricks under every fourth figure, that is, leave two figures unprickt, or between the pricks, and so proceed to the left, until you have done as here you see, 7 5 6 7 8 7 3 2 (the number of pricks show the number of figures that will be in the quotient. Then see by the Table before in this Chapter the nearest Cube to the numbers standing over the first prick to the right hand, which is 75, I search in the Table of Cubes and find the nearest number to it in the Table of Cubes to be 64, and its Root 4, which must be set down in the quotient, and likewise its Cube 64 under the prick; and if that number doth not amount to so much as the number standing over the prick, then subtract it from the same, and set the Remainder overhead. Then triple the quotient, and that triple you must set under the next number to the right hand, before that prick where you did last end. Multiply that tripled number by the quotient, and set it down under the first triple, and that number let be your Divisor. Then (as in common Division) must you look how many times the Divisor in the figures is standing over them, and place that in the quotient. This done, Multiply your quotient by your Divisor; and set it under your Divisor, with a Line between. Then multiply the last figure in the quotient by itself, and then in the triple, and set that figure under the former, one figure more to the right hand. Lastly, Multiply the last figure cubically, and set that Sum also one figure to the Right hand; then add all these three multiplications together, and subtract it out of figures standing over the first and second prick, and the Remainder set over them. This done, again triple the quotient, and proceed exactly as before etc. If your number be not an exact Cube, but some numbers remain whereof you desire to find the exact fraction, that is as near as possible may be, viz. to a tenth, hundredth, or a thousandth part etc. To find the tenths add three cyphers, the hundreds 6 cyphers, the thousands nine cyphers, at the Right hand of your figures, according to the directions given in finding the fractional of a square. But these Rules being something tedious to many men, we will for their encouragement and ease add a Table of Squares and Cubes whereby any man may find, by inspection only, the Square and Cube of any number of Inches, and parts of an Inch, to a tenth part, provided your number exceed not 100 inches, which will be found very necessary, and save much labour, as will appear by the following Examples. But first we will present you with the Table itself. A Table of Squares and Cubes, very useful for the speedy Extracting of Square and Cube Roots, for the Resolution of Questions in Military Affairs: Whether for the Ordering of Battalions, or Gunnery, etc. R Aq Ac 1 1 1 2 4 8 3 9 27 4 16 64 5 25 125 6 36 216 7 49 343 8 64 512 9 81 729 10 100 1000 11 121 1331 12 144 1728 13 169 2197 14 196 2744 15 225 3375 16 256 4096 17 289 4913 18 324 5832 19 361 6859 20 400 8000 21 441 9261 22 484 10648 23 529 12167 24 576 13824 25 625 15625 26 676 17576 27 729 19683 28 784 21952 29 841 24389 30 900 27000 31 961 29791 32 1024 32768 33 1089 35937 34 1156 39304 35 1225 42875 36 1296 46656 37 1369 50653 38 1444 54872 39 1521 59319 40 1600 64000 41 1681 68921 42 1764 74088 43 1849 79507 44 1936 85184 45 2025 91125 46 2116 97336 47 2209 103823 48 2304 110592 49 2401 117649 50 2500 125000 51 2601 132651 52 2704 140608 53 2809 148877 54 2916 157464 55 3025 166375 56 3136 175616 57 3249 185193 58 3364 195112 59 3481 205379 60 3600 216000 61 3721 226981 62 3844 238328 63 3969 250047 64 4096 262144 65 4225 274625 66 4356 287496 67 4489 300763 68 4624 314432 69 4761 328509 70 4900 343000 71 5041 357911 72 5184 373248 73 5329 389017 74 5476 405224 75 5625 421875 76 5776 438976 77 5929 456533 78 6084 474552 79 6241 493039 80 6400 512000 81 6561 531441 82 6724 551368 83 6889 571787 84 7056 592704 85 7225 614125 86 7396 636056 87 7569 658503 88 7744 681472 89 7921 704969 90 8100 729000 91 8281 753571 92 8464 778688 93 8649 804357 94 8836 830584 95 9025 857375 96 9216 884736 97 9409 912673 98 9604 941192 99 9801 979299 100 10000 1000000 101 10201 1030301 102 10404 1061208 103 10609 1092729 104 10816 1124864 105 11025 1157625 106 11236 1191016 107 11449 1225043 108 11664 1259712 109 11881 1295029 110 12100 1331000 111 12321 1367631 112 12544 1404928 113 12769 1442897 114 12996 1481544 115 13225 1520875 116 13456 1560896 117 13689 1601613 118 13924 1643032 119 14161 1685159 120 14400 1728000 121 14641 1771561 122 14884 1815848 123 15129 1860867 124 15376 1906624 125 15625 1953125 126 15876 2000376 127 16129 2048383 128 16384 2097152 129 16641 2146689 130 16900 2197000 131 17161 2248291 132 17424 2299968 133 17689 2352637 134 17956 2406104 135 18225 2460375 136 18496 2515456 137 18769 2571353 138 19044 2628027 139 19321 2685619 140 19600 2744000 141 19881 2803221 142 20164 2863288 143 20449 2924207 144 20736 2985984 145 21025 3048625 146 21316 3112136 147 21609 3176523 148 21904 3241792 149 22201 3307949 150 22500 3375000 151 22801 3442951 152 23104 3511808 153 23409 3581577 154 23716 3652264 155 24025 3723875 156 24336 3796416 157 24649 3869893 158 24964 3944312 159 25281 4019679 160 25600 4096000 161 25921 4173281 162 26244 4251528 163 26569 4330747 164 26896 4410944 165 27225 4492125 166 27556 4574296 167 27889 4657463 168 28224 4741632 169 28561 4826809 170 28900 4913000 171 29241 5000211 172 29584 5088448 173 29929 5177717 174 30276 5268024 175 30625 5359375 176 30976 5451776 177 31329 5545233 178 31684 5639752 179 32041 5735339 180 32400 5832000 181 32761 5929741 182 33124 6028568 183 33489 6128487 184 33856 6229504 185 34225 6331625 186 34596 6434856 187 34969 6539203 188 35344 6644672 189 35721 6751269 190 36100 6859000 191 36481 6967871 192 36864 7077888 193 37249 7189057 194 37636 7301384 195 38025 7415875 196 38416 7529536 197 38809 7645373 198 39204 7762392 199 39601 7880599 200 40000 8000000 201 40401 8120601 202 40804 8242408 203 41209 8369421 204 41616 8489664 205 42025 8615125 206 42436 8741816 207 42849 8869743 208 43264 8998912 209 43681 9129329 210 44100 9261000 211 44521 9393931 212 44944 9528128 213 45369 9663597 214 45796 9800344 215 46225 9938375 216 46656 10077696 217 47089 10218313 218 47524 10360232 219 47961 10503459 220 48400 10648000 221 48841 10793861 222 49284 10941048 223 49729 11089567 224 50176 11239424 225 50625 11390625 226 51076 11543176 227 51529 11697083 228 51984 11852352 229 52441 12008989 230 52900 12167000 231 53361 12326391 232 53824 12487168 233 54289 12649337 234 54756 12812904 235 55225 12977875 236 55696 13144256 237 56169 13312053 238 56644 13481272 239 57121 13651919 240 57600 13824000 241 58081 13997521 242 58564 14172488 243 59049 14348907 244 59536 14526784 245 60025 14706125 246 60516 14886936 247 61009 15069223 248 61504 15252992 249 62001 15438249 250 62500 15655000 251 63001 15813251 252 63504 16003008 253 64009 16194277 254 64516 16387064 255 65025 16581375 256 65536 16777216 257 66049 16974593 258 66564 17173512 259 67081 17373979 260 67600 17576000 261 68121 17779581 262 68644 17984728 263 69169 18191447 264 69696 18399744 265 70225 18609625 266 70756 18821096 267 71289 19034163 268 71824 19248832 269 72361 19465109 270 72900 19683000 271 73441 19902511 272 73984 20123648 273 74529 22346417 274 75076 20570824 275 75625 20796875 276 76176 21024576 277 76729 21253933 278 77284 21484952 279 77841 21717639 280 78400 21952000 281 78961 22188041 282 79524 22425768 283 80089 22665187 284 80656 22906304 285 81225 23149125 286 81796 23393656 287 82369 23639903 288 82944 23887872 289 83521 24137569 290 84100 24389000 291 84681 24642171 292 85264 24897088 293 85849 25153757 294 86436 25412184 295 87025 25672375 296 87616 25934336 297 88209 261980 298 88804 26463592 299 89401 26730899 300 90000 27000000 301 90601 27270901 302 91204 27543608 303 91809 27818127 304 92416 28094464 305 93025 28372625 306 93636 28652616 307 94249 28934443 308 94864 29218112 309 95481 29503629 310 96100 29791000 311 96721 30080231 312 97344 30271328 313 97969 30664297 314 98596 30659144 315 99225 31255875 316 99856 31554496 317 100489 31855013 318 101124 32157432 319 101761 32461759 320 102400 32768000 321 103041 33076161 322 103684 33386248 323 103329 33698267 324 104976 34012224 325 105625 34328125 326 106276 34645976 327 106929 34965783 328 107584 35287552 329 108241 35611289 330 108900 35937000 331 109561 36264691 332 110224 36594368 333 110889 36926037 334 111556 37259704 335 112225 37595375 336 112896 37933056 337 113569 38272753 338 114244 38614472 339 114921 38958219 340 115600 39304000 341 116281 39651821 342 116964 40001688 343 117649 40353607 344 118336 40707584 345 119025 41063625 346 119716 41421736 347 120409 41781923 348 121104 42144192 349 121801 42508549 350 122500 42875000 351 123201 43243551 352 123904 43614●08 353 124609 43986977 354 125316 44361864 355 126025 44738875 356 126736 45118016 357 127449 45499293 358 128164 45882712 359 128881 46268279 360 129600 46656000 361 130321 47045881 362 131044 47437928 363 131769 47832147 364 132496 48228544 365 133225 48627125 366 133956 49027896 367 134689 49430863 368 135424 49836032 369 136161 50243409 370 136900 50653000 371 137641 51064811 372 138384 51478848 373 139129 51895117 374 139876 52313624 375 140625 52734375 376 141376 53157376 377 142129 53582633 378 142884 54010152 379 143641 54439939 380 144400 54872000 381 145161 55306341 382 145924 55742968 383 146689 56181887 384 147456 56623104 385 148225 57066625 386 148996 57512456 387 149769 57960603 388 150544 58411072 389 151321 58863869 390 152100 59319000 391 152881 59776471 392 153664 60236288 393 154449 60698457 394 155236 61162984 395 156025 61629875 396 156810 62099136 397 157609 62570773 398 158404 63044792 399 159201 63521193 400 160000 64000000 401 160801 64481201 402 161604 64964808 403 162409 65450827 404 163216 65939264 405 164025 66430125 406 164836 66923416 407 165649 67419143 408 166464 67917312 409 167281 68417929 410 168100 68921000 411 168921 69426531 412 169744 69934528 413 170569 70444997 414 171396 70957944 415 172225 71473375 416 173056 71991296 417 173889 72511713 418 174724 73034632 419 175561 73560059 420 176400 74088000 421 177241 74618461 422 178084 75151448 423 178929 75686967 424 179776 76225024 425 180625 76765625 426 181476 77308776 427 182329 77854483 428 183104 78402752 529 184041 78953589 430 184900 79507000 431 185761 80062991 432 186624 80621568 433 187489 81182737 434 188356 81746504 435 189225 82312875 436 190096 82881856 437 190969 83453353 438 191844 84027672 439 192721 84604519 440 193600 85184000 441 194481 85766121 442 195364 86350888 443 196249 86938307 444 197136 87528384 445 198025 88121125 446 198916 88716536 447 199809 89314623 448 200704 89915392 449 201601 90518849 450 202500 91125000 451 203401 91733851 452 204304 92345408 453 205209 92959677 454 206116 93576664 455 207025 94196375 456 207936 94818816 457 208849 95443993 458 209764 96071912 459 210681 96702579 460 211690 97336000 461 212521 97972181 462 213444 98611128 463 214369 99252847 464 215296 99897344 465 216225 100544625 466 217156 101194696 467 218089 101874563 468 219024 102503232 469 219961 103161709 470 220900 103823000 471 221841 104487111 472 222784 105154048 473 223729 105823817 474 224676 106496424 475 225625 107171875 476 226576 107850176 477 227429 108531333 478 228484 109215352 479 229441 109902239 480 230400 11059200 481 231361 111284641 482 232324 111980168 483 233289 112678587 484 234256 113379904 485 235225 114084125 486 236196 114791256 487 237169 115501303 488 238144 116214272 489 239121 116930269 490 240100 117649000 491 241081 118370771 492 242064 119095488 493 243049 119823157 494 244036 120553784 495 245025 121287375 496 246016 122023936 497 247009 122763473 498 248004 123505992 499 249001 124251499 500 250000 125000000 501 251000 125751501 502 252004 126506008 503 253009 127263527 504 254016 128024064 505 255025 128787625 506 256036 129554216 507 257049 130323843 508 258964 131096512 509 259081 131872229 510 260100 123651000 511 261121 133432831 512 262144 134217728 513 263169 135005697 514 264196 135796744 515 265225 136590875 516 266256 137388096 517 267289 138188413 518 268324 138991832 519 269361 139798359 520 270400 410608000 521 277441 141420761 522 272484 142236648 523 273529 143055667 524 274576 143877824 525 275625 144703125 526 276676 145531576 527 277729 146363183 528 278784 147197952 529 279841 148035889 530 280900 148877000 531 281961 149721291 532 283024 150568768 533 284089 151419437 534 285156 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XXV. The Use of these Tables in Gunnery. QUEST. I. By knowing the Diameter and Weight of any one Shot, to find the Weight of another Shot, being both of one and the same Metal. THe Shot whose weight we know not, we must have in Diameter likewise, which is found thus, Gird the Shot with a Line, then divide that into twenty two equal parts, and seven of those is the Diameter or the height of the Shot. But if you have a pair of Callapars by you, the best way is to take the Diameter with them. The fashion and form of taking the Diameter of a Shot, is as here you see in the figure following. calipers measuring a shot Cube each Diameter, then multiply the Cube of the Shot whose weight is requited by the Diameter of the given Shot, and that Sum divided by the Cube of the known Diameter, the quotient is the Diameter of the Shot required. If an Iron Shot of 4 Inches Diameter weigh 9 l. what shall a Shot weigh whose Diameter is twice as much, that is, 8 Inches. Example. Inch. l. Inch. l. If 4 weigh 9 what 8 Answer 72. 12 l. 4 512 8 4608 (72 The weight of the Shot of 8 Inches Diameter. 16 18 64 644 4 459 8 6 64 4608 512 This question may also be performed by the former Table of Cubes, if you search in the Collum of Roots until you find your Diameters in a right Line with the same under the word Cube, you will find the Cube answerable to the number given, thus; you will find the Cube of 4 to be 64, and of 8 to be 512, and this 512 multiplied by the weight of the known Bullet, viz. 9 l. it makes 4608, which divided by 64, gives the weight of the Bullet to be 72 l. which was to be known. QUEST. II. Knowing the Diameter and weight of one Shot, to find the Diameter of a Shot that weigheth twice as much. Suppose the known Shot was 4 Inches Diameter, and weigh 9 pound, and it were required to find the Diameter of a Shot, whose weight is twice as much, that is ●8, find the Cube-Root of each Shots weight, then multiply the Diameter of the Shot whose weight is known, by the Cube of the Diameter of the Shot whose weight is required; and that Sum divided by the Cube of the Diameter of the known Shot and the quotient is the Diameter required. Example. By the former Rule, or by the Table, the Cube of the pounds will be found to be 2,08, and the Cube of 18 will be 2, 62, now multiply this last number by 4, and it makes 9, 48, which divided by 2, 08 will give in the quotient 5, 03 for the Diameter required. This question may very easily be wrought by the Line of numbers, thus; divide the distance between 9 and 18 into three equal parts, and that extent will reach from 4 Inches to 5, 03 Inches, the Diameter required. QUEST III. How the former question may be Resolved Geometrically. Make a Square of the Diameter of the lesser Bullet, then draw a Line from Corner to Corner, and this Line thus drawn shall be the Diameter of a Shot twice the weight of the other; which if you divide into two equal parts, setting one foot of your compasses in the middle, you may draw a Circle, and that circumference will represent unto you a Bullet twice the weight of the lesser Diameter. This work may be proved Arithmetically thus; the Diameter of the lesser Bullet is 4 Inches, the Square thereof 16, which being doubled is 32; and the square Root of this 32 is 5, 65, and so much is the Diameter of the greater Bullet, which weighed 18 l. There ariseth here a difference between this way and the former, but this way is the most true; not but that both Rules are true in themselves, but the former depending upon finding the Cube Roots, which cannot be found much more exacter than what I have done, and so working by them, and they not being exact, causes the difference in the work, QUEST. IU. How to find the Diameter for the Weight of any Shot assigned. Suppose a Shot of 27 l. be 6 Inches Diameter, how many Inches Diameter is a Shot of 64 l. Find the Cube of 64 in the Table, and it will be found to be 4; which multiply by 6, and it makes 24; which divided by 3, the Cube of 27, and it gives 8 Inches for the Diameter of the Shot or Bullet which was required. QUEST. V How this Question may Geometrically be resolved. Mr. Gunter in his first Book, Section 4. hath showed how to make a Line of Solids on his Sector; but this Rule shows us the proportion of the Diameters in Weight, having a Shot of one pound, two pounds, three pounds weight of Metal, or stone, etc. For if the given Shot be one pound, divide the diameter of that Shot into 4 equal parts, and 5 such parts will make a Diameter of a Shot of the said Metal, as is proposed, that shall weigh just twice as much. And divide the Diameter of a Shot that weighs just two pounds into seven equal parts, and eight such parts will make the Diameter of a Shot of 3 pounds' weight. And Divide the Diameter of a Shot of 3 pounds, into 10 equal parts, and 11 of such parts will give a Shot of 4 pounds' weight. And divide a Shot of 4 pounds' weight into 13 parts, and 14 such parts will make a Shot of 5 pounds in weight. And divide the Diameter of a Shot of 5 pounds' weight, into 16 equal parts, and 17 such parts will make a Diameter of a shot that will weigh 6 pounds. And so dividing the Diameter of a shot 6 pounds' weight into 19 equal parts, and 20 such parts will make a Diameter of a shot that will weigh 7 pounds. Thus dividing each next Diameter into three equal parts more than the next less Diameter was divided into, and with one part added to the Diameter of a shot it will weigh just one pound more, and so may proceed infinitely. A second way to Perform this work. Find exactly the Diameter of a shot whose weight is just one pound, then describe a Circle whose Diameter shall be equal thereunto, and divide it into four equal parts, as a b c d, and draw the two Diameters a c and d b crossing the Centre, and then take the distance d c in your Compasses, and lay it off from e to 2, and this will be a shot of two pounds' weight. Then take the distance d 2, in your Compasses, and set it off from e to 3, so will that distance be the Diameter of a shot of three pounds' weight; and so you may proceed in the same manner at your pleasure; as you may see by the projection. diameter of a shot QUEST. VI If a Shot of three Inches and a half weigh six pounds, what will a Shot of seven inches and three quarters weigh. You may for 3½ put 3, 50. and for 7¾ put 7, 75. then you may Cube them the common way; then multiply the second by the third number, and divide by the first, the Quotient gives the content. You may more easily work it by the Table of Cubes aforegoing; that is, against the Root 3, 50. you will find its Cube to be 42, 875; and against the Root 7, 75. you will find its Cube to be 46, 548. and this multiplied by 6, and divided by 42, 875, will leave 65, 14. that is 65 pounds and 14/100 parts of a pound. In this nature may any Fractions be wrought, even as easy as whole Numbers, especially if you reckon your Fractions the Decimal way, or bring them into Decimal Fractions by Reduction. QUEST. VII. The Proportions between Bullets of Iron and Bullets of Lead or Stone, that is, by knowing the Weight of an Iron Shot, to find the Weight of a Shot of the same Diameter made of Lead or Stone. The Proportion between Lead and Iron is as 3 to 2, so that a Shot of two pound of Iron is the same Diameter as a Shot of 3 pounds of Lead. Example. If a Shot of Iron of 3●/● Inches Diameter weigh 6 pounds, what will a Shot of Lead of the same Diameter? For 3½ Inches put 3, 5, and say, if 2 give 3, 5, what will 3 give? 35 1 15 105 52½ pounds. 9 22 105 This 52½ pounds is the weight of a Shot of Lead of 3 Inches and a half Diameter. The proportion between Iron and Stone is as 3 to 8, so that a Shot of 12 pound of stone is as big, or the same in Diameter, as the like Shot of Iron that weighs 32 pounds; but some say the proportion between Marble and Iron is as 15 to 34. A Bullet of Lead to the like of Marble is in proportion as 4 to 1. The proportion between Lead and Brass is as 24 is to 19 The proportion between Iron and Lead, as some say, is as 19 to 28. The proportion between Iron and Brass is as 16 to 18. By these Rules we may Calculate a Table very easily, to know if an Iron Shot be wanting, and a Shot of any of the other metals to be had, what height and weight either Shot of Lead Brass or Stone ought to be, to fit any piece of Ordnance; and by the same method we have here Calculated a Table, which doth show the weight of any Shot of Iron, Led or Stone; from 2 Inches to 9 Inches. This is worthy to be observed, that you ought not to have so much Powder to Load a Piece that must discharge a Marble Shot, as an Iron Shot; but the proportion must be abated as the proportions between Stone and Iron doth allow of. A Table of the Diameter and Weight of all such Shot as are generally used in England, from one to eight Inches Diameter, with the length of every Piece fitting to carry such a Shot. The Names of the Pieces of Ordnance. Diameter of the Boar. Length of the Gun. Weight of the Gun in pounds. Breadth of the Ladle. Length of the Ladle. Weight of the Powder. Diameter of the Shot. The weight of the Shot. He shoots point blank. The Parts. Inches. Inches. Feet. Pounds. Parts. Inches. Parts. Inches. Ounces. Pounds. Parts. Inches. Ounces. Pounds. Paces. [8 [8 [8 [8 [8 A Base. 1: 2 4: 6 200 2: 0 4: 0 0: 8 1: 1 0: 5 60 A Rabanet. 1: 4 5: 6 300 2: 4 4: 1 0: 12 1: 3 0: 8 70 Fauconets. 2: 2 6: 0 400 4: 0 7: 4 1: 4 2: 2 1: 5 90 Faucons. 2: 6 7: 0 750 4: 4 8: 2 2: 4 2: 5 2: 8 130 Ordinary Minion. 3: 0 7: 0 750/108 5: 0 8: 4 2: 8 2: 7 3: 4 120 Minion of the largest size. 3: 2 8: 0 1000 5: 0 9: 0 3: 4 3: 0 3: 12 125 Saker the lowest sort. 3: 4 8: 0 1400 6: 4 9: 6 3: 6 3: 2 4: 12 150 Ordinary Sakers. 3: 6 9/9: 0 1500 6: 6 10: 4 4: 0 3: 4 6: 0 160 Sakers of the oldest sort. 4: 0 10: 0 1800 7: 2 11: 0 5: 0 3: 6 7: 5 163 Lowest Demiculvering. 4: 2 10: 0 2000 8: 0 12: 0 6: 4 4: 0 9: 0 174 Ordinary Demiculvering. 4: 4 80/11: 0 2700 8: 0 12: 6 7: 4 4: 2 10: 11 175 Elder sort of Demiculvering. 4: 6 12/13: 0 3000 8: 4 13: 4 8: 8 4: 4 12: 11 178 Culverings of the best size. 5: 0 10/13: 0 4000 9: 0 14: 2 10: 0 4: 6 15: 0 180 Ordinary Culverin. 5: 2 12/13: 4500 9: 4 16: 0 11: 6 5: 0 17: 5 181 Culverin of the largest size. 5: 4 12/10: 0 4800 10: 0 16: 0 11: 8 5: 2 20: 0 183 Lowest Demicanon. 6: 2 11: 0 5400 11: 4 20: 0 14: 0 6: 0 30: 0 156 Ordinary Demicanon. 6: 4 12: 0 5600 12: 0 22: 0 17: 8 6: 1/● 32: 0 162 Demicanon of great size. 6: 6 12: 0 6000 12: 0 22: 6 18: 0 6: 5 36: 0 180 Canon Royal, or of 8: 0 12: 8000 14: 6 24: 0 32: 8 7: 4 58: 0 185 QUEST. VIII. How to make a Shot of Lead and Stone together (the Stone being first put into the middle of the Mould, in which the Lead must be afterwards Cast round about the Stone) to be of the like Diameter and Weight as an Iron Shot is of. It is found by Experience that if you take five parts Led, and one part of Stone, it will come very near the matter. By these Rules have we Calculated this Table. It is found by experience, that if Inches. Quart. Lead. Pound. Ou. Stone. Pound. Ou. Both together. Pound. Oun. 1 0 1⅔ 0 0⅔ 0 2 1 2 0 6¼ 0 1¾ 0 8 2 0 14 0 4 1 2 2 2 0 12 0 8 2 4 3 3 2 0 10 3 12 3 2 5 0 1 0 5 0 4 7 7 1 8 8 15 4 2 10 8 2 2 12 10 5 14 7 2 14 17 5 5 2 19 4 3 12 23 0 6 25 0 5 0 30 0 6 2 32 0 6 0 38 0 7 40 0 8 0 48 0 7 2 48 0 10 0 58 0 8 59 0 12 0 71 0 you take 5 parts Led, and one part Stone, it will come very near the matter, wanting not above 3 Ounces, which is nothing, respecting the difference you shall find in Pibble Stones. Here you have a Table how much Lead, and how much Stone must be together, to make the equal of Iron Shot, from 1 inch, and to every half in the first and second Column to 8 Inch. Diameter; the third Column is how much Lead, the fourth how much Stone, the fifth how much weight both together. It's use is thus; knowing the Diameter of the intended Shot, enter the Table in the first and second Columns, and against them, in the third and fourth Columns, you have the Weight of Lead and Stone, that will make a Shot of the same Diameter with a Shot of Iron, whose weight is in the fifth Column. Example. An Iron Shot of 2 inches Diameter, will weigh 1 pound, 2 ounces; If I enter this Table with 2 inches, in the first Column against it, I shall find that I must have 14 ounces of Lead, and 4 ounces of Stone, and this will make a Shot of 2 inches Diameter equal to the weight of the Shot of Iron. QUEST. IX. To find the solid Content, and thereby the weight of any Iron Shot. By the former Table or otherwise, find the Cube of the Diameter, which if you multiply by 11, and divide by 21, gives the solid Content of that Bullet in inches and parts. Now to know how many pounds weight any such body doth contain, multiply the solid Content by 4, and divide that Sum by 16, it will show how many pounds of Iron that Bullet weigheth, for an inch square of cast Iron weigheth 4 ounces. CHAP. XXVI. Questions about Pieces of Ordnance. BEfore we come to work what we intent concerning a Piece of Ordnance, it is necessary to understand these Propositions following. PROP. I. Having the Diameter of a Circle, to find the superficial Content. Multiply the square of the Diameter of any Circle by 785 398, and the product that shall come of that Multiplication is the Superficial Content. PROP. II. Having the Diameter of any Circle, to find the Circumference thereof. The common way of proportions is, as 7 to 22, so is the Diameter to the Circumference; but more exactly it is done, if you multiply the Diameter by 3, 14, 16, or it may be done thus, as 113 is to 355; so is the Diameter to the Circumference. PROP. III. Having the Circumference of a Circle, to find the Superficial Content. Multiply the Square of the Circumference by 079, 578 will give the Superficial Content, or Multiply the Diameter by half the Circumference, and that Sum is the Superficial Content. PROP. IU. Having the Circumference of any Circle, to find the Diameter. Multiply the Circumference by 318 308, gives the Diameter of that Circle. PROP. V To measure the Frustrum of a Cone or Pyramid, knowing both the Diameters and length of the said Frustrum. Multiply the Diameters one by the other, and add to them both their Squares, and that Sum divided by 785 39, the one third part of the Remainder is the Content of the Cone. PROP. VI By knowing the weight of any one Piece of Ordnance, to find the weight of any other Piece of Ordnance. If a Saker of 4 inches Diameter weigh 1400 l. how much will a Cannon of 8 inches Diameter weigh, supposing they be equally fortified, (otherwise this Rule will not hold true) Cube each Diameter, or seek in the foregoing Table, and you will find the Cube of 4 to be 64, and of 8 to be 512, then say as 64 is to 1400 l. so is 512 to 12919 pounds, and this is the weight of a Cannon that is able to carry a proportionable Charge. PROP. VII. To find the solid Content of the Concavity, Cylinder, or Soul of a Piece of Ordnance. By the Rules given in the first of these Propositions, find the Superficial Content or Ayrea of the end of the Cylinder, which multiplied by the length, will give the solid Content. PROP. VIII. To find the solid Content of the Soul or Concave of a Piece of Ordnance, if it be Tapering, or the Section of a Cone. The working of this Proposition is the same as in the fifth Proposition, or you may for brevity's sake, add both the Diameters together, and the half of that may be accounted the mean Diameter, by which you may find the Superficial Content by the first Proposition, which multiplied by the length, gives the solid Content. PROP. IX. How by knowing the weight of any one Piece of Ordnance, to find the weight of any other, being of the same shape. With your Crallapars take the greatest thickness of the Piece whose weight you know, and likewise of the Piece whose weight you know not; then by the former Table find the Cube of each Diameter, then say, as the Cube of the Diameter of the Piece whose weight is known, is to the weight of the same Piece, so is the Cube of the Diameter of the Piece whose weight is unknown, to its weight sought. But if the Pieces be not of one and the same Metal, after you have found the weight, supposing it to be the same Metal, than you must by the Rules given in the 24 Chapter, proportion the weight according to the Metal the Piece is of, whose weight you know not, and if the Piece whose weight you know, do differ in proportion, as if one be of Iron, the other of Brass, the proportion is as 16 to 18, etc. PROP. X. By knowing the weight of any one Piece of Ordnance, to find the weight of any other Piece of Ordnance, although differing in shape or form, knowing the Diameters at Britch, Muzzles, and length of the Pieces. By the Rules given in the ninth Proposition, find the solid Content of the Piece whose weight you know, supposing it to be a solid body without a Chamber. Then take the solid Content of the Concave part, by Rules given in the seventh Proposition, if it be a Cylinder; or by the ninth Proposition, if it be Tapering. This latter Content that is of the Concave being deducted from the former Content of the whole Piece, gives the solid Content of the whole Metal in the Piece. Observe the same Rule in finding the solid Content of the Piece whose weight is unknown; Cube both the solid Contents, and say, as the Cube of the solid Content of the Piece whose weight is known, is to his weight; so the Cube of the solid Content of the Piece whose weight is unknown, is to his weight; but if they be not of one and the same Metal, we must work by proportions, according to the Rules given in the 24th. Chapter. By these Rules, when Weights and Scales have been wanting, have I found out the weight of several Pieces of Ordnance; and if exact account be taken with good judgement and consideration had, of the difference of the Trunions and Britch end, especially if there be any great difference in the Pieces, you cannot err much; for the Rule being demonstratively true, the operation truly done, cannot err. PROP. XI. To find the weight of any Piece of Ordnance, where we have no other Piece of Ordnance, whose weight is known. Find the solid Content of the Metal according to the Rules given in the tenth Proposition; then multiply that by 4, and dividing that Sum by 16, will give the weight of the Piece, supposing it to be Iron; for it is generally allowed that one inch square of Iron will weigh just four ounces. If the Piece whose weight you seek be not of Iron, but of some other Metal; then work by the Rules given in the 24th Chapter, for the difference of the weight of Metals. CHAP. XXVI. To know the Allowance or Proportion of Powder proper for any Piece of Ordnance. THe general way is to allow for such Brass Pieces as are above 4000 l. five ounces and a half of powder to a hundred weight of Metal. But for Culverin of Brass fortified of above 4000 l. about 3 ounces and a half complete; yet there is used also generally for the proof of Shot three fourth's or four fifths of the weight of the Iron Shot, but for the Service not above half the weight of the said Shot. For Culverin, the whole weight of their Shot for proof and for action, is two thirds of its weight. The Saker and Falcon four fifths, the weight of their Shot; and for lesser Pieces the whole weight, and one third more for proof; but for action just its weight: but when they grow hot, a part must be abated according to discretion. You must note, if you know how much Powder will Load a Brass Piece, three quarters so much will Load an Iron Piece of Ordnance. SECT. I. If Weights and Scales be wanting, and Ladles and the Cartredge not marked, yet to judge a reasonable Charge for any Piece of Ordnance. The Allowance that may be made for Cannon is two thirds, the Diameter of the Cylinder for Culverin three Diameters, for the Saker three and a half Diameters, and for lesser Pieces four Diameters of the Cylinder, which length will also serve for the Cartredge. SECT. II. By the weight of Powder for any one Piece, to find the weight of Powder proper to any other Piece of Ordnance. To perform this work you must find by the foregoing Table the Cube of the Diameter of the bore of the Piece, whose allowance of Powder you know; also the Cube of the Diameter of the bore of the Piece, whose allowance of Powder you desire to know: Then say, as the Cube of the known Piece is the quantity of Powder known, so is the Cube of the Diameter of the unknown Piece to the quantity of Powder proper to the unknown Piece. SECT. III. Practical Experiments concerning the Allowance of Powder necessary to any Piece in time of Service. It is always necessary to take care in time of Service of over-loading a Piece, which Error many run into, only minding the bore of a Piece, and not minding whether the Metal will bear it, and so endanger themselves and other standers by. To avoid such errors observe these experienced Rules. To a Demi-canon fortified of Brass about 4400, or a little more, there is allowed by the Tower 5 ounces and a half of Powder to every hundred weight of Metal; yet in time of Service Gunners do allow but 3 ounces ¾ to every hundred weight of Metal, which doth amount to 10 l. ¼. Demi-canon Drake of Iron about 3800 l. is allowed by the Tower 3 ounces and a half of Powder to every hundred weight of Metal, which will be durable in time of Service; but there are Drakes of 4400 l. which must be allowed more, according to the proportion of their weight. Culverin fortified Brass of 4600 l. is allowed by the Tower 3 ounces and a half of powder complete to every hundred weight of Metal, which may be burnt in time of Service with very little abatement. Culverin Drakes of 40000 l. or thereabouts of Iron, for these Pieces may be allowed in time of Service 3 ounces to every hundred weight of metal, but proportionably must be allowed for Pieces of greater or lesser weight. The 12 Pounders fortified of Brass of 3200 l. for Guns of this weight and nature is usually allowed 3 ounces and a half for every hundred weight of Metal. Demyculverin Brass of 3300 l. there is allowed by the Tower for Pieces of Ordnance of this nature 3 ounces and a half and something more, to every hundred weight of Metal, the which is approved a very sufficient Allowance. Demyculverin Drakes of 2900 l. is allowed by most two ounces three quarters to each hundred weight of metal, which will be durable in time of Service. Saker fortified Brass of 2000 l. is allowed 3 ounces and something more for every hundred weight of Metal, but there may be a small abatement in time of Service. CHAP. XXVII. To know whether a Piece of Ordnante be truly bored or no. YOu must provide a Pikestaff, about a foot longer than the bore of the Piece, and at the end thereof fasten a Rammer head, that will just fill all the bore to the touch hole; and at the other end of the staff, you must boar a hole big enough to put through a Rod of Iron, which must hang from the same; and at the other end of the Rod must be made a weight about the bigness of a Saker Shot, this is done to make the Pikestaff and Rammer head to lie with the same side upward when they are taken out of the Piece, as they did when they were within the Piece; than you must put your Instrument thus prepared into the Piece, letting the Iron Ball (that is at the end of the Rod, which is put through the hole bored a cross the Pikestaff) hang perpendicular; then take your priming Iron, or some other bodkin, and put it down the touch hole to the Rammer head, making a mark therewith; this done, draw out your Instrument, and lay the same on a long Table, with the Iron Ball hanging off the end perpendicular, as it did when the Instrument was in the Piece; then observe, whether the mark you made upon the Rammer head when it was in the Piece, be just upon the uppermost part of the same, if it be, the bore of the Piece lies neither to the right hand nor to the left; but if you find it any thing to the right or left hand, so much lieth the bore either to the right or left, and the Piece in Shooting must be ordered and charged accordingly. But if you would know whether the bore lie more upwards or downwards, then bend a Wire at the very end, so that it being put in at the very touch hole, may catch at the metal when it is drawn out, then put the Wire down the touch hole till it touch the bottom of the metal in the Chamber, then holding it in that place, make a mark upon the wire just even with the touch hole, after draw up the wire until it catch at the metal on the top of the Chamber, and holding it there, make a mark as before; the difference between the two marks is the just wideness of the Chamber, and the distance between the first mark and the end of the Wire (having half the Diameter of the Chamber of the Piece substracted from it) will leave half the Diameter of the Piece, if the Piece be true bored; but if the Piece's number be more than half the Diameter of the Piece, the bore lieth too far from the touch hole, and the upper part of the metal is thickest, but if lesser, the lower part of the metal is thickest or hath most metal. CHAP. XXVIII. Of the necessary Instruments for a Gunner, with several other necessary things. A Master Gunner intending upon service, ought most chief to be prepared with these Instruments, as Calabers, Compasses, height board, Sight Rule, Gunners Scale, and a Gunners quadrant; to divide as well into 12 as 90 equal parts, with a Geometrical Square, to make Montures, Levels, heights, Breadths, Distances, and Profundities, (of which you shall read more in the Second Part;) also with a little brass Level, Scales, Weights, Priming-Irons, Moulds to make Cross-bar Shot for Muskets, a Book of Accounts, and an Iron wire or Spring, and a Transome to dispart a Piece of Ordnance; that the Transome may go up and down according to the Diameter and thickness of the Piece, let the Transom be long enough to reach the base Ring, from the touch hole. In the next place he ought to be very expert in the knowledge of cutting out, making up, and finishing all sorts of Ladles, Sponges, Rammers, Cartredges, etc. For which purpose you may have Recourse to the foregoing Table. And because it may sometimes happen by reason of the steepness, badness and unevenness of the way, you may be driven to dismount and remount your Piece, you get up to the top of a Hill; therefore you must carry with you a Gynn and a Wynch, with all the appurtenances thereunto belonging; as wind Ropes, an Iron Goats-foot, with a Crow, Pins, Truckles, Pulleys to help you at a dead lift. CHAP. XXIX. The making of Rammers, Sponges, Ladles, and Cartredges, Former's, Carriages, Wheels, Trucks &c. with the Height of Shot fit for any Piece. FOr the better expedition of this work we have in the former Table shown the length and breadth of each Ladle, always remembering that you cut each Ladle somewhat longer, that is, allowing so much more as must be fastened to the staff, or so much as the staff goes within the Plate. The Buttons or heads of the Ladles must be near the height of the shot. For Sponges, the bottoms and heads must be of soft wood, as Birch and Willow, and to be one Diameter and three quarters in length, and three quarters or very little less of the height covered with Sheep's skin, and nailed with Copper nails, so that together they may fill the hollow of the Piece; Let the bottoms and heads of the Rammers be made of good hard wood, and the height, one Diameter of the Shot, and the length one third of the Diameter of the Shot. To make Ladles for Chamber bored Pieces, open your Compasses to the just Diameter of the Chamber within one eighth part of an Inch, Divide that measure in two equal parts, than set the measure to one of them, and by that distance upon a flat or paper draw a Circle, the Diameter of that Circle is one fourth part shorter than the Diameter of the Chamber; Take three fifths of that Circle for the breadth of the Plate of the Ladle. But for Cannon, the length ought to be twice and two third parts, to hold at twice the just Diameter of the Powder. As for Example, The Diameter of a Circle drawn for a Cannon whose Chamber bore is 7 Inches, containeth six and three quarters, the circumference whereof is 21 Inches 6/7, and three fourth parts thereof is 12 ¾, and so much aught the Ladle to be in breadth, and in length 18 ⅔ parts. By this Rule you may make a Ladle for any Tapered Piece. Take notice for a general observation, that a Ladle 9 balls in length, and two balls in breadth, will near contain the just weight in Powder, that the Iron Shot for any piece weigheth. Lastly, for Cartredges, they are generally made of paper Royal or Canvas. Take the height of the bore of your piece without the vent of the Shot, and cut the cloth or paper of 3 such heights, for the Cannon in length 3 Diameters, for the Culverin 4 Diameters, for the Saker and Falcon etc. half of the height of their proper bores, and leaving in the midst at the top or bottom one other such height, to make a bottom for the Cartredge, cutting each side something larger for Sewing, glewing, or pasting them together; you must have a great care to augment the goodness of your powder, and likewise the heating of your Piece, and so augment or diminish the quantity of Powder. Let your Former be made to your Ordnance to the height of your Shot, and a convenient length longer than the Cartredge ought to be, and tallow it over first that the paper may slip off, and then put your paper on your Former. If you make your Cartredge of Canvas, half a Diameter more is allowed for seams, but if you make it of paper, half or three quarters of an Inch overplus for pasting will serve, being leapt once about the Former; having the bottom fitted upon the end of the Former, which must be hard and close pasted by the lower side of the Cartredge, then let the lower end of the Cartredge be pasted down hard round about the bottom, and let them be well dried before you fill them, and mark them how high they must be filled. And if you have no Scales nor weights by you for Cannons, put two Diameters and a half for the height the powder must come, for Culverin 3 Diameters, for Saker 3 and a half Diameters, for lesser Pieces four Diameters of the Cylinder. For Carriages of Pieces of Ordnance for Land service the Rules are given thus, one and a half the length of the Cylender is the length of the Carriage, and in depth four Diameters of the bore of the Piece at the fore end, in the middle three and a half, and at the end next the ground two and a half, let the thickness be the Diameter of the Shot, the wheels should be one half of the length of the Piece in height, but for Saker and Minion you must exceed the former proportion by one twelfth part, the Falcon and Faulconet by one sixth part. The Naves, the Cheeks called Limbres, and wheels, are usually made of Elm, but the Transoms, Axeltreees, Fore-Carriage and Cross beams, are made of Oaken Timber. For drawing of Guns by men in case horses be wanting, there is usually allowed to every sixty, eighty, or a hundred weight of metal to one man, according to the nature of the ground whereon they are to be drawn. As for Sea Carriages, they are so well known to every Carriage-maker that they need not to be spoken of. As for fitting Shot to each Piece, it is the opinion of most Gunners, that every Piece of Ordnance ought to have its Shot within one quarter of an Inch of the Diameter of the bore; others do say, that the one and twentieth part of the Diameter of the Piece's Cylender is more proper and correspondent for all sorts of Pieces whatsoever; Every man may make choice of that which by experience he finds best. CHAP. XXX. How a Gunner ought to charge a Piece of Ordnance. HAving showed the complete making of Pieces of Ordnance, and the preparing of powder and Shot, with the due allowance of powder fit for every Gun, with all the Instruments and Materials necessarily belonging to a Piece, as to its Rigging and Loading; It remains now, that we go Artist like to work to charge a Piece, and order all things for the best conveniency, and that the less danger may follow when you come to Action or Service; and for that purpose having planted your Piece upon the platform, have in readiness powder, Bullets, Linstocks, Scowrers, Rammers, and the rest of your things. Stick up your Linstock to Leeward of you; then to work with your Piece. First, clear your Piece within with the Scowrer, and see that the touch hole be clear, and not stopped, and so clear, that no dirt or filth be in the same; Then let him that is by to assist, (for a Piece cannot be managed by less than two) bring the Budg-barrel with the powder just before the mouth of your Piece, put then your Ladle into the same and fill it, and if it be over-full, give it a little ●og, that the overplus may fall down again into the barrel; after this, put it gently in at the mouth of the Piece, even until the end of the Ladle be thrust up to the Britch end of the Piece; then must you turn the Ladle gently and softly, and let it lie within the Chamber of the piece, drawing out your Ladle almost to the Muzzle of the Piece, put it back again to take up the lose corns, which were spilt by the way, and to bring them up to the Charge of powder; this done, the Gunner must draw out this Ladle, and take out of the Budg-barrel a second Ladle full, (by our former Rules given he must know the quantity of powder that his Piece will require) and so putting it in the Piece up to the former Ladle-full, than you may draw it out, and do as you did before, that no lose corns may lie in the bottom of the Piece; and in drawing out his Ladle, he must have a care that he let not fall any powder upon the ground; for it is a thing uncomely in a Gunner, to trample powder under feet. Then take a wisp of Straw, Hay, or any other thing, and put it hard in at the mouth of the Piece, then turn your Ladle end for end to come to the Rammer, thrust it into the Piece after the wisp, and drive it up with it, and it will carry all the lose corns which possibly may be scattered in the Mould of the Piece; having driven the wad up to the powder, give it two or three gentle shoves to make it lie close only, but drive it not too hard lest you break your powder too much, which would hinder its force; The wisp or wad being close to the powder, draw out the Rammer and put in the Bullet, which roll gently in the Piece up to the wad that was before put in to keep up the powder, the Shot being in, put in a second wad after the Bullet, and thrust it also home to the Bullet. Always remembering whilst the powder is putting in and wadding up, one be ready at the touch hole and keep it stopped with his thumb, that no powder fly out at the touch hole, but that it be likewise filled with powder, which may be supplied out of his powder-horn. The Gunner that Loads a Piece is to be very careful, and endeavour always not to stand before the muzzle of his Piece whilst he is loading the Piece, but on one side of the same, lest a danger or mischief might happen to him. And thus the Piece having its due Charge of Powder and Bullet, he must cover the touchhole with an Apron made of Lead, or for want of that, with dried Sheepskin; then let him levelly his piece and set away the Budg-barrel of powder with the rest of his things, in some hollow place under the ground covered over safe; he must then attend the Gentleman of the Ordnance, or other chief Commander, their Order or Command, before he give fire. Touching the Charges of Pieces, I have given full instructions necessary thereunto, with the weight of powder and Shot for any piece. But to say something here touching the quantity of powder, proper for a Load; we do find some difference amongst Authors; Some whereof do maintain, that there ought to be allowed to every Piece for its Charge so much powder as half the weight of the Bullet; others are of the opinion, that the more powder is put into a Piece, the swifter and farther the Bullet will fly, urging many reasons to prove it. But experience, the Mistress of this Art instructeth us better, for if a Piece be loaden with two thirds of the weight of her Shot in powder, it sends the Bullet or Shot going more swiftly, and will carry it farther, which hath been very many and often times tried, so that at this time, 'tis without contradiction. Again, others do maintain, that if one should forcibly Ram the Bullet, than the powder might take fire before it cast forth the Bullet, and then would cause the Bullet to fly farther than otherwise it would do; but you must consider in so doing, you either endanger the breaking of the piece, or else the making it crooked and unserviceable; because your ordinary Pieces will not bear so great a Charge of powder. This hath been tried by the Sea side before his Excellency Prince Maurice, of famous memory, where first one and the same Piece was Loaden with ten pound of fine powder, to see how far She would carry the Bullet; the place being marked where the Bullet rested. The Piece was loaden again with nine pounds of powder which shot as far as when the Piece was Loaden with ten pounds of powder. But last of all, this piece of Ordnance being Loaden or Charged with 7 pounds of the same powder, it carried her Bullet further than the two former Shots; whence one may observe that a piece of Ordnance may be overcharged, and therefore a good Gunner ought to have a singular care to give unto his Piece her due measure and Charge. CHAP. XXXI. Of the Office and Duty of a Gunner, with all his Properties, Endowments and qualifications. HE that intends to be a Master Gunner, and would not abuse himself nor others of the same profession, must be qualified according to our Instructions following, viz. He ought to be well skilled in Arithmetic, and to understand the Extraction of the Square and Cube Roots, and to have knowledge in Geometry, according to our Instructions in the second part, whereby he may be able to take heights, depths, breadths and lengths, and to draw the plot of any piece of ground, to make Mines and Countermines, Ramparts, Baskets of earth, and such like things used in time of war, as well offensive as defensive. He ought most chief upon Land-Service to be well skilled in the making Platformers, with Defences, Troniers, Gabbions, Loops, Parapets of Earth, and Faggots of 23 or 24 foot high; two foot high of Earth, bed upon bed, unto eleven foot high, and after three foot Terra plene, to raise the Tronniers and Loops, so that for the Cannon it be three foot wide in the Barb, and within twelve foot wide, without the lower part thereof to descend Scarpwise, the better to discover the Enemy's avenues and offend them more freely, for avoiding the blast and Smoke and ruin it would else make: for Culverin two foot and a half within, and nine foot without will serve; and for less Pieces the less measure. If the Battery be to be made with Gabbions', they being filled with Earth without Stones, moistened and Rammed 7 foot in Diameter, three Ranks between two Pieces, if the place will permit, or two at least; and three Rows also one before the other, setting one between two, so that if one Rank will have three, the second will have two, and the third one; but it will be hard to make a safe Battery with Gabbions', Cannon or Culverin proof. Concerning Plat-forms. Let the platform for a Cannon have thirty foot for reverse, and 27 foot for a Demi-canon, and he ought to see that his plat-forms be even, or rising one foot for 20 foot backward the better to stay the Reverse, and facilitate the bringing the piece when Loaden to the Loop. The platform ought to be made clean, that no stones or other things lie in the way for the wheels to run upon, whereby may be hindered the true intent of his Shot. He must before any service is, examine his Piece of its goodness or defect; according to our former Instructions given in this behalf, he must also be furnished with all necessary things for his Artillery, the particulars thereof we have mentioned in the 29 Chap. but because it takes not up much paper we will repeat them here again, viz. Wheels, Trucks, Axeltrees, Ladles, Rammers, Sponges, Worms, Tampions, height-board, Auger-bit, fitness and roundness of the Shot, Chane-Shot, Cross-bar Shot etc. Canvas or strong paper for Cartredges, Calabers, Compasses, Sight Rule, Gunners Scale, Quadrant, Scales, Weights, priming-Irons, and Aprons to cover the Touch hole. Before he come upon Service, he ought to examine and prove the goodness of his Powder and Match, and examine it according to the Rules given where we treat of the Examination of the goodness of Powder. A Gunner ought to be most careful to see that the Powder be placed safely from danger of his own, as also the Enemy's Ordnance, and to be furnished with artificial Torches, Dark Lanterns, with all sorts of Fireworks, of which you shall have a particular account in the Treatise of Fireworks at the end of this Book. He must have by him his Begin and Winch, Hand-Spikes, Crows, to mount and dismount Guns at pleasure as occasion may serve, also Coins, Budge-Barrels, Powder Baskets to carry Shot to your Piece, to keep his Linstocks well armed with good Match. He must always have by him a Ruler, Scale, Compasses, to measure the Diameters or Boar of every Piece, and likewise the length of the Cylinder within, the better to fit her with due Shot and Proportion of Powder. He must learn by such Instructions as we have already given, the Names, Length, Weight, and Fortification of every Piece about the Chamber, and to tell readily how much Powder is a due Charge for every Piece, and what Shot is necessary. How many Persons must attend in time of Service, how many Horses or Oxen will draw a Piece of Ordnance, and in case they be wanting, how many men will serve. How many pound weight of Shot one man may drive before him in a Wheel-barrow from place to place. A Gunner ought chief to Charge and Discharge a Piece of Ordnance Artist like; and when he opens, or orders to be opened the head of a Powder Barrel, let no Iron Tool be used thereunto for fear of taking or striking fire; for that purpose therefore it is usual to have wooden Mallets, which will prevent such dangers. Every Gunner before he beginneth to make a Shot, aught to consider that a wad of Hay, or of untwisted Ropes, will make the Shot shoot wide of the Mark. He ought to consider whether the Trunions be placed in their due place in the Carriage, whether the Carriage have its due length, whether one wheel be not higher than the other, or whether one wheel doth not reverse quicker or sooner than the other, for these will cause the Piece to err, and to shoot wide of the Mark. Every Gunner ought to consider, that if his Piece lie point blank or under Metal, than he ought to put in a sufficient wad after the Shot, to keep it close to the Powder; for if it should not be close, great danger might follow; for if the Shot should lodge any distance from the Powder, then in the firing of that Piece it would break off in that very vacant place between the Shot and the Powder, and so do damage to himself for standers by. If your Piece be mounted, you then use no wad at all after the Shot. Every Gunner ought to have standing by him some Tubs of water to wet his Sponges in, whereby to cool his Piece in time of Service, as also to be ready upon occasion to put out any Fire that might happen in time of Service. Every Gunner ought to try whether his Piece is truly bored or not; if it be not, he is to take it into consideration, and to order his proportion of Charge, according to the thinnest part of the Metal, to prevent all danger. A Gunner ought to take his Observation of the Mark or place he intends to direct his Shot to, just over the middle of the bore within the Piece, for by this means he may be able, by his Skill, to make a true Shot in a bad Piece. A Gunner, that he may the better direct his Shot to the place desired, aught to consider the difference of the Metal of the Piece at Britch and Muzzle, and thereby truly how to dispart a Piece, be in either true bored or not. Of disparting a Piece, I shall show how it may be done several ways in the following or second part of this Gunnery; where we come to the practical part of the Art in handling a Piece of Ordnance upon all occasions. THE Complete Gunner. THE SECOND PART. CHAP. I. The Description and use of the Geometrical Quadrant, for the taking Heights, Distances, Depths, etc. FIrst, you must make a common simple large Quadrant thus with your Ruler, draw the Line A B, and with the Distance A B in your Compasses upon the Centre A describe the Arch B D, then with the Distance A B, setting one foot of your Compasses in B, set it off upon the Arch B D, and it will reach to L, divide the Arch B L into two equal, parts and that will be at F; The distance O L, being set upwards from L, will reach to D, so then drawing the Line A D, will make the Quadrant A B D, and the Arch B O L D will be divided into three equal parts; now every one of those parts must again be divided into three equal parts, and every one of them into 10 equal parts, so will your Quadrant be divided into 90 equal parts, called Degrees. scale of degrees Of the Scale. From any part of the Lines A B and A D, at equal distance from the point A, as at g and h, raise two perpendicular Lines which will meet in the point m, which we divide here into 12 equal parts, but may be divided into 100 or a 1000 equal parts at pleasure, and the more parts they are divided into, the more exact will your work be; let these Lines g m and him be marked into the Divisions from the point A. Let two sights of Brass be placed upon the Limb of your Quadrant, at the places marked E and F. Let the Division upon the Line b m, being next the sights, be termed right shadow, the Division upon the side g m, left or contrary shadow. Let a Line with a Plummet be fitted to your Quadrant falling from the Centre A, as you see in your Figure. CHAP. II. The Use of this Quadrant in taking the Perpendicular or direct height, by help of the Sun's shadow. COnvey the left side of the Quadrant Geometrically towards the Sun, the Thread and Plummet having their free course, moving it up or down until both your sights have received the Sunbeams; then if your Thread be found in the twelfth part, all things that are upright or truly perpendicularly elevated, are equal in height with their shadows. If the Thread with the plummet be observed to cut any of those parts next the sights, called right shadow, between m and h, than every upright thing is more than the shadow, by such a proportion as 12 exceeds the parts where the Thread was found. If the Thread fall upon the first division, than 12 times the shadow is the height. If it fall upon the second Division, 6 times the shadow is the height. If it fall upon the third Division, 4 times the shadow is the height. If it fall on the fourth Division, 3 times the shadow is the height. In the fifth Division twice and two fifths of the shadow is the height. In the sixth twice, in the seventh once, and five sevenths in the eighth Division, one and a half in the ninth, one and a third in the tenth, one and a fifth part in the eleventh, once and the eleventh part of the shadow is the height on the twelfth part, than the length of the shadow is the height, as we said before. Or in few words it may be done thus, Multiply the length of the shadow by 12, the product divided by the parts in which you found the Thread, your quotient showeth the height. But if the part cut be on the contrary shadow, that is, if the Thread fall between g and m, augment then the length of the shadow by the parts declared by the plummet, and the increase divide by 12, and the product is the Altitude. degrees of shadows Example. In the Foregoing figure it is plainly to be perceived, when the figure falleth upon the 12 Division, the shadow is equal with the thing itself; In the 6 of the right, it is but half, in the 6 of the contrary it is twice the height, and so to conclude, as the side in the right exceeds the parts, so doth the Altitude the shadow; and the contrary in the contrary shadow. Behold the figure 6 where you will find the Thread cutteth 6 parts of the contrary shadow upon the Quadrant, the shadow B C then being 210 foot, multiply (as I have said) the length of the shadow 210 foot by 6, the parts cut by the Thread, and it makes 1260, and that divided by 12 riseth 105, which is the Altitude of such a body, that casts a shadow of 210 feet. Also the height of any unknown thing may be known by taking the length of its shadow, and the length of the shadow of any staff set upright whose length is known, saying, as the length of its shadow is to its height, so the length of the shadow of the unknown thing is to its height. CHAP. III. Without Shadow or any Supputation by your Quadrant Geometrical, to take heights approachable. LIft up ingeniously your Quadrant exactly made towards the thing to be measured, looking diligently through both sights backward or forward, as occasion is given, until you see the top, so that your Line or Thread fall just upon the middle or 12 Division; now if you measure your distance from you to the foot of the Object, which is the point directly under the top, then have you the Altitude of the highest summitie to the right point or base in heightequal with our standing, adjoining with it the height of your eye downwards. degrees of shadows CHAP. IU. With the Aid of two Stations to find out Inapproachable heights. SEek two Stations going hither and thither, yea, toward or from the thing you intent to measure, so that in the one place the thread may fall just in 12, and at the other Station in 6 points of a right shadow; then if you double the Distance of both places, the Summitie shall appear from that part of the thing measured, which is equal in height with your Eye; or if your standing be even with the Base, joining to that double distance the height of your eye, you have the whole Altitude from the ground, etc. If the one Station cause the Thread to fall in 12, and the other in 8 of a right Shadow, then triple the Distance between the two Stations, so have you the height also: Or if the one be in 12, and the other in 9 of right shadows, then quadruple the distance, the one under 12, and the other under 6 of the contrary shadow, and the place between both Stations is equal with that you measure, ever understanding from your Eye upwards. degrees of shadows CHAP. V How by the Quadrant, with Calculations, speedily to find all heights accessible. YOur Quadrant, as in the former Figure, handsomely elevated against or towards the thing to be measured, perceiving through both sights just the top, mark well the Division or points crossed by your Thread, whether it be of the right shadow, then multiply the distance between you and the foot of the Object by 12, and divide that Sum by the parts cut upon your Quadrant, which your Thread manifesteth; and the remainder is the height of the Object from your Eye. But if the Thread fall upon contrary shadows, work contrarily, that is, augment it by the part, and divide that Sum by 12; Remembering ever to add the height of your eye downward to your quotient; so have you your desire, the Base being equal with your standing. degrees of shadows Example. Admit the Thread with the plummet note 6 parts of contrary, as you may see in the foregoing figure, the distance from the base A to your standing B 115 foot multiplied by 6, so have you 690, which divided by 12 yieldeth 57 ½ foot; to this adjoin 5 foot (being the height of your eye from the ground) and so find the Altitude to be 62 ½ foot. To find what part of your Altitude is Level with your Eye. 'Cause the Plummet and Thread to fall upon the side of your Quadrant where the Degrees begin, which you will find before in the Description of the Quadrant to be the side A B, and then searching through the Sights that part, that which you can spy of your Altitude (the plummet hanging upon the said Line A B) is levelly with your Eye, the height whereof from the base compared with the Altitude of your Eye, discovereth the inequality or difference of the ground, that is to say, how much higher or lower the base of the thing to be measured is than the ground at your Station, which difference, as you shall see cause, added or substracted from your heights found as is before declared, yieldeth most exactly the true Altitude: And thus you may be assured never to err, how unequal or uneven soever the ground be. You may also by two things of one length joined thus in a right Angle, find the Altitude of any thing. right angle CHAP. VI To Measure the Distance any place is from the top of a Castle or Work. THis Work is Performed as the former in the 2d. Chap. only here with a Plummet and Line we take the height or depth from the top of the Castle A, to the foot of the Castle B; and suppose that to be equal to the distance there taken, and the distance B C equal to the height, and then work by the Rules there given, and you will find the distance C B. This is so plain there needs no Example. CHAP. VII. To get the Length or Distance of any place or Mark in sight, be it never so far, without Instrument. AMongst many practices I find this the onliest way to obtain our desire without the help of an Instrument, yet in this is necessarily required to have ground enough at liberty on one side. Then begin thus; at the beginning of your Length set up a staff or mark that may be seen afar off, then go from it Orthogonal or Square-wise on which side you will 200 foot; the more ground the better; Put up there a staff also: now convey yourself to the first staff or mark, going back from it 300 foot, more or less, at your pleasure, set up there a third staff so, that the first mark or staff and it agree all in a straight Line from your sight to the farthest part of your length by the judgement of your eye; now go side-wise from thence as far in a right Angle, until the second mark offer itself aright between the extreme part of your length and sight, and there put the fourth staff. All this performed, seek out the distance between the first staff and the Second, and that name your first distance; then the distance between the first and third, name your second distance; Again, the distance between the third and fourth staff is the third distance. Deduct your first distance from the third, so remaineth the Divisor; then multiply your third distance by your second, and the product divide by your Divisor, the quotient showeth the true length from the third staff to the fortress or mark desired: for plainness behold the figure. measure of distance Example. Here this Letter A represents the Castle, being the distance to be measured; B is your first staff; C the second staff, differing from B the first Orthogonal 100 foot; D the third staff, being distant back from the first in a Right line with the mark A 133 foot; E is the fourth staff, running sidewise Orthogonally, or in a Square, from the third, until the farthest part of your length A, is perceived in a right Line with the second staff at C; and this distance D E let be 120 foot. Now by Substraction take 100 from 120, there remaineth for a Divisor 20; then multiply 133 by 120, so riseth 15960, which divided by 20, and there cometh 798 foot, the true distance between D and A, from which if you abate A B 133, there remaineth B A your propounded distance. But forasmuch as this conclusion is to be done without Instrument, and here Orthogonal motions sidewise is required, it shall be requisite also to declare how an Orthogonal or Right angle is upon a sudden to be made; ye shall therefore (according to Pythagoras' Invention mentioned among the Definitions at the beginning of this Book) take 3 Staves, Cords, or such like, making the one 4 such parts, as the other is 3, and the third 5; This done, conjoin their ends together, and the angle subtended of the longest staff is a right, which first placed at B, and after at D, directing one of his comprehending sides to A, the other shall guide you to C and E; or if you desire with more expedition to dispatch, and not to tarry the proportioning of Cords, or such like, to this Pythogarick Rule, take any 3 Staves, Sticks, or Threads, and conjoin them, making a Triangle, it matters not of what form or fashion they be, then placing one angle thereof at B, turning one side to A, direct yourself sidewise to the other, always remembering to place the same angle at D, and departing sidewise again in like manner, in all the rest do as before is declared. Thus using any mean diligence, yvo shall most exactly measure any distance. CHAP. VIII. With Halbeards, Pikes, or any Staves, having no other Instrument, you may measure the Distance between any two Towers, Castles, or other Marks, lying in a right line from you, not coming near any of them. YOu must first (as we have declared in the last Chapter) prepare a Triangle, with joining any three Staves, or such like, together, which you must (at your standing) place in such sort, that one of the sides containing the Angles, may lie directly toward the Mark: Then setting up a Staff, Pike, or other Mark there, depart sidewise, as the other side of your Angle shall direct you, so far as you list, the more ground the better, and there set up your second Staff or Mark; then go directly back from your first Staff (always keeping it exactly between your sight and the Mark) as many score again, or Pike lengths, as you list, setting up a third staff; this done, you shall place the same Angle you used at your first Staff now again at your third staff, in all points as it was before; the one side of the Angle lying directly toward the first Staff, the other side will show you whither you shall go to place your fourth Staff; for passing still in a right line with that side of your Angle, you shall at the last find the second justly situated between you and the farthest Mark, and there set up the fourth Staff; then remove your Angle again to the second Staff, and placing there as before, the one side even with the first Staff, pass on in a right line with the other, until you come directly between your nearest Mark and the fourth Staff, and there pitch up the fifth. measure of distance Now you must measure how many Paces, Halbeards, or Pikes length, are between your first and second Staff, deducting that from the distance between the third and fourth, and this Remainder shall serve you for a Divisor; then multiply your distance between the second and fifth Staff by the distance between the third and fourth, the product divide by your reserved Divisor, and it yieldeth in the Quotient the true distance between these two Marks. See the foregoing Figure. Example. Let A B be the two Marks, whose distance I would measure; my standing place where I set up my first Staff, I; in the middle, my Triangle made of three Staves, Halberds, Bills or any such like things, K L M; the Staves or Halberds of which I make my Triangle N, which I first place at C, secondly at D, thirdly at E; and note, at C and D the situation of the Triangle is all one, but at E it somewhat differeth, as you may behold in this Figure, which I would have you note, lest haply you be deceived in your practice. C E the distance between the first and third, deducted from D F the distance between the second and fourth, there remains H F your Divisor; which measured, I admit 50 Halberds lengths, the distance between G E 30 Halberds lengths, the space between D F 100 Halberds length, now 100 multiplied in 30 produceth 3000, which divided by 50, leaveth in the Quotient 60. I conclude therefore the distance between A and B to be 60 Pikes lengths. This one thing is to be taken notice of especially, that whatsoever you meet the space G E withal, that you use the same in measuring H F; and as for D F it matters not what you measure it withal, for your Quotient shall bear the same denomination. Preciseness is to be used in placing of your Triangle, and in measuring E G, and H F, otherwise error may ensue; especially if D F be but a small distance, and the Angle at B very sharp. There needeth in this matter no further admonition, small Practice will resolve all doubts. CHAP. IX. To measure the distance between any two Forts, Castles, or other places, howsoever they be situated, though there be Rivers, or such like Impediments between, that you cannot approach nigh any of them; and that without an Instrument also. LEt your Angles, as before hath been said, be prepared of any three Staves, etc. you shall first at pleasure set up one Staff, and applying thereunto your Angle in such sort, that the one containing side lie directly to one of the Marks (which here for distinction sake I will call the first) go backwards too and fro until you find your second Mark precisely covered with your Staff, noting what part of the line or side subtending the Angle it cuts by your line visual, and there make a fine notch or mark upon that subtending Staff; which done, you shall go sidewise from the first erected Staff, as the other containing side of your Triangle will direct you, so far as you list, and then set up your second Staff; yet pass on from thence in a right line with that containing side of your Angle that riseth from your Staves, and cometh somewhat toward the Mark, and go so far until you spy yourself justly between your third Staff and your first mark, there set up your fourth Staff, then resort to your Angle again, and standing behind the second Staff, note whether a right line from the Angle to that notch (before made on the subtendent Staff or side of the Triangle) will direct you, for that way precisely shall you go on until you come in a right line with the second and third Staff, and erect there the fifth Staff; this done▪ measure the distance between the second and third Staff, reserving that for a Divisor; then multiply your distance between the first and third Staff, by the distance between the fourth and fifth Staff, the product divide by your reserved Divisor, and it yieldeth in the Quotient the true distance between the two marks. geometric figure Example. Let A B be the distance I would know, C my first Station where the first Staff is erected; I my Triangle made of three Staves, and placed at the Station, and directed with one of the containing sides to A which is the first mark, as you may see in the Figure, and with the other side to D and E the second and third Staves; H is the notch or mark upon the side subtended to the Angle, where the line visual from ☽ passeth too the second mark B; my Triangle now I situate at D, as it was before at C, the one contained side lying even with the erected Staves, the other directed to my fourth Staff F, placed in a right line with E the third Staff, and A the first mark. Again, my line visual proceeding from D to H, the notch in the subtended side of the Angle is extended to my fifth Staff G, situated exactly between E the third Staff, and B the other mark: This done, I measure the distance between my second and third Staff, finding it 20 foot, likewise between the fourth and fifth Staff, and find it 72 foot, finally between the first and third Staff 65 paces; so that according to the Rule before given, multiplying 65 by 72, I have 4680. which divided by 20, yieldeth in the Quotient 234, and so many paces is there between A and B. I have not set out the Figures in just proportions answering to these numbers, for that is not requisite, but in such form as may best open and make manifest the situation of the Staves and Triangle, wherein consists all the difficulty of this Practice. CHAP. X. How you may readily find out the distance to any Tower, Castle, Forts, etc. by help of the former Quadrant. LEt the Quadrant be made upon a square Board as is there marked A D B Q. Let D B be divided into 90 Degrees or equal parts; and instead of the 12 equal parts, or right and contrary shadows, g m and h m, let the two sides D Q and B Q be divided each into 1200 equal parts, or as many as you please, and marked from the Centre A, and have a Ruler or Index to be moved round upon the Centre A, having two sights upon it, set just upon the feducial line of the Index, and let it be divided into such equal parts as the Lymb B Q, or D Q. Let this Instrument thus fitted be handsomely placed upon its Staff, or otherwise, lay the feducial of your Index upon the beginning of the Degrees of the Quadrant, and turn your whole Instrument (the Index not moved) till you may espy through the sight your mark, then remove your Index to the contrary side of the Quadrant, placing the line feducial on the side line where the degrees end, and look through the sights, and in that very line set up a mark a certain distance, the farther the better; this done, take away your Instrument, and set up a Staff there, and remove the Instrument to the mark you espied; set your Index on the beginning of the Degrees, moving your whole Instrument, till you find through the Sights the Staff at the first Station, then remove your Index (your Quadrant keeping its place) till you may again espy through the Sights your mark; which done, note the Degrees cut by the line feducial, and then work thus, upon some even smooth Superficies, whether it be Board, Plate, or Paper: Draw first a straight line, and open your Compasses to some small distance, call that space a score, and make so many such divisions upon your Line as there is scores between your Stations; then upon the end of your line raise a perpendicular, and fixing one foot of your Compasses at the other end, opening it to what wideness you please, draw an Arch rising from the same line that represents your Stationary distance, and dividing it into 90 equal parts or Degrees (as you was taught in the making your Quadrant) extend from the Centre to the number of Degrees cut by your feducial line, a right line, until it concur with the perpendicular before erected; then see how much of that space (which representeth the score in dividing your Stationary distance) is contained in the perpendicular; so many score is the mark off from your first Station, and by dividing the Hypothenusal line, you may find the Distance from the second Station. Example. A the first Station, C the second, D the mark, A C 80 paces, Degrees of the Quadrant cut by the line feducial at the second Station is 71 d. ½, and H is the unity or measure representing one score, E F 4 parts, G F 12, G E 12 ⅔, or thereabouts: Thus may you conclude the mark to be distant from the first Station 12 score paces; the Hypothenusal line or distance of the mark from the second Station, 12 score and 13 paces. See the Figure. measure of distance To perform this Work by Calculation. In the foregoing Figure, B is the place to be measured, A the mark where I first disposed my Instrument, from it I go Orthogonally to C, the Index, suppose cuts there 400. In the right side of your square, the distance between B and C, I have supposed 80 paces; wherefore multiply. 1200 by 80, and there cometh 96000, whfch divided by 400, declareth unto me 240 paces, the true length from A to B. Or by dividing 1440000, the square of 1200, with 400 the parts cut, you shall produce in the Quotient 3600, your proportionable part found by the Rule of Reduction, which augmented in 80, yieldeth 288000, and that divided by 1200, bringeth in the Quotient 240, which is the length A B agreeing with the former operation. But if you would find C B, or the Hypothenusal line being the distance between the second Station and the mark; then by the former Table of Squares, or with your Pen, find the Square of A C, and the Square A B the distance already found from the first Station, these two Squares added together, the Square Root of that Sum is the distance C B, viz. 253 paces; or if the Sum of the Square of A B and A C be sought for in the Table of Squares, you will find against it 253 paces, the length of C B, which was to be found; for the Square of A B more, A C is always equal to the Square of C B, and the Square of C B less, the Square A C is equal to the Square of A B. CHAP. XI. To measure the distance between any two marks that lie in one right line from the Eye. THis may be resolved by the former Proposition, measuring how far either distance is from yourself, and then deduct the one from the other; or thus, another way, the side of your Geometrical Square directed towards them, depart Orthogonally, as is before declared, 100 or 200 paces at your pleasure, but the more the better; then place your Instrument again, turning the side of it towards the first Station, remove then the Index to either marks, noting what parts at either place the Index doth cut of the Scale; and if the Index at both times falls on the left side, deduct the lesser from the greater; with the number remaining, augment this distance between your Stations, and dividing by the whole side of the Scale, your Quotient is the distance. If the Index fall on the right side at either time, then must you by the Rule given in the Ninth Chapter, reduce them into proportional parts; or if at one time it fall on the left side, and at another time on the right, then shall you only reduce the parts cut on the right side; which done, deduct as before is said, the lesser from the greater, and with the remainder multiply your distance Stationary, the product divided by 1200, yieldeth how far one mark is beyond another. Behold the Figure. measure of distance Example. Admit A B the marks in a right line from C your first Station, D the second Station Orthogonally situated from C, where your Square being placed, suppose your Index first cut 800 parts on the left side, and after 900 parts on the right side; you must divide the Square of 1200 by 900, as was taught in the former Chapter; so will your Quotient amount to 1600, from which if you withdraw 800, the parts cut on the left side, there will remain 800, which multiplied by 200 paces, the distance Stationary C D, there amounteth 160000, this divided by 1200, yieldeth in the Quotient 133⅓; therefore the distance from A B, your mark, is 133 paces, 1 foot, and 8 inches. CHAP. XII. To measure the Distance between any two marks lying in one plain level ground, howsoever situated, without Arithmetic. THis at two Stations may be done, as we have done before; but we will here suppose but one Station, knowing the distance from that Station to each place, and the Angle it makes with each Station; then by help of a pair of Compasses, and any line of equal parts, this is most easily wrought, as is well known to small Practitioners in this Art, it being also the 4th Question in Rightlined Obliqne Triangles. I did intent to show the working of every one of these Questions by Logarithms; but considering a Gunner hath not always such Tables by him (and if he have them and understands rightlined Triangles, doubtless he may easily apply them to this work) I therefore thought what I have done in this case to be sufficient. CHAP. XIII. The Description of an Instrument, whereby to plot out any Coast, Country, City or Garrison, and to take the distance to every Remarkable Object. THis Instrument is four square, with a Circle in the middle, divided into 360 equal parts or degrees. Let the division of the square be from 1 to 100, or as many as you can; you must also have fixed to it an Index, with sight upon the same, as you may see by the Figure following in the next Page. It is called a Circumferenter or Geometrical Square. To draw a Plot of any Coast or Country in such sort that you may readily tell how far any place is distant from you, or one from another. plot of distance Example. There is a Sea Coast having sundry Harbours, Towns, Villages, Castles, and such like situated thereon, whose Plot in due proportion I require, with the exact distances of every place one from the other. Having therefore elected a lofty seat, from whence I may behold all these places (my Instrument situated as is declared) removing the Index to a Castle that is farthest, being a Castle standing in the mouth of a Haven, having received it through my Sights, the line fiducial of my Index cutteth 30 degrees; then I remove it to the next, being a Village or Fish Town, and the Index cutteth 50 degrees, and so round to all the rest; and thus I shall have the Table of my first Station, as followeth, The Table of my first Station. Deg. The Castle. 30 The Village. 50 The City. 75 The Eastern Head of the Bay. 95 The Western Head of the Bay. 97 ½ The Fort within Land. 130. This done, I behold another Hill or high place; from whence I may in like manner view all those places, and turning my Index thereunto, I find the Line fiducial lying upon 180 Degrees; then carrying my Instrument thither, and placing it in all points there, as it was at the first Station, I turn my Index again to my first Mark or Castle, and find it to cut in 15 Degrees, at the second 25, etc. as you may see in this second Table. The Table of my second Station. Deg. The Castle. 15 The Village. 25 The City. 40 The Eastern Head of the Bay. 50 The Western Head of the Bay. 55 The Fort within Land 80. With these Tables I repair to a Paper, Parchment, etc. and by the former Rules draw the Figure following. scale of distance Having thus completed your Plot, and found the distance between A and B to be 5 miles, make a Scale according to that distance, divide it into miles and parts, and with it you may measure your distance from place to place, or the distance from any of your Stations to each place, according as you have occasion. Thus passing or changing your Station, you may make several Plots, containing the true proportion and distance of Towns, Villages, Ports, Roads, Hills, Rivers, and all other notable places throughout a whole Realm. Thus I suppose we have writ all such propositions of measuring of heights, distances, and profundities, etc. as may be necessary to our work. We will next come to the more Practic part, of managing a Piece of Ordnance to do the best Service. CHAP. XIV. The Description and use of the Gunners Scale. gunners 'scale Edward Fage in Hosier Lane Londini Fecit You will observe by this Instrument, that the Ladle is but 3 Diameters of the Shot in length, and 3/5 part of the Circumference, from the Cannon to the whole Culverin, and the charge of Powder will be found to be about 2 Diameters of the Piece; from the Culverin to the Minion, the Charge may fill 2 Diameters and a half; and from the Minion to the Base 3 Diameters; but of this matter we have spoke at large in the first part of this Book; but there having left out the Table of Periors and Drakes, I thought good here to insert it. A necessary Table of Periors and Drakes proportioned. Names of Pieces. Height of the bore in inches. Length in Diameter. Weight in met. pound. Weight of Powder. Length of the Ladle. Canon Perior. 9 10. 12. 8 3500 3, 3 ⅓ 4 3 D. Canon Drake. 6 ½ 16 3000 9 pound. 4 ●/2 Culverin Drake. 5 ½ 16 2000 5 4 ½ D. Cul. Drake. 4 ½ 16 1500 3 ½ 4 ½ Saker Drake. 3 ½ 18 1200 2 4 ½ CHAP. XV. How to make a true Dispart of any true bored Piece of Ordnance. KNow first, that to dispart a Piece of Ordnance, is no otherwise than to bring the Diameter at Muzzle to be equal to the Diameter at the Base Ring; in true founded Ordnance, half of the Diameter of the Cylender is the dispart; but more generally it may be done thus, Gird the Piece round about the Britch with a thread, after do the like by the Muzzle Ring, lay these two strings straight upon a Table at length, and make two marks for the length of each string; divide the distance between each of these two marks into 22 equal parts with your Compasses, and 7 of them are their Diameters; then measure how much each Diameter is in length, and subtract one Diameter from the other, then take the just half of the difference, and that is the true dispart of your Piece in inches, and part of an inch. But these Diameters are better and more artificially taken with a pair of Crallipars, as we have showed before in taking the Diameter of a Shot, and then measured upon your Scale of inches and parts, will give you the true Diameters of the Piece both at Britch and Muzzle, with which work as above. Also you may find the true dispart of a Piece thus; Put a small Wyer or priming Iron in at the Touchhole of the Piece to the bottom of the Concave; then mind what part of that Iron is even with the Base Ring, and make a mark there; then take it out and apply it to the Muzzle, and place it upon the lower edge of the Concave of the Piece as upright as you can, and mind what part of the Iron or Wyer is even with the upper part of the Muzzle Ring, and there make a mark; for the difference between these two marks, is the true dispart of the Piece: or after you have placed your Iron upon the Muzzle as before, cause a dispart to be raised so high as that mark which was made upon the Iron when 'twas put down the Touchhole. If from the top of the dispart a fine thread or line be carried to the Muzzle Ring, you will see how high you may make a dispart at the Trunions. Or thus a dispart may be made at the Trunions; lay a piece of soft Wax upon the Trunions, and let one raise it high, or depress it, until that the Metal at the top of the Base Ring, the Wax between the Trunions, and the dispart of the Muzzle, be all three of one height precisely; but the former way with a thread is more exact. A Piece of Ordnance may be disparted thus; take two sticks (each of them must be longer than the Piece) and also make a Plummet of Lead to hang in a small thread made fast to one end of the stick, which lay cross the top of the Base Ring, to and fro, until the Plummet descending from the end thereof, may just touch the side of the Metal of the said Ring; then keeping fast the stick in that place, hang your Plummet down by the other side of the stick, until it on the otherside just touch the Metal of the Base Ring; when you have done, cut off the stick just in that place by which the Plummet descended, perpendicularly, and this length is the just Diameter of the Base Ring; after this manner you must proceed to take the Diameter at the Muzzle. Then lastly, set these two sticks together even at one end, and mark their difference in length or height; for just half of that difference is the dispart of that Piece. I would advise all Sea Gunners upon some occasions to use Disparts between the Trunions of their Pieces, made of a just height, on purpose to serve that place, by the method we have even now prescribed, and let them be tied about the Piece with a twine, because else at every Shot they will be to seek, when upon a sudden they should use them, and they will much avail and stand them in great stead. I could express other ways, only I think these sufficient. CHAP. XVI. How to give Level with a Piece of Ordnance to make a Shot at any Mark assigned. SEt your dispart on the Muzzle Ring, just over the Centre of the mouth of the Piece, which you may best do by putting a stick cross the bore, and dividing it into two equal parts; then with a Plumb line hanging over the mouth of the Piece, being guided by the divided stick, you shall have good aim where to set your Dispart; this being done, go to the Base Ring, if the Piece be true bored, then find which is the highest part, and middle of that Ring; but if the Piece be not true bored, then find which part of the Base Ring is just over the Cylender, and take that for your true line: when you have found out the dispart, and placed it, and also found what point in the Base Ring is to answer to it, then make some very small mark on the Base Ring in that place, hold your head about two foot from the Base Ring, and there you may best observe, as the Piece is traversing, when you are in a direct line with the mark; this done, give one of your men order to raise and fall the Piece with his Hand-spike as you shall appoint him, until you can, holding your head two foot from the Britch of the Piece, with your eye perceive the mark at the Base Ring, and the top of the dispart in a direct line with the mark you must shoot at; at that instant stop the motion of the Piece with a Coin, that it may remain as you have directed it; then Prime your Piece, and give fire. finding level Before you place your Dispart, you are to take notice whether the ground be Level whereon the Wheels of the Gun stand, or if they be not one higher than the other, and if the Trunions stand just over the Axletree of the Wheels or no; whether one Trunion lie higher on the Carriage than the other: whether the Gun be truly placed in the Carriage or not; that is, that it be not nearer one side than the other: whether the Carriage be truly made according to the direction we have already prescribed in the first part; whether the Axletree be placed just cross the Carriage or not. CHAP. XVII. How, if a Shot do carry to the right or to the left, under or over the mark, by reason of some known fault, to amend it in making the next Shot. AFter you have made one Shot, and find the Piece carry just over the mark, then do all that has been taught again, and when your Piece lies directly against the mark, observe how much the last stroke of the Shot is above the mark, so much longer make your dispart, that the top of it may be just seen from the Britch of the Piece, in a direct line with the stroke of the Shot; when it is of this length, then levelly your Piece with this new dispart to the assigned mark, Give fire, and without doubt it will strike the same. If the first Shot strike under the mark, then bring the Piece in all points as before to pass, mark how much of the dispart is over the stroke of the Shot, and cut it just so short, as being at the Britch you may discern the top of it, with the mark on the Base Ring and stroke of the Shot in a just right line, and when you perceive it is of such a length, levelly the Piece to the assigned mark, as at the first, then Prime and Give fire. If the first Shot strike on the right hand of the mark, to mend it you must levelly the Piece as formerly; you standing behind the Britch of the Piece, observe the stroke of the Shot over the dispart, and that part of the Base Ring as you at that instant look over in a right line towards the dispart, and the stroke of the Shot, set up in that place a Pin with a little soft Wax on the Base Ring; so this Pin will be in a right line with the dispart and stroke of the Shot: This being done, levelly your Piece to the mark assigned by this Pin and the dispart, and without question you will make a fair Shot; for when you levelly by the Metal of the Base Ring where the Pin is placed, and the mark of the Piece standing at that direction, look over the top of the dispart from the notch in the Base Ring, and you shall find it to lie just so much to the left, as the former Shot struck to the right, from the assigned mark, which should in all likelihood now strike the mark. But if a Shot be both too wide and too low, than you must use both the directions above taught, to make the next Shot: first regulate the dispart by cutting it shorter, according as the Shots mark is lower than the assigned mark; when this is done, then proceed to my directions to mend shooting wide, and these things performed with care and diligence, cannot choose but mend a bad Shot. CHAP. XVIII. Of shooting at Random at a Mark beyond the right line of the Pieces reach, or right Range of a Shot; and the way of framing a Table of Randoms, by help of the Gunners Quadrant. FOr the effecting of this matter, we must have a Quadrant with a Thread and Plummet (which is described in the first Chapter of this second Section) to one side of this Quadrant; so that one end of the Ruler may go into the Cavity of the Piece, and let a Piece of Lead be fastened to the end of the Rule, to make it lie close to the bottom of the Metal within, the Quadrant hanging without, and the Plumb-line swaying or hanging down from the Centre of the Quadrant, perpendicular to the Horizontal line; for the Quadrant being thus placed, you may mount a Piece to what degree you shall find fit to shoot by. Now every one that will learn to shoot at Random, must draw his Piece on a level ground, where first shooting level, he must observe that distance in feet or paces, then mount his Piece to one degree, and mark where that shall graze; thus finding the distance of every degree from the level to the tenth degree, by these distances make a Table, to which annex the degrees against the distance; by which Table you may (using the Art of Proportions) find how far another Piece will convey her Shot from degree to degree, and in Loading your Piece for this work you must have your Powder exactly weighed, and likewise the Wad, and let the Piece cool of itself, and this you must do every time; and if the Piece be mounted, there needs no Wad after the Shot; also you must have a special care of the strength of the Powder, and let the Powder equally, and with the same force and strength be pressed home, as near as possible you may. CHAP. XIX. An effectual way to make a Shot out of a Piece of Ordnance at Random. HE that intends to be expert at these things, ought principally to endeavour, at one time or another, to obtain so much liberty of his Superior Commanders, as to make two, three, or more Shot with the Piece he chooseth, or intends for most Service; then must he measure the distance from the Platform to the first graze of the Shot; and must apply it to the Table, which I have here inserted, being the experience of such as have been knowing Gunners. But first I shall set down Mr. Nye of Worcester's Experiment, not as he is Mathematician, as he writes himself (which Title none of our Learned Mathematicians of England do assume) but as he was a Practical Gunner, and made these several experiments upon four several degrees of Mounture, viz. 1 deg. 5 deg. 7 deg. 10 deg. from thence was found these Randoms. At 1 degree, the Shot did light from the Piece or place of standing 225 paces. At 5 degrees, the Random was 416 paces. At 7 degrees, the Random was 505 paces. At 10 degrees the Random was 630 paces. And by these Experiments a Table may be framed according to this Rule. As the known degree of Mounture, is to the number of paces the Piece carries; so is the number of degrees proposed, to the distance required. The use of this Table will plainly appear in one only Example. A Table of Randoms. Degrees. Paces. 0 206 1 225 2 274 3 323 4 370 5 416 6 461 7 505 8 548 9 589 10 630 Suppose you make trial of your Piece of Ordnance, according to the method prescribed in the last Chapter, and find that at 6 degrees of Random upon a level ground, the Shot is conveyed 619 paces, and you are to ply your Piece against a place which lies beyond the point blank, the distance being 498 paces, to know the degree the Piece must be elevated too, do thus; in this Table of Randoms against 6 degrees, there is 461 paces; then say as 619 paces is to 461, so is 498 to 375; which number, or the nearest to being sought, in this Table is 370, and stands against 4 degrees, but because it is not exactly the same number, you must find out the part of a degree or minute, by a Table of proportional parts; but if the mark you shoot at be lower or higher than your Platformer, than you must add or subtract so many degrees or minutes from the degrees and minutes found, and the remainder is the degree you ought to mount your Piece to. Now that we may be understood-well, we must know that there are two sorts of Ranges or Motions of a Shot, of which you may see more in Chap. 20. the one is called the Right Range, and the other is termed the Curved or Crooked Range, and these two there termed a Compound Range, is called the Dead Range; that is to say, the whole distance from your Platform from whence the Shot was made, to the place where the Bullet first grazes; yet the perpendicular descending of the Bullet is also called the Natural motion, as you may see by the figure hereafter placed. Captain Hexham in his Book of Gunnery, shows how by finding out the Random of a Cannon for the first degree of Mounture to find the Random for every degree to 45 degrees, which is the utmost Random, after this manner; First, find out how many paces the Cannon will shoot, being laid level by the Metal (which he accounts for one degree of Mounture) divide this distance by 50, then multiply the Quotient by 11, and that will bring out the number of the greatest digression or difference between Range and Range, which being divided by 44, the Quotient will show the number of paces which the Bullet will lose in the other Ranges from degree to degree. Example. A Battering Cannon being laid by the Metal, will shoot his Bullet (as he saith) 1000 ordinary paces, two foot and a half to each pace; which being divided by 50, the Quotient will be 20, which multiplied by 11, is 220 paces, which is the number of the next digression made in the second degree: which 220 divide by 44, the number of the remaining degrees yields 5, which is the number of paces to be diminished in each degree; and by this Rule this Table is framed. A Table of Randoms to 45 Degrees, accounting 2 Foot ½ to the Pace. Paces diff. The Degrees of Mounture. 0 0775 225 1 1000 220 2 1220 215 3 1435 210 4 1645 205 5 1850 200 6 2050 195 7 2245 190 8 2435 185 9 2620 180 10 2800 175 11 2975 170 12 3145 165 13 3310 160 14 3470 155 15 3625 150 16 3775 145 17 3920 140 18 4060 135 19 4595 130 20 4325 125 21 4450 120 22 4570 115 23 4685 110 24 4795 105 25 4900 100 26 5000 95 27 5095 90 28 5185 85 29 5270 80 30 5350 75 31 5425 70 32 5595 65 33 5560 60 34 5620 55 35 5675 50 36 5725 45 37 5770 40 38 5810 35 39 5845 30 40 5875 25 41 5900 20 42 5920 15 43 5935 10 44 5945 5 45 5950 Butler this Table of Alexander Bianco for all sorts of Ordnance, I do account as one of the best. A Table of Randoms for the six points of the Gunners Quadrant. 1 2 3 4 5 6 Faulconet. 375 637 795 885 892 900 Falcon. 550 935 1166 1254 1309 1320 Minion. 450 765 954 1026 1071 1080 Saker. 625 1062 1325 1425 1487 1500 D. Culverin. 725 1232 1537 1653 1725 1740 Culverin. 750 1275 1590. 1710 1785 1800 Demi-Canon. 625 1062 1325 1425 1487 1500 Canon of 7. 675 1147 1431 1489 1606 1620 Double Canon. 750 1275 1660 1710 1785 1800 The use of this Table is thus; having resolved upon what point of Mounture, look in this Table for the name of the Piece, and right under that point against the name of the Piece, that is in the common Angle, you shall find the number of paces of her Random sought. CHAP. XX. How to find the right Range of any Shot Discharged out of any Piece, for every Elevation by any one right or dead Range given for the Piece assigned. THe right Range of every Piece being discharged in a level, or parallel to the Horizon, is allowed by some not to exceed 185 paces, that is 5 foot to a pace, yet some reckon much more, but then they account ordinary steps or paces of two foot and a half; and Batteries made with such Pieces are usally made at 100 or 120 such paces, at which distance they do the best execution. The utmost Random likewise of any Piece that is from the Platform to the first graze of the Bullet, I find by some to be about ten times the distance of the right Range; and accordingly I have so set it down in the Table. As for the Ranges to the other degrees and points of the Quadrant, I find these Tables in Good Authors. This Table is rather proportional A TABLE OF Right Ranges, or Point Blanks. Randoms, or the first Graze. The Degrees of the Pieces Mounture. 0 The Right Range in Paces, 5 Foot to a Pace. 192 The Degrees of Mounture. 0 The Paces of the Random, 5 Foot to a Pace. 192 1 209 1 298 2 227 2 404 3 244 3 510 4 261 4 610 5 278 5 722 6 285 6 828 7 302 7 934 8 320 8 1044 9 337 9 1129 10 354 10 1214 20 454 20 1917 30 693 30 2185 40 855 40 2289 50 1000 50 2283 60 1140 60 1792 70 1220 70 1214 80 1300 80 1000 90 1350 90 than real, and doth best agree with greater Ordnance; but by help of it, working by the Rule of proportion, you may know the Random of any Piece of Ordnance; by first (as we have said before) making one Shot, and measuring from your Platform that distance. You may make a Table for your Piece thus, Suppose a Saker being mounted to 5 degrees, shoot the Bullet 416 paces, how far will it shoot being mounted 10 degrees? As 722 the Tabular distance for 5 degrees of Mounture, is to 416 paces the distance found, So is the Tabular distance for 10 degrees of Mounture, 1214. to the distance required, which will be found to be 699, 5 paces. Now if you desire to know how much of the Horizontal line, is contained directly under the right line of any Shot, called the right Range, made out of any Piece at any elevation. First, know that in plain Triangles, the violent motion or right line of a Shot is supposed to be the Hypothenusal, the Angle of Mounture to be the Angle at Base; these are given, and the Horizontal line is the Base which is to be found, there the proportion will run thus; As the Radius 90 deg. is to the number of paces in a right Range; So is the Sine Compliment of the Angle of Mounture, to the Horizontal Base, or the right line which lies parallel to the Horizon under the way of the Shot. CHAP. XXI. Of the violent, crooked, and natural motion or way of a Shot, from the time he is discharged, until it is descended. BY the third and fourth propositions of the second Book of Tartagilia, his Nova Scientia, he showeth that every body equally heavy, as a Shot in the end of the violent motion thereof, being discharged out of a Piece of Ordnance, so it be not right up or right down, the curved Range shall join with the right Range, and to the natural course and motion betwixt them both, which distinct motions you may see in the last foregoing figure. In the 17 proposition of the same Book, he proveth that every Shot equally heavy, great or little, equally elevated above the Horizon, or equally obliqne or level directed, are among themselves like, and proportional in their distance, as the figure following showeth, as A E F is like and proportional in right and crooked Ranges unto H I, and in their distances or dead Ranges A F unto A I. And in his 4th and 6th propositions of the same Book, he proveth that every Shot made upon the level hath the mixed or crooked Range thereof equal to the Arch of a Quadrant 90 degrees; and if it be made upon an elevation above the level, that then it will make the crooked Range to be more than a Quadrant: And if that be made embased under the level, that then the crooked Range thereof will be a Quadrant. And in his 9th proposition of the same Book, he shows, that if one Piece be Shot off twice, the one level, and the other at the best of her Random at 42 ½ deg. Mounture, that the right Range of the length is but the ½ of the dead range of the best Random. He that desires a further Demonstration of these Propositions, may peruse his said second Book de Nova Scientia. distance of shots CHAP. XXII. The making of a Gunners Rule, which will serve for the elevation of a Piece, which is sometimes better than a Quadrant; and the dividing it into degrees by help of a Table, fitting it for any Piece from 5 foot to 14 foot long. BEcause the Quadrant cannot be conveniently used at all times, especially when the wind blows hard, and, being near the Enemy's Guns, the Plumb-line is too long before it stands still; to remedy this, the Gunners Rule was invented, the figure hereof is as followeth; it must be 12 or 14 inches long, according as the Gun will require, it must have a long slit down the middle thereof like the Eye-Vane of a Quadrant or back Staff, the head thereof make circular or a little hollow, as you see in the figure the Instrument is described standing, at 'tis to be placed upon the Britch of a Piece of Ordnance; in the middle of the small narrow slit you must place a Lute string or a well twisted Silk with a Bead running upon the same to be set to any number of inches and parts, or to such a degree of the Quadrant, as you must mount your Gun unto; and on the one side of the slit you must place a division of inches, and let every inch be divided into 10 parts, and then it will serve for all sorts of Guns; but if it be for a particular Gun, then on the other side you may place the degrees and parts, when you shall find by the length of your Piece, how many inches and parts of an inch goes to a degree; but to use it with all sorts of Ordnance, let it only be divided into inches and parts. ruler To fit this Rule for one Gun only, here is the Rule for the decimation of the degrees; note, this Table hath 11 Columns, the first shows the length of the Piece in feet and half feet, the other 10 Columns in the head are 10 degrees, and under is inches and the 100 parts of an inch, from 1 degree to 10 degrees; and so you may take them out of the Table, and put them on your Ruler. The len. of the Piece. 1 Degree. 2 Degrees 3 Degrees 4 Degrees 5 Degrees 6 Degrees 7 Degrees 8 Degrees 9 Degrees 10 Degr. Feet and ½ Feet. Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 4 Foot long. 1 3 2 6 3 8 4 11 5 14 6 16 7 19 8 82 9 25 10 28 5 Foot and half. 1 14 2 28 3 42 4 56 5 70 6 84 7 98 9 12 10 26 11 40 6 Foot long. 1 22 2 44 3 66 4 88 6 10 7 38 8 58 9 78 11 8 12 29 6 Foot and half. 1 36 2 72 4 8 5 44 6 80 8 17 9 53 10 89 12 25 13 63 7 Foot long. 1 47 2 94 4 41 5 88 7 35 8 82 10 30 11 77 13 24 14 73 7 Foot and half. 1 58 3 14 4 71 6 28 7 85 9 42 10 99 12 55 14 14 15 71 8 Foot long. 1 68 3 36 5 4 6 72 8 40 10 8 11 76 13 44 15 12 16 82 8 Foot and half. 1 79 3 58 5 37 7 16 8 95 10 74 12 53 14 32 16 12 17 92 9 Foot long. 1 89 3 79 5 68 7 58 9 47 11 37 13 27 15 18 17 8 18 98 9 Foot and half. 2 00 4 0 6 0 8 0 10 0 12 10 14 2 16 3 18 4 20 4 10 Foot long. 2 10 4 20 6 30 8 40 10 30 12 61 14 73 16 84 18 56 21 8 10 Foot and half. 2 21 4 41 6 69 8 88 11 81 13 28 15 48 17 68 19 89 22 10 11 Foot long. 2 31 4 62 6 93 9 24 11 56 13 88 16 22 18 51 20 82 23 14 11 Foot and half. 2 42 4 48 7 26 9 68 12 10 14 53 16 95 19 37 21 80 24 21 12 Foot long. 2 53 5 6 7 59 10 12 12 65 15 18 17 72 20 25 22 78 25 33 12 Foot and half. 2 63 5 20 7 89 10 52 13 15 15 78 18 41 21 4 23 67 26 33 13 Foot long. 2 74 5 48 8 82 10 96 13 70 16 44 19 48 21 92 24 68 27 40 13 Foot and half. 2 84 5 68 8 52 11 36 14 20 27 4 19 88 22 72 25 56 28 42 14 Foot long. 2 95 5 90 8 85 11 80 14 75 17 70 20 65 23 60 26 56 29 53 The use of this Table in graduating the Rule is very plain; for if your Piece of Ordnance be 8 foot long, and you would mount your Piece two degrees, seek for 8 foot under the title length of the Piece, and in the common Angle against the length of the Piece under two degrees you will find 3, 36, to make a degree; that is 3 inches and 36 parts of an inch, divided into 100 parts, and to this you may set your Bead. The use of the graduated Rule is thus: having loaded your Piece, and brought your Piece of Ordnance in a right line with your mark, the dispart being placed upon the Muzzle Ring, in like manner place your Rule upon the Base Ring, and let one standing by hold it, for the foot of it let it be fitted round to the Gun; so you may be sure to place it right, and you may estimate on its perpendicular well enough; now having before the distance to the mark you intent to shoot at, and admit you have found it to be 461 paces, and the first Shot you made for practice out of that Piece conveyed her Shot at two degrees of Mounture 274 paces; then by our former Rules and the Tables of Randoms, there I find 461 against 6 degrees, which is the degrees I must mount my Piece to reach 461 paces. Then to find by this Table how many inches and hundred parts of an inch 6 degrees will require, look in the Table above, and find on the left hand in the first Column the length of the Piece, and just under the degrees (as is aforesaid) you shall find the inches and parts of Mounture, to which set your Bead on your string, that is in the sight, to so many inches and parts as the Table gives; then mount the Piece higher or lower, until you bring the Bead to the top of the dispart and mark, all in one line; stop then the Piece in such a position with a Coin, then prime and give fire. If you will shoot by the Metal of the Piece without a dispart, then subtract the height of the dispart out of the inches found by the Table, and to the remainder mount your Piece. If you have no Quadrant nor a Ruler, and would make a good Shot, look in the Table, and find the length of the Piece and the inches that you ought to raise your Piece unto, then cut a piece of stick just of that length, and set it upon the Base Ring, and bring the top of that stick, the top of the dispart, and the mark, all in a right line with your eye, and you will make as good a Shot as if you had a Rule and Bede, or Quadrant. If you will have no dispart, take your dispart and measure it upon the aforesaid stick at the Base Ring, and from it cut off the length of the dispart, and the remainder use upon the Base Ring. But if the Mounture should be so small that the inches of the dispart should be more than the inches answerable to the degrees of Mounture; then cut off from the dispart so much as 'tis longer than the other, and place it upon the Muzzle Ring, and bring the upper part of the Base Ring, the dispart, and mark, in a right line with your Eye, and you will this way make a level with a stick without Instrument, as well as if you had Ruler or Quadrant. CHAP. XXIII. How to make a Shot at the Enemy's Light in a dark night, and to make at a Company of Horsemen or Footmen passing by, and also to make a good Shot at a Ship Sailing; and how a Shot lodged in a Piece, so that it will not be driven home to the Powder, may be shot out without hurt to the Piece. TO shoot by night at the Enemy's Lights, dispart your Piece with a lighted and flaming Wax Candle, or with a lighted Piece of Match, that with your Eye you may bring the Base Ring, the fired Match on the Muzzle Ring, and the Enemy's Light, in a right line, or mark; then give fire, and you will make a good Shot. If you make a Shot at a Company of Horse passing by, take a Piece that will reach the way the Horse or Foot are coming in a right line, then let your Gun be so loaded with Powder as it may presently take fire, and let your Shot be fit for your use; then take notice of some Hillock or some turning cross way for the mark, and when the Enemy comes near to that way in a right line with your Gun, give fire; but for shooting at a Ship upon the River, you must put your Piece to some eminent mark on the other side of the River, and when the Head of the Ship shall begin to be between the Piece and the mark, then give fire. But if by some mischievous accident a Shot is lodged in the concavity of a Piece, and there sticks, and will not go home to the Powder, or come out; then the Gunner, to save his Piece from breaking, must embase the mouth of the Piece, or put it under the line of level, then put in at the Touchhole fair warm water at several times, so that it may run out at Muzzle or Mouth of the Piece; and when all the Salt-Peter is washed from the Powder, which is known by the taste of the Water, then let the Gunner clear the Touchhole, and put in as much Powder as possible he can, and prime and give fire, and it will serve to draw out the Shot. But when a Shot hath lain long in a Piece until he is grown rusty, and so sticks fast, put strong Vinegar warm into the mouth of the Piece, and with the Rammer strike the Shot until it doth move; then put in Vinegar until it run clear through the Powder and Shot; prime as before, and give fire with good Powder, and if it do not run through after it hath stood three days, clear the Touchhole, prime and give fire. A man may also shoot farther than ordinary in one and the self same Piece, if the Powder be gently driven home, and wadded accordingly; then the Shot being compassed with Paper, Leather, Oakam, or such like, to fill close to the Powder with a good Wadd, putting after it a Tampion of Cork, and with a Sponge moisten it with Oil, anoint the vacant Cylender, and so Barricado the Piece that it may not reverse in the Discharge. CHAP. XXIV. A Discourse by way of Dialogue between a General and Captain, concerning the Assaulting a Town or Work, etc. General. HAving brought your Approaches near unto a Town or a Fortress, whether would you choose a Bulwark or a Curtain to be battered with your Ordnance? Captain. A Town may be assaulted in divers places; sometimes you assault one side, when as you make your Battery on another; sometimes you choose a Bulwark, otherwhiles a Curtain to be battered, with this intention, to take in the Town as soon as possible may be. As for me, if I were to take in a great Town which is populous, I had rather choose to batter a Curtain, than a Bulwark, which hath a high cat, or mount upon it: especially, seeing that in great Towns the Bulwarks lying one far from another, they do show the skirt of the Curtain very open. Gen. Why would you rather choose a Curtain than a Bulwark? Capt. Because your Bulwarks are always stronger, and better fortified than your Curtain, and being it is the principal strength of a place, and better furnished with Platforms▪ Flanks, etc. it will require more time, labour, and charge to batter, than your Curtain. Gen. But what General is so ill experienced, as to labour to batter a Curtain, having two strong Bulwarks on both sides of him, to flanker him when he is to put over his Gallery, and to give an assault upon the Curtain: peradventure for his labour and pains, he may be well beaten. Capt. Soft (Good Sir,) Suppose that after a great deal of labour and pains you have battered a Bulwark, and falling up to the breach to assault it, you find it cut off, an Enemy lodged in it, must you not then begin to sap forward again, to make a new battery? whereas on a Curtain there is not that means of cutting it off, as upon a large Bulwark. Gen. Have you ever seen the experience of it? Capt. Yes Sir, the Prince of Orange took in the Bosch by a Bulwark, and also Breda, but Mastrick was taken in by making a breach, and springing of a mine, upon the Curtain between Jonger Port and a Bulwark; howsoever the Town of Cortes upon the frontiers of Franee, was first battered by the Archduke of Austria upon the point of a Bulwark, near unto the very joint of the Curtain, where a high and a strong turret stood, which did annoy us much, so that we could not advance forward, but were constrained to leave off our approach on that side, and began to make a new Battery for a breach in a Curtain on the Field-side, where there lay a strong Bulwark to defend it, which did our men a great deal of harm; but howsoever, with great difficulty and much ado, we took in the Town that way, by lodging ourselves in the Curtain. Likewise the City of Cambray was battered, and taken in upon a Curtain, for all there were two strong Bulwarks that flankered it, which if we had run our line upon a Bulwark, we should not have forced it so soon; yea such an occasion might present itself, that a General may be forced to batter both the one and the other, or to find out some secret way by undermining a wall, and blowing it up with powder. Gen. This is for your great Towns; but what say you to a Castle, a Citadel, or some narrow Fortress, how will you go to work to take in those with the best advantage? Capt. As for your Forts, and Castles, it is much better to batter them upon a mount or a Bulwark, than upon a Curtain: my reason is this, that in these your Bulwarks lying close one by another, will flank one another with the greater force, and hid the Curtain much better to defend it, so that one cannot so easily force it, if the said defences be not taken away. Gen. Go to then; a Town then being to be battered, either upon a Curtain or a Bulwark, how many Pieces of Ordnance would you have to do it, and, how and in what manner would you place, and plant your Ordnance upon your batteries to make a good breach? Capt. To effect this, I would have 18 Pieces of Canon and half Canon, (for lesser Pieces for Battery are now grown out of use.) Gen. Whether would you choose more whole Canon or half Canon? Capt. To batter a place well either upon a stony or earthy wall, you may assure yourself, the more whole Cannon you have, the greater and the more sufficient your breach will be: for your great battering Pieces do spoil and beat down any thing, which doth meet with their great force and violence: Howsoever of late years experience hath taught at divers Seiges that your half Canon which are more portable, having good store of them, will do the business aswell as your whole Canon. Gen. But at what distance would you make your Batteries, for these 18 Pieces of Canon, and how near unto the place, which you intent to Batter. Capt. I would counsel a General to approach as near unto that place as possible may be, and make his Batteries some two or three hundred paces one from another, and that if it were possible to advance covertly the Approach and sap, even up to the Counterscharfe, and very brink of the Moat, to prepare a way for his Gallery: not only to Batter that place being at hand with the greater force, but also to keep in, and hinder an Enemy from Sallying out upon the Besiegers, to discover and dismount their Ordnance in Casemates, or if they have sunk any in their Walls or Falsebray, and so to terrify them, that they dare not stir out. Gen. I am also of your opinion, and hold it for good, yet I fear this will not be so soon done, and is sooner spoken, than executed, and that before you can bring your approach and sap so far, it will cost you warm blood, and a great many men's lives, if you have a stout Enemy within to deal withal, and one that is very Vigilant, and careful to stand upon his Guard, and his defence. Capt. 'Tis true, this cannot be done without danger, and the loss of men, but he that is fearful must stay at home, and not come into the Wars where there is neither place nor time, which doth free or exempt him from danger: yet the danger is not always so great, especially in such places, where you have Earth enough to work with, to cast up your sapps, and to heighten and deepen your Approaches, which will show you the way, for the more higher you find the ground in Approaching to the edge of the moat, the deeper Trenches you may make, and cover yourself by casting up of blinds continually, to keep you from the sight of the Besieged; and it is better, when you have brought your approach as it were under them, than if you were 200 or 300 paces distant from them. Gen. I pray you Good Sir, how would you plant, and divide these 18 Pieces of Canon? Capt. I would make a great Battery with 8 of them to beat upon a right line, either upon a Curtain, or the point of a Bulwark (which the General shall find fittest) Two Batteries with each 3 Canon to play slope-wise from the great Battery; as the ninth plate and 28 and 29 figures shows, and two Batteries, with two half Canon a Piece, to play as it were upon the breach. And thus you see your 18 Pieces planted upon 5 Batteries, as you may observe in the 9th. Plate, and the two Figures of a Curtain and of a Bulwark following. Gen. Good Sir tell me I pray you how many shot will these 18 Pieces of Canon make in 10 hours, and how much powder will they require. Capt. In 10 hours they may make some 1500 shot, and will require a matter of 25000 pound weight of powder, that is 150 barrels full, each barrel containing 160 pound weight in it. Gen. You make your account then that every Piece in the space of 10 hours is to shoot 80 shot, that is 8 shot an hour for every Piece. Capt. You may make 10 shot in an hour if you please, if your Pieces be renforced; but as for your ordinary Pieces, they have not metalline substance enough to bear it: considering also that after you have made 40 shot out of a Piece, it will be so heated, that it must have a cooling time, which must be at least an hour, for otherwise your Piece being grown over hot, it may cause danger. Gen. Methinks that 80 shot for a Piece in so long a time were too little, having often heard, that in that while, a Piece may well be shot off 130 times; can you give me your resolution upon this? Capt. I will tell you Sir what happened once in the Island of Bomble, Anno 1599 we planted a Piece by a mill, by which we did annoy the Enemy very much, so that they were forced to make a Battery, and planted a whole Canon, and a demy-Canon upon it, seeking to dismount ours. Now shooting with this Piece from four of the clock in the morning, till eleven toward noon, this Piece had a cooling time the space of two hours, and about one of the clock we began to play with it again, and continued shooting with it till 4 a clock in the afternoon; but this Piece being not able to endure the force and heating of so many shot, we were constrained to leave off with it: and yet ceased not shooting with our other Pieces from another Battery by command from Don Lewes de Valasco, General of our Ordnance, and shooting with some other of our Pieces, we put the Enemies two Pieces to silence in the space of an hour; a Soldier of ours standing by, was curious to keep a tally of the number of all the shot we made from the morning till four a clock in the afternoon, and shown me 80 notches, which deducting the two hours cooling, our Piece planted at the Mill made 8 shot in an hour, which was as much as could be required of it. Senior Diego Uffano give your Translator leave to interrupt you a little, and so to conclude this discourse. If you remember at the Siege of Ostend, which you mention ofttn in your Chapters and Dialogues, you were without, and I was within the Town, that on the seventh of January, Anno 1602. Stilo Novo, After Sir Francis Vere of famous memory (who defended and kept the Town against you) had deluded you with a Parley, only to gain time, and to make up our Canon and Sea-beaten works along the skirt of the old Town, his Highness the Archduke resolved to assault us, and that morning began to batter Sandhill and Schotenburgh, to make a breach for yoù against that night, with intent to Assault us (as you did) and to have entered the Town, and have put us all to the Sword, the Relation whereof you shall hear in the end of this Book. Now you had placed and planted your 20 Pieces of Cannon to batter them in this manner, 8 from your Battery at the foot of the Downs, 8 from a Battery on the right hand of the Downs, 6 from your pile Battery, 6 more which you had made upon the Sand, and as it were raised out of the Sea: the first shot upon the breach in a right line, and the other two slopewise, as your two figures following do demonstrate. These 20 Pieces of Canon towards noon had a cooling time, for a matter of some 2 hours, just as you have said; and afterwards you began to batter the breach and old Town again, till it was almost twilight, and then they cooled again, till you were ready to give us an assault; and before you fell on, as I do well remember, you shot off one of your Cannons with a hollow Bullet, which flew over the Town and made a great humming noise, as a warning Piece to the Count of Bucquoy, who lay on the East-side, that you were then ready to fall on, and that he should do the like, this was your Signal. Now General Vere knowing well your intent, gave order to the Gentleman of our Ordnance who had the guard upon Sandhill, that he should keep a true Tally, and an account of all the shot you made that day, with your 20 Pieces of Cannon upon the breach and the old Town, which being cast up, there were found to be made that day from morning till night 2200 shot, which was found to be an 110 shot for every Piece, and 11 shot an hour for every Piece, which is more than 8; but I verily believe your Pieces were renforced. This by the way, and so I return again to your own Dialogue. Gen. (Good Sir) I pray show me how you would batter the point of a Bulwark (as the figure 28 following demonstrates,) and give me some reasons aswel defensive as offensive. Capt. I am willing to give your Lordship content, and say, If I were to batter the point of a Bulwark or a Bastion, I would have the same number of battering Canon, and planted in the same form and manner as they were for the Curtain, and to shoot sloap and also; and if your approaches were advanced so far, they should be planted upon the very brink of the moat and upon the Counterscharfe, I would plant 4 of them so, that they should dismount the Enemy's Canon in their Casemates, or any, if they had sunk them in their Falsebray, which should wait upon that occasion. Gen. I am of your mind, and prefer such a batter before all others, who are of the opinion that they had rather choose a Curtain than a Bulwark to be battered. Capt. You have heard my reasons for that, and see the figures following traced out to you. But as for your Bulwark the besieged may cut it off (as you may mark in the figures of Retrenchments and Cuttings off in the second part of this book) for indeed it will be a hard matter to force an Enemy out of a Bulwark, who is resolved to lose it by piecemeal and degrees; and there is not so much danger in assaulting of a Curtain, which being once well battered and beaten down with your Ordnance, you have an easier way and entrance to fall on with your Troops of men, to enter the Town or Fortress; but for the defence which is made from your Flanking Bulwarks, or your Casemates, you must make Batteries upon the brink of the moat against them, (as is said) to dismount the Enemy's Pieces, and to flanker with your Ordnance the Parapets of the Bulworks to beat them about their ears, that the Bulworks may lie the more open to you, and I think this way is the least danger. Gen. But the Besieged, their cuttings off, may they not be made aswel upon a Curtain as upon a Bulwark. Capt. No, for the Rampire being thinner, you have neither so much ground, nor the like accommodation in a Curtain as in a Bulwark; and indeed, a Governor of a Town, or of a Fortress, if he were put to his choice, had rather to be assaulted on a Bulwark (than on a Curtain) by cutting it off into the form of a half moon, that he might make a new resistance, and defend it with a less number of men. Besides, in a Bulwark the Besieged have this advantage over the Assailants, which is very dangerous for them, that they may make a Mine within the bowels of their Bulwark when an Enemy shall attempt to assault it, and thinking to enter the Breach and take the Town, they may be blown up into the Air by a Countermine; the like also may happen to the Besieged, the Assailants springing their Mine also in a Bulwark, when they think they stand upon their best defence. Gen. May not the like be done also in a Curtain? Capt. No, it will not take the like effect as in a Bulwark; for a Breach being once made in a Curtain, for as an Enemy may assault it at large, so they may bring a greater number of men to fight, to help to defend it; whereas in a Bulwark they are penned up and straightened in a narrow place, which may be cut off, and will require a fewer number of men to defend it, whereas those which are to force it, must be constrained to bring up a great many men to assault, who in an instant may be in danger of blowing up. Gen. Your reasons (Good Captain) are not to be slighted; but as for me, I hold it safer, to batter and assault the breach of a Bulwark, than of a Curtain. For though the besieged may cut it off, and defend it with a fewer number of men, yet the Assaulters have this advantage over the Besieged defendants, that they have more place and elbow room, and may find a less resistance than in a Curtain, seeing that one may make as a great a breach in a Bulwark as in a Curtain, because your Ordnance may beat it flat, and levelly with the ground; and choosing rather a Bulwark: I will herewith conclude this discourse, and now show you the figures both of the one, and of the other in this following plate. CHAP. XXV. Containing the demonstration of Mortars, and the use of them. YOur great and small Mortars, are not only serviceable in a War offensive, by shooting and casting of great Granades, as of 100, 150, 170 pound weight, and smaller of 40, and 50 pound; but also by casting of Fire-balls, Stones, old Rubbish, and Pieces of Iron, into Cities, Towns, and Fortresses; and may be used also defensively, to be shot from Towns and Forts into any Enemy's works, and approaches; especially they are of singular use, when an Enemy hath covertly approached, and lodged himself under some Bulwark, Tower, or Turret, and is a beginning to undermine them; which if they do, you may plant one of these Mortars at a reasonable distance, on the inside of your Wall, and shooting your Granado, as it were bolt upright into the air, by its natural fall, it may light just into the Enemy's works, and there with great violence breaking among them, it will make them cry, fly, and forsake the place; you may also fire them out of a place, by casting good store of Hand Granades down among them, and so annoy them, that the work will be too hot for them. how to bombard a courtine How one must Batter a Courtine how to bombard a bulwark How one must Batter a Bulwark The use of them is not to shoot in a right line, as other Ordnance do, but in an obliqne line, as you may see by the two Figures following, unless your Mortar be mounted to 90 degrees, mounting them usually above 45 degrees, namely to 60, 70, 80, and sometimes more or less, as the distance and fall of your Granado or Shot shall require. Having before shown you the making and use of the Quadrant, it remains now that I come to the charging and use of a Mortar; now before you put in your Powder, it must be well sponged and cleared, whether you charge it with lose Powder, or Cartouch, turning the mouth almost bolt upright; the Powder being put into the Chamber, you must stop it with a Wadd either of Hay or Oakam, and after a Tampkin of some soft wood, and this with the Powder that was put in first, it must fill up the whole Chamber thereof, that there may be no vacuity between the Powder and the Wadd, or between the Wadd and the Shot; this done, the shot shall be put in at the mouth, with another Wadd after it; but you must have a care that your Mortar be not much mounted, lest your shot flies out too soon, and the Wadd between the Tampkin and the shot will not only save the shot from the Tampkins breaking of it, but also is to avoid vacuities which may endanger the breaking of the Piece by second expansions. Now then having resolved of the premises, touching your Piece, Shot, and Powder, as abovesaid, and upon the distance and mounture of your mark, as the Rules and Tables following shall direct you, then for the bending and disposing of it to the assigned mark; lay first a strait Ruler upon the Mouth of your Mortar, and upon it place a Quadrant (as you may see by the Figures) or some other Instrument , to set the Mortar upright, for shuning of wide shooting, and then placing them foreright to elevate it into the resolved degree of Mounture, to avoid short or overshooting, accordingly as the Tables following will teach you; for having made one shot, you may thereby proportion the rest, considering whether you are to shoot with or against the wind, or whether it blows towards the right or the left hand, whether weakly or strongly, and so accordingly to give or abate the advantage, or disadvantage, which judgement and discretion will induce you thereunto, and the help of the Rules following. Now we will come to the use of a Mortar, and that in this example following; Suppose an Enemy be approached to the Basis, or foot of a Wall or a Bulwark, and there is a rooting, and gins to make a Mine, and having Chambered his Powder, intends to blow it up, and that there is no other means left you, to repulse and hinder their egress and regress into it; but by shooting out of your Mortars some Granades, Fire-Balls, Stones, and Rubbish among them, or at least by casting many Hand-Granadoes down upon them. To do this either by force or policy, it behoveth a good Canonier or Fire-worker, to know first (as hath been taught) how far his Mortar will carry a Granado, or any solid thing else, which shall be shot out of it, being set upon such and such a degree and elevation as the Mortar Figure will show you. As for Example, take your aim levelly with the mould or mouth of your Mortar, noted A upon the Quadrant, and it will carry 200 paces, where you see the Granado falls upon the letter A; but your mortar being elevated to the mark B, it then will carry its Bullet 487 paces; if to the second C, then 755 paces; if to the third D, it will carry 937 paces; if to the fourth E, then 1065 paces; if to the fifth elevation F, than 1132 paces; if to the sixth G, which is in the midst of the Quadrant, and lies then upon its highest elevation, it will carry 1170 paces, as you may see by the several falls of the Bullets upon every Letter. The second Figure shows you a Mortar casting a Granado upon a Castle, as you may see by the Example. Another Table of Diego Uffanoes for Mortar Pieces, with their Randoms made for every degree, between the Level and 90 degrees, as followeth. Deg. Pac. Deg. 0 100 89 1 122 88 2 143 87 3 364 86 4 285 85 5 204 84 6 224 83 7 243 82 8 262 81 9 280 80 10 297 79 11 314 78 12 331 77 13 347 76 14 363 75 15 377 74 16 392 73 17 406 72 18 419 71 19 432 70 20 445 69 21 457 68 22 468 67 23 479 66 24 490 65 25 500 64 26 510 63 27 518 62 28 524 61 29 526 60 30 534 59 31 539 58 33 543 57 34 549 56 34 552 55 35 558 54 36 562 53 37 568 52 38 573 51 39 477 50 40 580 49 41 582 48 42 583 47 43 584 46 44 582 45 582 mortar shooting castle A Mortar Shooting upon a Castle paths of falling mortars How you are to use the Quadrant afore described for a Mortar, as you may see by the falling of the Granado upon the Lettors THE Complete Gunner THE THIRD PART. OF ARTIFICIAL FIREWORKS. THe number of artificial Fireworks which are practised as well in Armies upon Land in the attacking and defence of places, as in defence of Ships at Sea, whereby warlike Executions may be performed, are many and various, according to the ingenuity of the Fire-Master: And the ways of preparing them are so many, as it is impossible for us in this room we have allotted to prescribe all that are known. We shall therefore be contented to make choice of some of the best and principal things among so great a number, but more particularly of some most admirable inventions; and we shall give a Chapter to every kind of Firework, considering they differ among themselves both in fashion and effect, and every one hath its name which is particularly applied to it. But before we begin with our composition we shall begin with the particulars, and their preparation unto this work, whereby they may be the more exalted, and have the greater efficacy. The more principal materials, that is, Peter, Charcoal and Sulphur, are mentioned at large in my first part of Gunnery, and therefore we shall proceed. CHAP. I. To prepare Oil of Sulphur. TAke a good quantity of clarified Sulphur, (the way of Clarification we have showed before) melt it over a very gentle fire in an Earthen or Copper Vessel, then take old red Tiles that have been already used in buildings, or if you cannot find such, take new Tiles that are well baked, and that have not taken dirt, break them in pieces as small as a Bean, and throw them into melted Brimstone, then mingle your Brimstone with the remaining fragments of the Bricks, until they have drank up all the Sulphur, then let them be put into a Limbeck upon a Furnace to distil, and after the Oil is drawn according to a Chemical order it will be very excellent, and above all, have a very combustible quality, proper to the Compositions of artificial fires. To prepare Oil or Balsam of Sulphur. Fill a long body of Glass full of Sulphur well powdered, then pour upon it Oil of Turpentine, or Oil of nuts, or Juniper, in such a quantity that the oil with the Sulphur may fill but the half part, place it in an Iron Kettle, with Sand round about it, and a small heat for 8 or 9 hours, and you will see that the Oil of Turpentine will convert the Brimstone into a red Oil, as fiery and combustible as before. There are those that take the following matter to the preparing the oil of Sulphur, to the end it may be rendered more combustible, viz. Sulphur 1 l. of quick Lyme half a pound, of Salarmoniac 4 ounces. Above all this, the Chemists know how to prepare a certain oil of Sulphur, (which they call a Balsam) of which the virtues are so admirable, that they admit not any body, either living or dead, to be touched with putrefaction, but will conserve it in so perfect and entire state, that neither the pernicious Influences of the celestial bodies, nor that corruption which the Elements produce, nor that which reduces things into their Principles, can any way damnify it, if anointed with it. There is also from it prepared a certain fire (as Tritemius teacheth) with flowers of Sulphur, Borax and Brandywine, which will remain many years without extinguishing of itself. Others that are knowing, do attest that a Lamp may be filled with such like Oil, from whence all that are within the Light of it, will appear as if they had no heads. There is another way of making Oil of Sulphur which is very admirable and excellent, which is prepared thus. Incorporate well together an equal proportion of Sulphur and Salt-Peter, reduce them into most subtle Powder, and pass it through a fine sieve, than put them into an Earthen Pot that hath never been used, and pour upon them Vinegar made of White-wine or Aqua-vita, as much as will cover the Powder; Close the Pot in such manner that no air may any wise enter, and put it thus in any hot place so long time until all the vinegar be digested and vanished. Lastly, take that matter which rests in the Pot, and draw from thence an oil, by Chemical Instruments proper to this work. CHAP. II. The preparation of the Flowers of Benjamin. TAke Benjamin a certain quantity of ounces, put it into a Gourd or a Limbeck glass, and close it well with a blind head (as they call it) then have in readiness an earthen vessel, set it upon a Tresfoot, or for the more certainty upon a small Furnace, place it in your glass body, and compass it well about with fine Sand or ashes so high as the matter is in the glass; after make a moderate fire under it, for fear the Limbeck heat too soon, and be too hot, for that will make the flowers become citrine or yellow, when they ought to be as white as Snow. Observe when you see the flowers begin to raise a vapour or small fume, continue your fire in that same degree the space of one quarter of an hour; after you shall see the flowers risen unto the internal Superficies of the blind head, then take it away carefully, and put to it another that shall be quite cold, and put that which you have taken off upon a white paper until it be cold, then gently with a Feather or wooden Spatula, cause the flowers to come forth of the blind head, and gather them together carefully: thus you may add a third or fourth blind head, and in time many, until all the Benjamin cease to fume. Benjamin may be made into flowers another way, thus; put into a glazed pot a certain quantity of ounces of Benjamin, and place it upon warm ashes, and when you see it begin to fume, cover the vessel with a Cornet of paper made in the form of a Cone, and a little larger than the orifice of the pot, leave it there about one quarter of an hour, after take off the Cornet, and take the flowers and gather them together; then put upon the vessel another Cornet of paper, and let it stand as long as before; take it off, and gather the flowers to the former, and continue thus putting Cornet after Cornet, until your flowers be entirely evaporated. CHAP. III. The preparation of Camphire. TAke Juniper Gumm (which is called sometimes) Sandarach, white varnish, or Mastic most subtly powdered 2 l. white distilled vinegar as much as is necessary to cover the Gumm in a glass, set it deep in horse-dung the space of 20 days; then take it and pour it forth into another glass Vessel with a wide mouth, and let it stand thus in digestion a whole month, and in it you shall have Camphire congealed in form of a Crust of bread, and which hath in some measure the resemblance of the veritable or true Camphire. The Camphire hath such a love for the fire, that being once lighted, it goeth not out until it be quite consumed. The flame that comes from thence is very clear, and of a very agreeable odour; after it hath remained suspended in the air some time it vanisheth insensibly. The cause that produceth all these rare effects from Camphire, is by reason its parts are extreme subtle and airy. I do add to all this, that it may be easy to reduce Camphire into Powder, to make it useful in artificial fireworks; if a man crumbles it and beats it gently, rolling it with Sulphur. The oil of Camphire, which serves also for the same effect, is made by adding a little of oil of sweet Almonds, and stir them well together in a brass Morter, and pestle of the same metal, until all be converted into oil of a greenish colour. Or a man may put it into a Glass Viol. which must be close stopped, provided also that the Camphire be true and natural, and not a Cheat; then put that Glass into a warm Furnace, and draw it out, when you shall see all the Camphire turned into a pure clear oil, which will burn with an admirable vivacity. CHAP. iv Water of Salarmoniac. TAke Salarmoniac 3 ounces, Salt-Peter 1 ounce, reduce them into a most subtle Powder, and mix them well together, after put them into a Limbeck, and then pouring on them some of the best and strongest Vinegar, you may distil the same into a water with a small fire. CHAP. V Of a certain artificial water which will burn upon the Palm of your hand without doing any harm. TAke Oleum Petroli, and of Terebinthi, and of Calx vive, of Mutton fat, and of Hog's Lard, of each equal parts, beat them well together, until they be well incorporated, then cause them to be distilled in warm ashes, or upon burning coals, and you shall draw from thence an excellent oil. CHAP. VI To prepare Fire-Spunges. TAke of the oldest and greatest Toad-stools which grows at the Root of Ash, Oak, Birch, and Fir-tree, with many other Trees which produce them freely; get a good parcel, string them, and hang them in the Chimney, and leave them to macerate; being well mortified and macerated, take and cut them in pieces, and then beat them with a wooden Mallet; this done, boil them over a small fire in a strong Lie, and a sufficient quantity of Salt-Peter, until all the humidity be evaporated: At last, having put them upon a Plank or even board, put them in a warm Oven, and let them well dry there; having drawn them from thence, you must beat them with a wooden Mallet as before, until it become wholly subtle and soft; being thus prepared, you must keep them in a commodious place to serve you upon occasion. CHAP. VII. How to prepare Match or Tow for Artificial Fires. MAke Cords of Tow, Hemp, or Cotton, which you please, of two or three twists, not made too hard, put them in a new Earthen pot Vernished, pour upon them Vinegar made of good white Wine four parts, of Urine two parts, of Aqua vitae one part, of Salt Peter purified one part, of Cannon Powder reduced to Meal one part: Make all these Ingredients boil together upon a great Fire, to the Consumption of all the Liquor; then spread upon a great smooth Plank or Board, the Meal or Flower of the most excellentest Powder that you can get. Having drawn your Match out of the Pot, roll them in the Powder, and then dry them in the shade or Sun, for it matters not which, and the Cords or Match that are thus prepared will burn very quick. Francis jouchim Prechtelin, in his second part of his Fireworks Chap. 2. describes a certain Match, which is extreme slow in burning, and is thus made; take Mastic two parts, Colophonia one part, Wax one part, Salt-Peter two parts, Charcoal half a part, then, having melted all and mixed them well upon the fire, take a Match made of Hemp or Flax of a sufficient bigness, and draw it through this Composition, making it go down to the bottom of the Vessel, drawing it often through, until it hath gotten the bigness of a Candle, and when you desire to use it, light it first, and when it is well lighted blow it out, and there remains none but a burning Coal. CHAP. VIII. Of certain Antidotes excellent and approved against the burning of Gunpowder, Sulphur, hot Iron, melted Led, and other like accidents, drawn from the particular Experiments of Cozimu Nowicz. SECTION. I. Boil Hogs grease in common water, over a most gentle fire, the space of some time; then take it from the Fire, and let it cool, and after expose it to the fair and clear weather three or four nights; after having put it into an Earthen pot, melt it again upon a small fire, and being melted, strain it through a Cloth into cold water, after wash it many times with good clean and fresh water, until it come as white as snow; this done, put it into a glazed pot to serve you at your occasions. The use is thus, you must anoint the part as soon as you can, and you will see a quick and admirable effect. SECT. II. Take Plaintain water, Oil of Nuts of Italy, of each as much as you please. SECT. III. Take Mallows water, Rose water, Plume Alum, of each as much as is necessary, and mix them well together with the white of an Egg. SECT. iv Take a Lixivium, made of Calx Vive and common water, add to it a little Oil of Hempseed, Oil Olive, and some whites of Eggs, mingle all well together, and anoint the place with this Composition. All these Ointments cure burn without causing any pain. These I have often experimented upon myself. Some Receipts from divers Authors. Take Oil of Olives, Oil of sweet Almonds, Liquid Varnish, each one part, juice of Onions two parts, with these chase the part affected. If there be already blisters raised and Ulcerations in the parts, this following Ointment is most excellent. Boil a great quantity of the second Rind of Elder tree, in Oil of Olive, then pour it through a Linen cloth; add to it a little after two parts of Cerus or burned Led, of Lytharge of Gold, of each one part, put them into a Leaden Mortar, and then stir them about and mix them so, that they become in the form of a Linament. Take melted Lard, pour it into two Ounces of Morrel water, and one Ounce of Oil of Saturn, then mingle them well together: this Remedy is sovereign. Take the Mucilage of the Roots of Henbane, and of the Flowers of Poppies, of each one Ounce, Salt Peter one Ounce, mingle them all with Oil of Camphire, and make a Linament according to Art. Or take the juice of Oynions roasted in embers two Ounces, Nut Oil one Ounce, mingle them all well together. Or take of the Leaves of Ivy two m. or handfuls well beaten up with Plantain water, Oil Olive one pound, make all boil with four Ounces of good white Wine, until the Consumption of the whole Wine, at the end of the decoction add Wax as much as is necessary, to give him the form and consistency of a Linament. Again, take old Lard, let it be melted over the flame, and poured into two Ounces of the juice of Beets and Rue, of the Cream of Milk one Ounce, Mucilage of Quince-seeds and Gum Tracanth, of each an Ounce and a half, mix them well together, and make thereof a Linament. This remedy is none of the worst, we took it from Joseph Quercetanus, in libro Sclopetrio. CHAP. IX. Of Hand Granades. THe Hand Granades respecting their form, are Globically or perfectly round and hollow in their interior part in manner of a Sphere; they are called Hand Granades, or Handy Granades, because they may be grasped in the hand, and thrown to the Enemies; and if we should dwell upon the denominations of the Latin, we may call them as they do, Granades Palmares, they are commonly of the bigness of a Bullet of Iron of 5, 6, and 8 l. they weigh sometimes 1 l. and sometimes one pound and a half, some are of two pounds, and others of three pounds; there is given to these sort of Globes the names of Granades, by reason of the great resemblance they have with the Fruit Punic, which we call Pom-granad; for as these do shut up in their rinds a great quantity of grains; so our Military Globes are filled with a number of Grains of Powder, almost innumerable, the which having received the Fire, do break into a thousand and a thousand shivers, leaping against the Enemy, and piercing if it could all such things as it meets opposing its violence. They are generally made of Iron or Copper, carrying in its Diameter about three Ounces, being about the length of a Barley Corn in thickness of Metal; they are filled commonly with Gunpowder, and sometimes of other Compositions, there is added to its Orifice a small Pipe commonly called a Fuse, which is filled with a matter or Composition that is slack or slow in burning, but nevertheless very susceptible of the Fire, and capable to hold fire some time, for fear that it should break in the hands of those that manage it, and intent to throw it. There is amongst Fire-Masters accounted three sorts of Hand Granades, the first and most common are made of Iron; others are made of Brass, allayed with other Metals in the melting; the third sort is of Glass. If you cause them to be made of Iron, take such as is most fragile, and as little wrought as possible you can get; if you will cast them of Copper, you must allay six pound of Copper, with two pounds of Tyn, and half a pound of Marcasite, or you may put one part of Tyn with three parts of Latin or of Auricalque. Those that are made of Iron are in thickness about the ninth part of the Diameter; those that are made of Brass must have one tenth part of the Diameter in thickness of Metal. Lastly, such which you cause to be made of Glass, must have one seventh part of their Diameter in their thickness. The largeness of the Orifice in which you must put in your Fuse made of Wood, whose upper part must be about 2/9 the Diameter of the Granado, and the small hole in the Fuse should have the largeness of 1/18 of the same Diameter, the rest of the capacity of the Shell must be filled with well grained Powder, the length of the Fuse must be about ⅔ of the Diameter, and the top must be broad, and a little rounding like a Hemisphere, the hollow and inner part of the Fuse must be about 1/9 Diameter at the small or inner end, and ⅔ at the outer end: Men do generally fill the void place with Powder ground most subtly, which must be moistened with Gum-water, or dissolved glue, that it may join the better. As for the Fuses, they must be filled or charged with one of the Compositions hereunder written; afterward you must fasten it well and close with Tow or Okham, and the Pyrotechnian Lute which the Germans call Kit, which is made of four parts of Ship Pitch, two parts of Colophonia, one part of Terrebinthe, and one part of Wax; you must put all these Ingredients in a glazed Vessel, and melt them upon a small fire, then mix and mingle them well together. Compositions for Charging the Fuses of the Hand Granades. Powder 1 l. Salt-Peter 1 l. Sulphur 1 l. Powder 3 l. Salt-Peter 3 l. Sulphur 1 l. Powder 4 l. Salt-Peter 3 l. Sulphur 2 l. Powder 4 l. Salt-Peter 3 l. Sulphur 1 l. Another sort of Granades. I shall here represent you with a Hand Granado, which may be hid at the entering of a passage, or any such place where we suppose the Enemy must come: This Granado hath two holes opposite, passing just cross the Diameter, in which must be fastened a Fuse of Wood or Metal with holes in several places, and all about it within let there be beaten Powder, and through it you must pass a common match, lighted at one end, and at top let there be a third hole, by which it must be charged with a good grained Powder, which must be close stopped again with a Tampion, and then is your Granado prepared. I suppose it not necessary to say much of the use of this Granado, and since it is so easy to be understood by what we have said, and that the occasion you will have of such things will forge your Inventions enough to put them in practice. CHAP. X. How and where a man ought to heave Hand-Granadoes. ACcording to the definition which we have given of them, it is most evident, and I suppose no body will doubt, that they are to be taken in the hand, and that we must grasp them to throw them at the Enemy. It is said before that this kind of Arms is as well defensive as offensive; therefore we shall not rest upon the proof of these things; those that have been at the managing of them must instruct them that are ignorant. We shall say only this, that the Places where these Hand Granades are used at Sea, are where Ships are Board and Board to clear the Enemy's Decks, so that the way may be cleared there. Upon Land Service they are used immediately after the good and happy success of a Mine which hath made a great overture in a Rampire, overthrowing one part of the Wall, Bulwark, or Bastion, to give place to the Assailants, to do their endeavour to get into the breach; it is there that the Besieged as well as Besiegers may make use of these Hand Granades; 'tis there where you shall see the more generous of both sides armed with Fire and Flames, defending valiantly the quarrel of their Prince, the interest of their Party, their Liberties and their Lives. They are employed also upon other occasions, to wit, when the Besiegers are come up to the Walls of the Rampire, and so well placed, that making winding Stairs in the thickness of the Platform, they mount insensibly by retact; so that the Besieged cannot any way hinder by the defence of their Flanks, nor be kept safe by the Rampires themselves. Upon these occasions I say, the Besieged aught to pour down a a quantity of Hand Granades from aloft, or from the top of the Walls, upon their underminers. And sometimes they are also thrown at a distance greater than ordinary, according to the occasion; but when this cannot be done by the natural strength of a Soldier, without the aid of some artificial Instrument, the Masters in this Art have invented certain small Engines, made like unto one of our Ducking-Stools, with a Rope at one end to pluck it down by force, and at the other end a hollow place to lay the Balls in that are to be thrown, and with this Engine well contrived, one may throw upon the Enemy, not only Hand Granades; but also a quantity of other Artificial Military Fires, as glistering or shining Globes, Bombards, Fire-pots, and many other such like things, of which we shall speak in their place, may be thrown at a greater distance than is possible by the hand only. This Instrument is not very difficult to make, it may easily be comprehended by what we have said. I shall only advertise you of one thing, that the longer the arm of the Engine is on that side that is to hold the Granades, more than the other part to which the Rope is fastened, the greater force the Engine will have; but you must understand this measure to be made from Axes or Iron Rolls, upon which the Arm moves. CHAP. XI. Of glistering or bright shining Fire-balls. DIssolve upon the fire in a Brass or Earthen Vessel an equal portion of Sulphur, black Pitch, Rozin, and Turpentine; then take a Ball of Stone or Iron, that the Diameter be far less than the Diameter of a Cannon, or Mortar Piece, for which you intent this Globe; plunge this Shot in this melted matter until it be all over covered with the matter about its exterior part, draw it from thence, and role it gently in Corn Powder, that done, cover it all over with a Cotton Cloth; then plunge it again in your Composition, and reiterate the rolling it in Powder, as before, then cover it a second time with another Cotton Cloth; and thus continue dipping your Bullet, and wrapping it about with Cloth, until your Shot has acquired a just bigness, exactly to fill the Orifice of the Engine, remembering that the last Coat of the Shot must be of Corned Powder: Being then thus prepared, it must be put into the Cannon or Morter Piece naked, without any other thing compassing it, immediately upon the Powder in the Chamber, which must make the Bullet come forth; Then give fire freely to your Piece, to throw the shot where you intent it. CHAP. XII. Of Balls which Cast forth so great a smoke, that they blind whomsoever they come near. IT is accustomed to do great execution by favour of the night, in occurrences of War, as well as in many other occasions: I mean not here to speak of the darkness of the night, for that is naturally effected by the first Causer of all things, from the order that he hath established amongst the Being's; but I intent only here to treat of the darkness that is made Artificially, and particularly such as may be produced and made to last a little time in a close or narrow place, according to the Rules of our Art, to be made for the blinding of the Enemy, which would force into our beings, and would attaque us by main strength, in a design to take away our Lives, Honour, and Goods; or when we have a design to facilitate the passage for the Assailants, in confounding or oppressing the Besieged in their Forts, with a cloudy and thick fume, in such a sort that one may take them as amazed Fish in troubled waters. For this purpose are Globes prepared, which whilst they are on fire, produce a smoke so vehement and unpleasant, and in so great abundance, that 'tis impossible to withstand the incommodity without bursting asunder; see here the Method. Take Ship Pitch in the Stone 4 l. Liquid Pitch 2 l. Colophonia 6 l. Sulphur 8 l. Salt-Peter 36 l. melt all these Drugs upon burning Coals in any vessel whatsoever, adding after 10 l. of Coal of Sawdust made of the Pine or Firr-Tree 6 l. Crude Antimony 2 l. incorporate and mix them very well together; then put into this melted matter Tow, Hemp, and Linen a great quantity, and boil them well in this Composition, and when they have drank up all the matter, than form them into Balls of such a bigness as you please, so that it may be cast with the hand, or with the Engine mentioned in the last Chapter, according as you shall find most convenient. And this is our true way to make Night at Noonday, to obscure the Sun itself, and to blind the Eyes of the Enemies for some time. And this is the most lawful way that one may follow, because it shows its original from natural things, and we may believe that it is always sufficient justice, so that the Wars where such things are practised, be not unjustly enterprised. CHAP. XIII. Stink Balls. STinking Globes are made to annoy the Enemy by their stinking vapours and fumes disagreeable to Nature; nay so unsufferable to the Nose, and to the Brain itself, by its most violent stink, that by no means it can be endured. The preparation is as followeth, Take of Powder 10 l. of Ship Pitch 6 l. of Tar 20 l. Salt-Peter 8 l. Sulphur Colophonia 4 l. make all these Ingredients melt at the fire by a small heat, in an Earthen or Copper vessel, and all being well melted, throw into the melted matters 2 l. of Coal dust, of the cuttings or filings of Horse's Hoofs 6 l. Assafoetida 3 l. Sagapenum 1 l. Spatula foetida half a pound. Mingle and incorporate them well together; then put into this matter Linen or woollen Cloth, or Hemp or Tow, so much as will drink up all the matter, and of these you may make Globes or Balls of what bigness pleaseth yourself best, according to the method and order as we have heretofore prescribed. The Globes or Balls may be made Venomous or Poisonous, if to their Composition be added these things following, viz. Mercury sublimate, Arsenic, Orpiment, Cinaber, to which may also be added many other Poisonous matters, which I shall forbear to mention, considering every one by Nature is apt enough to learn to do that which is mischievous. CHAP. XIV. Of the Shooting of Shot made red hot in the Fire. IT is a practice that hath been practised in former times to shoot red hot Fire-balls, and was counted of great defence, as you may find amongst many other things in the Works of Diodorus Siculus, where he says, Tyrios' immisse in Alexandri Magni machinamenta massas magnas ferreas candentes: Out of many Authors may be proved the customary use in former times of Shooting red hot Pieces of Iron, which we shall not dwell upon, but come to the Practice. First, you must Charge the Piece of Ordnance according to the customary manner, his due proportion of Powder, upon this Powder you must put a Wooden Cylender or Fidd, of a just and equal wideness with the bore of the Piece, which must be driven very stiff home to the Powder, and for your better security, you must put upon this another wad made of Straw, Hay, or of Oakam, or Tow; this being done, let the Piece be laid a little under Metal, and then cleanse the vacant place or hollow of the Piece with a Sponge, so that all the Grains of Powder that are there, may be taken away. This being done, lay your Piece to bear with the place you intent to shoot at, according to the method we have given in the second Part of Gunnery, and let your Piece thus remain until you have put in your red hot Bullet: your Bullet must be sure to be exactly round, and not so high, but that it may run freely down in the Piece to the wad, the Shot being red hot, take it out of the fire with a pair of Tongues made for that purpose, and put it into the Piece, and give an attentive Ear, for as soon as the Shot is supposed to be up to the Wad, give immediately Fire to your Piece of Ordnance. There are others which put into their Pieces Boxes made of Plate, of Iron or Copper. Others do put into their Pieces Potter's Clay, and upon them the fiery Bullet, which with a quick hand they thrust home with a Rammer, which ought to be defended from fire by lining the Rammer head with Copper. But these are more perilous; and therefore we account that method above to be the best, and most free from danger. CHAP. XV. To Arm Pikes to defend a Ship or any other place. TO arm Pikes, to defend a ship, or breach, or to enter the same, or to stick in the sides of a ship, or other place, take strong Canvas, and cut it in length about a foot, or 14 inches, and six inches high in the Centre, and let the ends be both cut taper-wise, then fasten the Canvas at both ends with strong twine, and fill it with this receipt. Powder bruised 8 parts, Peter in Roch 1 part, Peter in meal 1 part, Sulphur in meal two parts, Roch three parts, Turpentine 1 part, Verdigrease ½ part, Bolearmonick ⅓ part, Bay salt ⅓ part, Colophonia ⅙ part, Arsenic ⅛ part, mix them very well together, and try them in the top of a Brass Candlestick, when the fire doth burn furiously with a blue and greenish colour, then fill the Canvas, and roll it over, being first armed with strong twine all over, with this liquid mixture melted in a pan, Pitch four parts, Linseed Oil 1 part, Turpentine ⅓ part, Sulphur 1 part, Tarr ⅓ part, Tallow one part; and as soon as this is cold, bore two holes in each of the same next the Iron an inch deep, with a sharp Iron Bodkin, filling the same with fine bruised powder, and putting in every hole a little stick of two inches long, which are to be taken out when you would fire the same; this composition will burn furiously. And remember you cut off the staff some three inches from the work, and put thereon a brass socket of five or six inches long, and then cut the end of your staff to fill the socket, for when you fire your work, you may stick it in the side of a ship, and pull the staff out again, so will not the work be so easily avoided, as when the staff was on, and hangs at length, because the very weight of the staff, and length thereof, will be a means to weigh down the work, or that the enemy may come, and thereby pull it out, or beat it off quickly; let the Composition and work contain in weight about 7 pounds, then will it do execution, and work a better effect, than if it were of less weight, by much, by reason the composition else would be wasted, before it comes to effect its Execution. To burn the sails of Ships a pretty distance, or to fire Thatched houses, Corn-stacks, or any other combustible matter apt to burn, when you cannot come to the same; it is good to have certain strong Crossbows to bend with Racks or Gaffels, and so shoot Arrows armed at the heads with Wildfire, made of the composition as above, and about three inches in length, and one inch and a half in the Diameter, tapred as afore in all points: or you may have long bows, but then let your Arrows be also longer, which for divers services may do great good. CHAP. XVI. To charge Trunks with Balls of Wildfire. TO charge Trunks to shoot little Balls of wildfire, either to offend or defend, you must first charge him with two inches of good Powder, and then with a Ball of wildfire a little lower than the concave of the Trunk, let the Ball be bored through cross-ways, and primed full of fine powder. Lastly, with slow receipt, then with powder, then with a Ball again as aforesaid, until you have filled the same within ¼ of an inch of the mouth, which would be filled up with fine powder and receipt mixed together. Some do use to have at the mouth two Iron stirts to stick them in the side of any thing, or to defend one's self from the Enemy from taking it off with a thrust while they do Execution. To make the Ball. The Ball of Wildfire must be thus made, Take untwisted Match, Tow, and Hemp, the which would be moistened in Aquavitae, or boiled in Salt-Peter water: then take of bruised Powder six parts, of Salt-Peter one part, of Brimstone finely beaten one part, of coal made of light wood moistened with a little linseed-oil and Turpentine wrought together, one part: then lay the Tow or Oakam, abroad in thickness of the back of a knife, and as broad as a great Oyster-shel, put into the same as much as you can grasp together in your fist, and tying the same hard with a pack-thread, coat it over with molten Brimstone, and when you would use the same, bore it through with a Bodkin, and fill the holes full of fine powder bruised. To make Bullets of Wildfire to shoot out of a Trunk, which will be as hard as a Stone. Take Sulphur in meal six parts, of in meal six parts, melting the same in some Pot over a slow fire: then take stone pitch one part, of hard wax one part, of Tarr ¼ part, of Aquavitae ½ part, of Linseed Oil ½ part, of Verdigrease ¼ part, of Camphire ⅛ part, melting all these together. Likewise stir into the same of Peter in meal two parts, and taking it from the fire, put therein four parts of bruised powder, working the same well together in your hands, and roll it round of the bigness you mean to make your balls of, boring two holes through the same cross-ways, which must be primed with bruised powder. These balls being cold, will grow very hard, and fired will burn furiously. To make Hedgehogs. To make Hedgehogs, or balls, you must fill them with the same receipts you do your Arrows, and Pikes, and let them be five inches in the Diameter, and well armed with twine before you coat them, and after boared two holes, and primed with fine powder: then put in two sticks, and using them, pull them out again, and at the said holes fire them. The spikes end of Iron must be like Death's Arrow heads, five or six stirts a piece to hang in the sails, or stick in or upon any place assigned; and remember in the arming, to leave a noose to throw him being fired, out of your hand. To make Powder-pots. They are made of black Potter's clay, or thick glass, round Bottles with ears to tie matches, lighted at both ends, the pots or glasses are to be filled with dry fine powder, and thrown upon the decks, or other where, which will much prejudice the Enemy, and many times fire their own Powder-chests. ARTIFICIAL FIREWORKS FOR RECREATION. AMongst all Artificial fires that have been put in practice many years, the Fuzees (which the Latins call Rochetae, and the Greeks Pyroboli) have always had the first Rank; (nevertheless this Greek word doth not well agree with the Etymology of the word Rochetae) seeing that 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 signifies properly Tela ignita, that is, burning darts or Arrows, the Italians call them Rochetae and Raggi, the Germans Steigen de Kasten, Ragetten, and Drachetten, the Poles Race, the French Fuzees, the English Rockets, or Serpents. If we consider the invention of them, it hath been of so ancient standing, that the construction is now very common and familiar amongst all the Pyrobolists and Fire-masters; the which, although it appears very easy in itself, yet there is in it labour, and requires that he that applies himself to this work should not be careless, but on the contrary take all the care and diligence that possibly he can have for the preparing of such perilous things, considering likewise the expenses and losses are irreparable after the experiment made; and seeing that nothing can be put in practice in public Recreations without these Fuzees, therefore I think I am something obliged here to show the true way of preparing them, with their particular use. CHAP. I. How to make Rockets. I Intent not here to write the Construction of Moulds fit for this purpose, but rather leave the more curious Students herein to the works of Casimier Siemienowicz, Lieutenant General of the Artillery in the Kingdom of Polonia, in his great Art of Artillery written in the French Tongue and Printed at Amsterdam, and also in our Countrymen Mr. Bate and Mr. Babington etc. That which I intent to do, is to teach you how they may be made by hand, or by help only of a Rouler to Roul the Paper upon; let it be turned to the thickness you intent, only let the Rouler be 8 times the Diameter in length. If it be three quarters of an inch in thickness, the length will be three inches. Roul your Paper hard on the Rouler until the thickness be one inch and a quarter Rouler and all; then glue the uppermost paper, and the Case is made. On the choking or contracting the paper together at one end, within one Diameter of the end, except only a little hole, about one quarter the Diameter of the bore thereof, to contract these Cases on this manner, do thus, wet the end about one inch in water, than put the Rouler in again, and tie a great packthread about the wet within three quarters of an inch of the end, put another thing almost of the same Diameter with the Rouler in at the wet end about half an inch, hold it there, get some other body to draw the packthread together, you holding the Rouler and Rammer, one put down to the end within one inch, and the Rammer which must be little less than the Diameter to meet with that end within half an inch, in which the contract or choking must be; the packthread having drawn it together, tie it fast on that place, take out the Former, let it dry, and it is done; when the hole is contracted together, make it so wide as is before taught, with a round bodkin, which you must provide for that purpose. CHAP. II. How to make Compositions for Rockets of any size. THese ways which I will teach you I take them not upon trust out of every Author, but such as are men of known experience, as that Casimier before spoken of, and others of the like repute. And first, for Rockets of 1 ounce, you must use only Cannon-powder dust being beaten in a Mortar, and finely sifted, and this will rise swift, and will make a great noise, but carries no tail: Those of most beauty in their operation are made of 1 ounce of Charcoal-dust, eight ounces of Powder, this Composition will hold for Rockets of one, two, or three ounces; but for those of four, take three ounces of Charcoal-dust, to one pound of Cannon-powder dust, continuing that Rule until you come to Rockets of ten ounces, and from thence to Rockets of a pound; for there used to be one pound of Powder-dust to 4 ounces of Charcoal-dust. But for better satisfaction observe these Rules. For Rockets of one pound. Take Powder 18 l. Salt-Peter 8 l. Charcoal 4 l. Sulphur 2 l, For Rockets of two or three pound. Take of Salt-Peter 60 l. Coal 15 l. Sulphur 2 l. For Rockets of four or five pound. Take of Salt-Peter 64 l. Coal 16 l. Sulphur 8 l. For Rockets of six seven or eight pound. Salt-Peter 35 l. Coal 10 l. Sulphur 5 l. For Rockets of nine or ten pound. Salt-Peter 62 l. Coal 20 l. Sulphur 9 l. For Rockets from eleven to fifteen pound. Salt-Peter 32 l. Sulphur 8 l. Coal 16 l. For Rockets from sixteen to twenty pound. Salt-Peter 42 l. Coal 26 l. Sulphur 12 l. For Rockets from thirty to fifty pound. Salt-Peter 30 l. Coal 18 l. Sulphur 7 l. For Rockets from sixty to a hundred pound. Take Peter 30 l. Sulphur 10 l. Coal 10 l. CHAP. III. To fill the Rockets with this Composition. PLace the mouth downwards where it was choked, and with a knife put in so much as you can of the receipts provided for that size at one time; then put down your Rammer, which must be longer and narrower than the Former or Rouler upon which you made the Cases, and with a hammer of a pound weight, give three or four indifferent knocks, then put in more composition with your knife, until it be full, at every time knocking the like as before with the Rammer, until the composition come within one diameter of the bore of the top, there put down a piece of pasteboard, and knock it in hard, prick three or four little holes therein, then put fine pistol powder in almost to the top, and upon that another cap of paper, upon which put a piece of leather, that it may be tied on the top of the Rocket, and fast glued on, then get a straight twig, and bind it upon the Rocket with strong packthread; it must be no heavier, than being put upon your finger, two or three fingers breadths from the mouth of the same, it may just ballast the Rocket; than it is prepared for use. CHAP. IU. How to give fire to one or more Rockets. SEt your Rockets mouth upon the edge of any piece of timber, battlement of a wall, top of the Gunners carriage wheel, or any dry place whatsoever, where the rod or twig may hang perpendicular from it, then lay a train of powder that may come under the mouth thereof, give fire thereunto, and you have done. But if you would fire more Rockets than one, that as one descendeth, the other may ascend by degrees, make this composition following of Roch peter 8 ounces, Quick Brimstone 4 ounces, and fine Powder dust 2 ounces, which lay in a line from one Rocket to another, they being placed ten inches or a foot one from another, give fire to this composition, and it will work your desire, by causing one to mount into the air when the other is spent; but before you place your Rockets, remember to prick them with the bodkin. CHAP. V Divers and sundry Compositions for Stars. A Composition for Stars of a blue colour mixed with red. TAke of Powder mealed 8 ounces, Salt-Peter 4 ounces, Quick Brimstone 12 ounces, Meal all these very fine, and mix them together with two ounces of Aquavitae, and half an ounce of Oil of Spike, which let be very dry before you use it. Another Composition which maketh a white and beautiful fire. Take Powder 8 ounces, Salt-Peter 24 ounces, Quick Brimstone 12 ounces, Camphire 1 ounce, Meal these Ingredients and incorporate them: Now to meal your Camphire, take a brass pestle and mortar, wet the end of the pestle in a little of the Oil of Almonds, and it will meal to powder, then keep it close from the air, else it will become of no use. Another white fire which lasteth long. Take Powder 4 ounces, Salt-Peter 16 ounces, Brimstone 8 ounces, Camphire 1 ounce, Oil of Peter 2 ounces, Meal those that are to be mealed, and mix them according to the former directions. CHAP. VI The manner of making Stars; and to use them. TAke little four square pieces of brown paper, which fill with the composition you approve of best, of the three last taught: so double it down, rolling it until you make it round, about the bigness of a nut, or bigger, according to the size of your Rocket, that you intent them for, prime them, withdrawing thorough them Cotton-week, and they are prepared. You may also make them after this manner, you must have a rouler which must be as big as an ordinary arrow, which shall be to roll a length of paper about it, and with a little glue past it round; when it is dry draw out the rouler, and fill it by little and little, with a thimble; still thrusting it down, every filling of a thimble, with the rouler; which being filled, cut it in short pieces, about half an inch long; then having in readiness either hot glue, or size, mingled with red lead, dip therein one end of your short pieces, lest they take fire at both ends together, and because that it may not so easily blow out: these being thus finished, set them to dry until you have occasion to use them: and then putting the open end in powder on the top of the Rocket, in that place after the first pasteboard, or cover, is placed in a Rocket; next the composition, where I taught you before to put powder for to make a report: which now you must leave out to place in these Stars; after this manner make two or three holes in that pasteboard, which prime with powder-dust: and thereupon put a little Pistol powder, to blow the Stars out when the Rocket is spent: after the powder, put as I have said before, the open ends of these Stars, down upon that powder: when you have put them so close as they can stick one by the other, put a little small corned powder on the top of them, to run between them, and put another tire of Stars upon that, and in like manner a third tire upon them, till you come to the top of the Rocket-case, there put a paper over the head of it, and tie it close about the top, that none of the powder come from under or between the Stars. How to prepare the Cotton-week, to prime the first sort of Stars. Take Cotton-week, such as the Chandler's use for Candles; double it six or seven times double; and wet it thoroughly in Saltpetre water, or Aquavitae, wherein some Camphire hath been dissolved, or for want of either in fair water, cut it in divers pieces, roll it in mealed powder, dry it in the Sun, and it is done. CHAP. VII. How to make silver and golden Rain, and how to use them. NOw I show you the order of making golden Rain, which is after this manner; you must provide store of Goose-quills, which being provided, you must cut them off so long as they are hollow, the composition to fill these must be made thus; two ounces of coaldust to one pound of powder well mixed; having filled many of these quills, you shall place them in the same place as I taught you to put the powder and Stars, first putting a small quantity of Pistol powder under them, to blow them out when the Rocket is spent: upon this put your quills, as many as will fill the top of the case, with the open end downwards; so soon as the Rocket is spent, you shall see appear a golden shower, which by some is called golden Rain: The like way you may make silver Rain, filling the quills with the Composition for white Stars. CHAP. VIII. How to make Fisgigs, which some call by the name of Serpents, and to use them. YOu must provide a small rolling pin, about one quarter of an inch in thickness, upon which roll seven or eight thicknesses of paper: fill them four inches with powder dust, sometimes putting between the filling a little of the Composition for Rockets of 10 ounces: and at the end of four inches choke him; fill two inches more with Pistol powder; then choke the end up: at the other end put in a little of the mixture for Stars, and choke between that and the composition, and you have done: put divers of these with the Starry end downwards, upon the head of a Rocket, as you did the quills, with powder to blow them out; when the Rocket is spent, they will first appear like so many Stars; when the Stars are spent, taking hold of the powder dust, they will run wriggling to and fro like Serpents; and when that Composition is spent, they will end with every one a report, which will give great content. I shall have occasion to speak of these Fisgigs in other Fireworks. CHAP. IX. How to make Girondels, or (as some call them) Fire-Wheels. A Fire-Wheel is often required in great Works for pleasure, and therefore I have thought fit and necessary, to set down their description, as well as of all other sorts of Fireworks; First, you must make a Wheel of Wood, so big as you please, to make Girondels, and unto these bind Rockets very fast of a mean bigness, with the mouth of one towards the tail of another, thus continuing until you have filled your Wheel quite round, which done, cover them with paper pasted very curiously, that one taking fire, they may not take fire all together; and daub Soap upon them quite round, leaving the mouth of one of them open to give fire thereto; for the first Rocket having burned, will give fire to the next, keeping the Wheel in continual motion, until they be all spent: there may be bound fire Lances to these Girondels, either upright, or near, overthwart, which will make to appear diversity of fiery Circles; Your care must be, to place the Girondels at a convenient distance, from other Fire-Works, lest they should cause confusion, and spoil all your Work. CHAP. X. How to represent divers sorts of Figures in the Air with Rockets. I Have taught you to make a report upon the head of a Rocket, and also to place golden or silver Hair or Rain, or Stars, or Fisgigs, which when you have divers Rockets to make for a great Firework, let one be with a report, the next with Stars, another with Gold Hair, or Rain, one with Silver Hair or Rain, for standing just under the Rocket it appeareth like Rain, but being aside hand, like Golden or Silver Hair: and upon the head of another Rocket place the Fisgigs, which when the Rocket is spent will first appear like so many Stars, after they are ended, they will show like Serpents wriggling to and fro, and lastly, give every one his report. It is a rare thing to represent a Tree or Fountain, in the air, which is made by putting many little Rockets upon one great one, passing all the rods of the little ones thorough wires, made on purpose upon the sides of the great one, or some other way, as your industry will discover; now if the little ones take fire while the great one is mounting up, they will represent a Tree, but if they take fire as the great one is descending or turning down again towards the ground, than they will be like a fountain of fire; if there be two or three little Rockets amongst others, that have no rods, they will make divers motions contrary to the rest, very pleasing. If before you put the Fisgigs upon the head of a great Rocket, you with a small string tie them together, a foot of line between; when they are on fire in the Air you will see very great variety of Figures, because as they wriggle to and fro, they will pull one another after them, to the speculators great content: it will be pleasant if you tie them not altogether, but three or four, which will in the firing of them, be distinguished from the rest, with great variety. CHAP. XI. How to make a Rocket, which firing it out of your hand, shall continually be in agitation, either on the earth, or in the air. HAving prepared a Rocket with a report in the head, such as I taught you first to make, tie it to a bladder, so that the end of the Rocket may come to the mouth of the said bladder, and bind it over very strongly, then firing it out of your hand, cast it away from you, it matters not which way, so it will come to the ground; there, by reason of the bladder, it cannot stay, but presently rebounds upwards, moving to and fro, until all be spent: there is another sort, and that is a small rocket, put into a bladder, and so blown up round about it, and tied about the neck thereof, which will have delightful motions. CHAP. XII. Of the many defects in Fuzees, how they may be avoided, and of such things as aught to be observed in their good Construction. THe first and most notable defect which is observed in Fuzees, is that after they are lighted or risen into the Air the height of 1, 2, or 3 Perches, they break, and do dissipate without making their entire effects. The second, which is little better, is after it is remaining suspended upon the nail it consumes but very leisurely, without going away or raising itself in the Air. The third is, when they are raised in the Air, they describe only an Arch of a Circle like a Rainbow, and return upon the earth again before the Composition in the Fuzee be consumed. The fourth is when it moves in a spiral manner, whirling in the Air without observing an equal motion; that is not right as it ought to be. The fifth is when it mounts sloathfully and negligently, as if it disdained or refused to elevate itself into the Air. The sixth and last is, that the Case or Cartouch remains hanging upon the Nail quite empty, and the Composition doth rise and dissipate alone into the Air. There is many other vexations and inconveniencies which may give trouble to the Practitioners in these Arts with vain expense, which would lose too much time to repeat: It will be sufficient if you take notice of these which are principal, whereby, if by ill fortune you be fallen into any of these defaults, you may correct your error easily, and then immediately correct those faults. And for this purpose, observe the rules given in the next Chapter. CHAP. XIII. Infallible Rules by which you may make Fuzees, or Rockets, without any default. FIrst, that they have their height proportionable to the Diameter of their Orifice, as we have before declared. Secondly, the Cartouch ought to be of wood, or glued or pasted paper, not too thick, nor too thin. Thirdly, they ought to be made of strong paper of indifferent dryness, properly rolled and well compacted close upon the Former. Fourthly, the necks ought to be bound about very strongly and firm, in such a sort, that the knot of the thread, and the folds of the Cartouch, may not lie amiss one upon the other. Fifthly, all the Materials of the Composition must be exactly weighed according to the proportion of the Orifice of the Fuzee that you would charge, and also well beaten and sifted particularly; after, having weighed them again, and mixed them in one body well together, you must pound them again, and pass them through the Sieve as you did before. Sixthly, that the Salt-Peter and Sulphur be powdered and clarified as much as possible may be, and the Coal perfectly well burned and exempted from all humidity, and made of wood that is light and soft, as the Teile, the Hazle, and the branches of the Willow Tree; and on the contrary, 'tis necessary to have a care, that you make not use of such Coals as are made of Birch, Oak, nor Maple, because they contain in them much weighty and terrestrial matter. Seventhly, matters for Rockets or Fuzees ought to be prepared immediately before they are intended for use, and not before. Eighthly, the matters of Composition ought to be neither too dry nor too moist; but moistened a little with some Oliganious matter, or with a little Brandy wine. Ninthly, there must be put into the Cartouch always an equal quantity of the Composition at a time, and so beat it down alike; and thus do until it be filled. Tenthly, you must beat the Composition always with the Rammer right up, or perpendicularly, and take care that in the beating it be not made crooked. Eleventhly, You must strike down the Composition with a wooden Mallet, that is of heft proportionable to the bigness and thickness of the Rocket, and always with an equal strength, and just number of strokes, every time you put in any of the Composition. Twelfthly, in Cartouches made of paper, you must put in round pieces of wood hollowed; but in those that are made of wood, you must put such as are smooth, without any channel or hollowing, to the end that it join the better to the sides of the Fuzee, where it must join firmly, as well without as within. 13. The Fuzee must be pierced with a Bit or Awl that is convenient, in such a sort that the hole be not too big nor too strait, nor too long nor too short. 14. The hole must be made the most straight and perpendicular that may be possible, and just in the middle of the Composition, to the end that it lean not to any one side, more than to the other. 15. The Fuzee must not be pierced before it be intended for use, and after it is pierced you must handle it tenderly, only with the ends of your fingers, for fear of deforming it. 16. The Perch or Stick to which you fasten the Fuzee, aught to be proportionable as well in length as weight; it must not be crooked nor winding in any manner, neither unequal, nor full of knots, but straight as possible can be made, and must therefore be made smooth, and straightened with a Plain, if need requires. 17. After they are Charged, they must not be laid into too dry a place, nor in a place too moist, for the one or other of those accidents may hurt them; therefore let the place be temperate. 18. When you would use them and put them into action, hang them upon a nail perpendicular to the Horizon. 19 You must not think to raise a bundle of a great weight, or that has too great a disproportion to their strength, you must adjoin them together so rightly, that all together may have a proper form, and reasonable to pass into the Air, and to elevate itself on high without any difficulty, and in such a sort, that those bundles may not by any means give hindrance or stoppage to their rising in a straight line; and take care most exactly that the Fuzee be not so big, but that they may retain as near as you can a Pyramidal or Conical form, when all its weight that may be is adjoined to it. 20. Men ought to shun as much as possible those nights that are rainy, moist, and when the Sky is darkened with black clouds, as being very incommodious and offensive to the Fuzees. And more than that, avoid impetuous Stormy winds, and the Whirlwinds hinder no less than the first. 21. You may not reject above other causes, the different effects which are produced by sundry Fuzees (although they be charged with one and the same Composition) no otherwise than thus, that they were not made with an equal diligence either in the Charging or Piercing, or in the other Circumstances, which you were obliged to observe; or in this, that it may be some may have been kept in a more moister place than the others, where they have acquired too much moisture, which causeth to them, effects much different one from another, as well in Rising as in Consuming. 22. If you would make appear in the Air streams of fire, or a quantity of burning sparks or stars, or long large rays to dart from the Fuzees; there is accustomed to mix with the Composition some small quantity of powdered Glass grossly beaten, filings of Iron, Sawdust. One may also represent fire of divers colours, as we have showed before in the fifth Chapter; but more particularly thus; if you put a certain portion of Camphire in your Composition, you will see in the Air a certain fire which will appear, white, pale, and of the colour of Milk; if you put Greek Pitch, which is a light yellow Pitch used in Plasters, called Pix Burgundy, it will represent unto you a red flame, and of the colour of Brass; if you put in Sulphur, the fire will appear blue; if Sal-Armoniack, the fire will appear Greenish; if from Crude Antimony, the flame will be Red, Yellowish, and of the Colour of Honey; if the filings of Ivory be added, they will render a Silver-like, White and shining flame, yet something inclining to a Livid Plumbous colour; if the powder of Yellow Amber be added, the fire will appear of the same colour, with the Citrine; lastly, if black Pitch be added, it will throw forth an obscure smoky fire, or rather a smoke that is black and thick, which will darken all the Air. CHAP. XIV. Of Odoriferous Aquatic Balls. 'Cause to be made by a Turner, Balls of wood, hollow within, about the bigness of a Wild Apple, which you must fill with some one of these Compositions hereunto annexed, and they being all prepared and charged, you may throw them into the water after they are lighted, but it ought to be done in a Chamber or close place, that the fume may be the better kept together, and this must be done with some small end of our Match made of prepared Flax or Hemp, to the end that the Composition which is shut up in the Globe may take fire with the greater facility. The Compositions are these that follow, viz. Take Salt-Peter, Storax Calamite, one Dram; Incense one ounce, Mastic one ounce, Amber half an ounce, Civet half an ounce, of the Sawing of Juniper wood two ounces, of the Sawing of Cypress wood two ounces, Oil of Spike one ounce; Make your Composition according to the Art and Method given. Or, Take of Salt-Peter two ounces; of Flower of Brimstone, Camphire, half an ounce; powder of yellow Amber half an ounce, Coals of the Teile tree one ounce; Flower of Benjamin, or Assa sweet, half an ounce; Let the matters that may be beaten be powdered, afterwards well mingled and incorporated together. CHAP. XV. Compositions to Charge Globes or Balls, that will burn as well under as above water. FIrst, take Salt-Peter reduced into fine meal 16 l. Sulphur 4 l. of the sawing of wood which hath been first boiled in a Nitrous water, and afterwards well dried, 4 l. Of good Corned powder half a pound, of the powder of Ivory 4 ounces. Or thus, Salt-Peter 6 l. Sulphur 3 l. of beaten powder 1 l. Filings of Iron 2 l. of Burgundy pitch half a pound. Or thus, Salt-Peter 24 l. of beaten powder 4 l. Sulphur 12 l. of Sawdust 8 l. of yellow Amber half a pound, of Glass beaten in gross powder half a pound, of Camphire half a pound. For that which concerns the manner of preparing all these Compositions; it differs nothing from what we have prescribed in the making of Rockets, only 'tis not necessary that the materials be so subtly beaten, powdered nor sifted, as for those Fuzees, but nevertheless to be well mixed one among another. Care must be taken that they be not too dry when you charge the Globes or Balls, and for that purpose they may be moistened with linseed-oil, Oil of Olives, Petrole, Hempseed, Nuts, or any other fatty humour that is receptible of fire. Note, that amongst all these Compositions of matters that will burn in the water, which I have here proposed from my own particular experience, every one may make them as pleaseth himself best, provided he always take the materials in proportion one to the other, as they ought. But nevertheless I shall counsel you to experience from time to time your Compositions, for the greater surety, before you expose them to the public view of the world. It is also amongst the rest very necessary that you learn the force and strength of every material you put into the Compositions, whereby you may at your pleasure know how to alter and vary your proportion, as you shall judge fit. CHAP. XVI. Of Stars and fiery Sparks, called by the Germans Stern-vever and Veverputzen. I Have showed the Composition of Stars in Chap. 5. I have also shown the way of making them up, and their use, and also I have showed the manner of giving to them various Colours, as in the 22 Rule of the 13 Chapter, where I had an intent to say no more of these things: But finding in Master Cazimier's Artillery these Compositions, which I judge may prove very excellent; therefore I thought good to insert them, that I might leave out nothing that might make more perfect any thing we treat of. First, you must know that between fiery Sparks and Stars there is this difference, that the Stars are greater, and are not so soon consumed by the fire as the Sparks are, but do subsist longer in the Air, and do shine with greater substance, and with such a light, that by reason of their great splendour, they are in some manner comparable with the Stars in the Heavens. They are prepared according to the following Method. Take Salt-Peter half a pound, Sulphur two ounces, Yellow Amber powdered one Dram, Antimony Crude one Dram, of beaten Powder three Drams. Or, Take Sulphur two ounces and a half, Salt-Peter four ounces, Powder subtly powdered four ounces, Olibanum, Mastic, Crystal, Mercury sublimate, of each four ounces, White Amber one ounce, Camphire one ounce, Antimony and Orpiment half an ounce; All these materials being well beaten and well sifted, they must be mixed together with a little Glue or Gum-water, made with or Tragacant; then make them into small Balls about the bigness of a Bean or small Nut, which being dried in the Sun, or in a Pan by the fire, may be kept in a convenient place for such uses as we have spoken of in the fifth Chapter of this Book. You must only remember, that when you would put them into Rockets or Recreative Balls, they must be covered on all sides with prepared Tow, of which we have showed the way of preparing in the seventh Chapter of the first Part of our Fireworks. Sometimes Fire-Masters are aecustomed to take in the places of these little Balls, a certain proportion of melted matters, of which we have spoken in the first Part of Fireworks; But if these do not please you, by reason of their swarthy colour, but you rather desire to see them yellow, or inclining somewhat to white, then take of or Tragacant four ounces, powder it and pass it through a Sieve, of Camphire dissolved in Aquavitae two ounces, Salt-Peter a pound and a half, Sulphur half a pound, Glass grossly powdered four ounces, White Amber an ounce and a half, Orpiment two ounces, make all these Ingredients into one mass, and make Globes of them as before. I Learned this, saith my Author, from Claude Midorge. For the method of making Sparkles in particular, it is thus; Take Salt-Peter one ounce, of this Liquid matter half an ounce, of beaten Powder half an ounce, of Camphire two ounces; after you have beaten all these materials into powder, every one by itself, put all of them into an Earthen Pan, and put upon them the Water of Gum Tragacanth, or Brandywine, wherein you have dissolved some Gum Tragacanth or Arabic, until it be of a good consistency; that done, take an ounce of Lint, which has first been boiled in Brandywine or Vinegar, or in Salt-Peter, and after dried again, and the threads drawn out; then put it into the Composition, and mix them well together, so well and so long until it has drank up all the matter; of these Compositions make little Balls in the form of Pills, and of the bigness of great Peas, which you must roll in mealed Gunpowder, and dry them, whereof you may serve yourself, according to the method we have prescribed. Besides these, there are certain odoriferous Pills prepared, which are employed in small Engines and fiery Inventions, which are showed in Chamber Roams, or close Cabinets, these are commonly prepared of Storax, calamity, Benjamin, Amber, white and yellow, and of Camphire, of each one ounce, Salt-Peter three ounces, of Coals made of the Teil Tree four ounces; beat all these Ingredients to powder, then incorporate them well together, and moisten them with Rose Water, in which is dissolved or Tragacanth, to make thereof little Balls; at last, having fashioned them, expose them to the Sun or to the fire to dry. THE DOCTRINE OF PROJECTS APPLIED TO GUNNERY. By those late famous Italian Authors GALILAEUS AND TORRICELLIO. Now rendered in ENGLISH. LONDON, Printed in the Year 1672. THE PREFACE. GALILAEUS in his 4th. Dialogue of Motion, hath largely treated of aequable and accelerate or increasing Motions, as also of that of Projects, or things shot, and thence derived several Propositions or Conclusions, and hath likewise made several Tables touching the Amplitudes or Base Lines, and the Altitudes or Heights of the Semiparabola's or Curves described by the Motion and Ranges of Projects. The which Doctrine the late Famous Torricellio of Florence, having with great Judgement much advanced and facilitated, applying the whole to the Art of Gunnery; that the benefit of his pains might redound to the English Reader, that is especially Delighted or Exercised in the Affairs of Mars, it was thought fit to render the same into English. THE DOCTRINE OF PROJECTS APPLIED TO GUNNERY. PROPOSITION. The Impetus B A (that is, as much as is that of the movable naturally falling from B to A by the * Which Definition is; when we name an Impetus given, we determine it in spaces, according as Galilaus useth; Exemp. Grat. When we say, let the Impetus given be A B, than we mean, let the Impetus given be so much as is requisite to throw the Project from A to the highest point of the perpendicular B; or, which is the same, as much as is the Impetus of a movable naturally falling from B to A. Definition) as also the Direction A I, according to which the Projection is to be made with the said Impetus being given: it is required to find the Amplitude, Altitude, and the whole future Parabola of this Projection. projection measurement Again, I say, that this Parabola is described by the Impetus given, for A E, E F, and E B, or those three lines equal to D G the Altitude, G F the Semi-base, and G L are in continual proportion. Wherefore G L is the sublimity, by the V Proposition of * De metu Projectorum. Galilaeus, and its Corollary. Then thus: the Impetus of the Parabola A G in the point A, is as much as that of the Cadent naturally falling from L to D, (by X. of Galilaeus) that is, from B to A, or of the Project ascending from A to B: therefore the Parabola hath in the point A the Impetus that was given: wherefore that is done which was required. But because this Proposition is of great moment, for clearing of those that follow, we will prove it another way. projection measurement First, it is manifest that the point P cannot be in the line L D; because since the line A C toucheth each Parabola, that I D the common Axis should be cut into two equal parts in two points by the Vertex's of the Parabola, is absurd. Nor can it be in the line E G: for drawing the Diameter, suppose M N, through the Vertex, that M N should be cut into two equal parts by the line E G, is absurd▪ for only I D, of all the lines parallel unto it in the angle C A D, can be cut into two equal parts. Now let the point P fall any where at pleasure, and draw the Horizontal line P R S: for as much as P N and P M are equal, by the TWO of * Which second Proposition is, that the sublime point of the Range of any Project [P] doth cut the Perpendicular [M] intercepted betwixt the Horizon and line of direction, into two equal parts. this, N R and R A, P R and R S shall be equal. And because the Parabola A P hath the Impetus B A; that is, O M, the Point O shall be its sublimity: and for that reason the lines O P, P R, and P M shall be in continual proportion; and the Rectangle O P M equal unto the square P R: and changing the lines with their equals, the Rectangle B S A shall be equal to the square S R: therefore the R is in the point Periphery of the Semicircle: which is absurd; for the right line A F shall meet with the Periphery in two several points: wherefore, etc. COROLLARIES. projection measurement 2. In the Book of Galilaeus de motu naturaliter accelerato, it is proved, that projects thrown with the same Impetus out of A, if born up by plains of several inclinations, do always arrive unto one and the same Horizontal plain. But here it appeareth, that the several ascensions of projects do vary when they are thrown through the pure Air, without any fulciment put under them, according to several elevations. For the movable shall less ascend, which is emitted along the line A B less elevated, than that which shall be projected along A D more elevated. 3. It is manifest also, that no Altitude can in such sort ascend, as that it may reach unto the Horizontal parallel that is drawn thorough E the highest point of the perpendicular projection. 4. It is also manifest, that all Amplitudes do always increase from that projection which is called the point blank Randon, until you come to the projection made at the Semi-right Angle. And from the Semi-right unto the perpendicular, they always diminish until they come to nothing; which happeneth in the perpendicular projection, which hath no Amplitude. projection measurement 6. It is manifest likewise that the Altitudes and Sublimities of projections equi-distant from the Semi-right, are reciprocally equal to one another, that is, the Altitude of the one is equal to the sublimity of the other. projection measurement 8. It is manifest also, that the whole Amplitude of the Semi-right Parabola is double to the line of the Sublimity, or the Impetus A B: for it hath been demonstrated to be Quadruple of the right line C D, that is double to A B. PROP. II. The Impetus and Amplitude being given, I incite this Proposition, as being also cited in the ensuing Discourse. to find the direction according to which the Parabola was made; as also to find the Altitude. projection measurement In this place I have thought fit to insert the Tables following: the first Classis of which containeth three Tables, the same with those of Galilaeus, which we placed Part. I. Dial. 4. Page 241. of this present Tome, but different in many of the Numbers, as being desumed from the Tables of Sines and Tangents, whereas Galilaeus Calculateth his with much labour, according to the Principles of his Doctrine of Projective motion, laid down in that his fourth Dialogue. The second Classis consists of two Tables added by Torricellius, the one of Durations, the other of Elevations or Randons': the Explanations and Calculations of which are annexed to them by the Author, but here omitted on the account of brevity. TABLE I. The Amplitudes of the Semiparabola's described by the same Impetus. The greatest Amplitude is supposed to be of 10000 parts; and the Numbers of the Table are double to the right Sins of the arches of the elevation. Degr. of Elevat. Ample of Semi-P. D. of Elev. 1 349 89 2 098 88 3 1045 87 4 1392 86 5 1736 85 6 2079 84 7 2419 83 8 2756 82 9 3090 81 10 3420 80 11 3746 79 12 4067 78 13 4384 77 14 4695 76 15 5000 75 16 5299 74 17 5592 73 18 5870 72 19 6157 71 20 6428 70 21 6691 69 22 6947 68 23 7193 67 24 7431 66 25 7660 65 26 7880 64 27 8090 63 28 8290 62 ●● 8480 61 30 8660 60 31 8829 59 32 8988 58 33 9135 57 34 9272 56 35 9397 55 36 9511 54 37 9613 53 38 9703 52 39 9781 51 40 9848 50 41 9903 49 42 9945 48 43 9976 47 44 9994 46 45 10000 45 TABLE II. The Altitudes of the Semiparabola's, whose Impetus is the same with that of the precedent Table. The greatest Altitude is supposed to be of 10000 parts; and the Numbers of the Table are double to the halfs of the versed Sins of the Arches of the Elevation. D. of Elev. Altit. of Semi-P. D. of Elev. Altit. of Semi-P. 1 3 46 5174 2 12 47 5349 3 27 48 5523 4 49 49 5696 5 76 50 5868 6 109 51 6040 7 149 52 6210 8 194 53 6378 9 245 54 6545 10 302 55 6710 11 364 56 6873 12 432 57 7034 13 506 58 7192 14 585 59 7347 15 670 60 7500 16 760 61 7650 17 855 62 7796 18 955 63 7939 19 1060 64 8078 20 1170 65 8214 21 1284 66 8346 22 1403 67 8470 23 1527 68 8597 24 1654. 69 8716 25 1786 70 8830 26 1922 71 8940 27 2061 72 9045 28 2204 73 9145 29 2350 74 9240 30 2500 75 9330 31 2653 76 9415 32 2808 77 9494 33 2966 78 9568 34 3127 79 9636 35 3290 80 9698 36 3455 81 9755 37 3622 82 9806 38 3790 83 9851 39 3960 84 9891 40 4132 85 9924 41 4304 86 9951 42 4477 87 9973 43 4651 88 9988 44 4826 89 9997 45 5000 90 10000 TABLE III. The Altitudes and Sublimities of 〈◊〉 Semiparabola's, whose Amplitudes 〈◊〉 equal, Viz. always 10000 parts; 〈◊〉 Altitudes are the halfs of the Tangents of the Angles of the Elevations and the Sublimities are the halfs of the Tangents of the Compliments of the Elevation. D. of Elev. Altitudes. Sublimiys. D. of Elev. Altitudes. Sublimities. 1 87 286450 46 5178 4828 2 175 143186 47 5362 4663 3 262 95406 48 5553 4502 4 350 71503 49 5752 4346 5 437 57150 50 5959 4196 6 525 47572 51 6175 4049 7 614 40722 52 6400 3906 8 703 35577 53 6635 3768 9 792 31569 54 6882 3633 10 882 28356 55 7141 3501 11 972 25723 56 7413 3373 12 1063 23523 57 7699 3247 13 1154 21657 58 8002 3124 14 1247 20054 59 8321 3004 15 1340 18660 60 8660 2887 16 1434 17437 61 9021 2772 17 1529 16354 62 9404 2659 18 1625 15388 63 9813 2548 19 1722 14521 64 10252 2439 20 1820 13737 65 10723 2332 21 1919 13025 66 11230 2226 22 2020 12375 67 11779 2122 23 2122 11779 68 12375 2020 24 2226 11230 69 13025 1919 25 2332 10723 70 13737 1820 26 2439 10252 71 14521 1722 27 2548 9813 72 15388 1625 28 2659 9404 73 16354 1529 29 2772 9020 74 17437 1434 30 2887 8668 75 18660 1340 31 3004 8321 76 20054 1247 32 3124 8002 77 21657 1154 33 3247 7699 78 23523 1063 34 3373 7413 79 25723 972 35 3501 7141 80 28356 882 36 3633 6882 81 31569 792 37 3768 6635 82 35577 703 38 3906 6400 83 40722 614 39 4049 6175 84 47572 525 40 4196 5959 85 57150 437 41 4346 5752 86 71503 350 42 4502 5553 87 95406 262 43 4663 5362 88 143186 175 44 4828 5718 89 286450 87 45 5000 5000 90 Infinita. 00 TABLE iv The Durations or Impetus of Projects made by the same Impetus compared to the Horizon. The greatest Duration or Impetus is supposed to be of 1000 parts; and the Numbers of the Table are the right Sins of the Elevations. Degr. of Elevat. Dur. of Impet. D. of Elev. Dur. of Impet. 1 75 46 7193 2 349 47 7314 3 523 48 7431 4 698 49 7547 5 872 50 7660 6 1045 51 7771 7 1219 52 7880 8 1392 53 7986 9 1564 54 8090 10 1736 55 8192 11 1908 56 8290 12 2079 57 8387 13 2250 58 8480 14 2419 59 8572 15 2588 60 8660 16 2756 61 8746 17 2924 62 8892 18 2090 63 8910 19 3256 64 8988 20 3420 65 9063 21 3584 66 9135 22 3746 67 9205 23 3907 68 9272 24 4067 69 9336 25 4226 70 9397 26 4384 71 9455 27 4540 72 9510 28 4695 73 9563 29 4848 74 9613 30 5000 75 9659 31 5150 76 9703 32 5299 77 9744 33 5446 78 9781 34 5592 79 9816 35 5736 80 9848 36 5878 81 9878 37 6018 82 9903 38 6157 83 9925 39 6293 84 9945 40 6428 85 9962 41 6561 86 9976 42 6691 87 9986 43 6820 88 9994 44 6947 89 9998 45 7071 90 10000 TABLE V The Degrees of Elevation to which the Piece is to be mounted, that the Amplitude of the Projections may be made of the given measure. We suppose all the Projection to have the same Impet. that is to be made by the same Piece, & that the greatest is 4000 paces. Spaces, or equal increases of the Projection. Spaces. Deg. of Elevat. Compliment. Spaces. Deg. of Elevat. Compliment. 10 00 17 89 43 510 15 20 74 40 20 00 34 89 26 520 15 40 74 20 30 00 52 89 08 530 16 00 74 00 40 1 09 88 51 540 16 21 73 39 50 1 26 88 34 550 16 41 73 19 60 1 43 88 17 560 17 02 72 58 70 2 00 88 00 570 17 23 72 37 80 2 18 87 42 580 17 44 72 16 90 2 35 87 25 590 18 05 71 55 100 2 52 87 08 600 18 26 71 34 110 3 09 86 51 610 18 48 71 12 120 3 27 86 33 620 19 10 70 50 130 3 44 86 16 630 19 22 70 26 140 4 01 85 59 640 19 54 69 06 150 4 19 85 41 650 20 16 69 44 160 4 36 85 24 660 20 39 69 21 170 4 54 85 06 670 21 02 68 58 180 5 11 84 49 680 21 25 68 35 190 5 29 84 31 690 21 49 68 21 200 5 46 84 14 700 21 13 67 47 210 6 04 83 56 710 22 37 67 23 220 6 21 83 39 720 23 02 66 56 230 6 39 83 21 730 23 27 66 33 240 6 57 83 03 740 23 52 66 08 250 7 14 82 46 750 24 18 65 42 260 7 32 82 28 760 24 44 65 16 270 7 50 82 10 770 25 11 64 49 280 8 08 81 52 780 25 38 64 22 290 8 26 81 34 790 26 06 63 54 300 8 44 81 16 800 26 34 63 26 310 9 02 80 58 810 27 03 62 57 320 9 20 80 40 820 27 33 62 27 330 9 38 80 22 830 28 03 61 57 340 9 56 80 04 840 28 34 61 26 350 10 14 79 46 850 29 06 60 54 360 10 33 79 27 860 29 36 60 21 370 10 51 79 09 870 30 14 59 46 380 11 10 78 50 880 30 50 59 10 390 10 29 78 31 890 31 27 58 33 400 11 47 78 13 900 32 05 57 55 410 12 06 77 54 910 32 45 57 15 420 12 25 77 35 920 33 28 56 32 430 12 44 77 16 930 34 13 55 47 440 13 03 76 57 940 35 02 54 58 450 13 22 76 38 950 35 54 54 06 460 13 42 76 18 960 36 52 53 08 470 14 01 75 59 970 37 58 52 02 480 14 21 75 39 980 39 16 50 44 490 14 40 75 20 990 40 57 49 03 500 15 00 75 00 1000 45 00 45 00 The use of the Precedent TABLE. projection elevation I know that its very seldom, and perhaps neverfound, that the greatest Range of a Piece of Ordnance is just those 4000 Paces, as it seemeth to have been supposed in the Calculating of our Table, and also in those of Signiore Galileo, so that the said Table might seem unuseful: but we shall show, that the supposed number of 4000 doth not therefore serve to any great particular Machine, to the end it might serve to all in general. It is necessary therefore to take notice, that that same suppositious Number of 4000, is not of Paces, or of els, or of Yards, or of any other determinate measure, but of abstracted parts, such yet, whatever they are, as being convertible into any kinds of possible measures, they do make the Table general, as well for the Culverin, as for the Mortar-Piece or Cross-Bow. And to give an example how it may be adapted and applied to all the Species of Artillery, and how the Abstract parts may be reduced into Geometrical paces, we will do thus. The greatest Range of a Canon, by experiment made thereof, is found to be, suppose 2300 paces; and I would with the same Piece make a shot that should be 860 paces, I do thus: If the greatest Range 2300 give 860, I ask what the number 1000, the greatest of the Table will give? I work and find 374: which number being sought in the Table, is found to be betwixt 370 and 380. Therefore taking the part proportional according to my Judgement, I find the Arch of its Elevation ought to be Grad. 11. very near, or its Compliment gr. 79. And thus it is certain, that that same Piece which being mounted to six points did carry 2300 paces, being elevated gr. 11. or 79. of the Quadrant, shall carry 860 paces, as we did desire. PROBLEM. How by a Shot made casually, one may find the greatest Range of an Ordnance. projection elevation The Angle of Elevation CAB gr. 30, being given, the right Angled Triangle EAC shall be given in Specie: and because AB is given in paces, A shall be given, which is the fourth part thereof, namely 600 paces. Let us therefore, to find the quantity of AD, work in this manner by Calculations and Sins. Say, if as the Right Sine 86602 of the Angle ACE, gr. 60. that is, of the Compliment of the Elevation, is to the side A, which is 600: so is the whole Sine 100000 to a fourth number 693: and thus the Hypothenuse AC shall be 693 Paces. But because that the right angled Triangle ACD is given in Specie, begin again and say, as the right Sine 50000 of the angle ADC, which is equal to the angle given of the Elevation EAC, is to the right Line AC, which is found to be 693 paces, so is the whole line to a fourth number 1386. And thus the right line sought AD, shall be 1386 paces. But because AD, being the line of Impetus or Sublimity, is equal to half the greatest Range; if we double 1386, we shall make the number of 2772 paces; for so much shall be the length of the desired greatest Range of that Gun, which being elevated to the Random of gr. 30, is found to carry 2400 paces. But with much more brevity, and at one single working, we may perform the same thus. Suppose the whole Sine to be CF, than FAVORINA and FD shall be the Tangents, one, of the angle of elevation, and the other of its Compliment. Say, therefore, as the whole Sine is to CF, which is 600: so is 230940 (which is the sum of both those Tangents) to a fourth number 1386. And thus the right line AD is found, as before, 1386 paces: which being doubled, will give the measure of e the Semirect, or greatest Or the best of the Random. Random, as you well call it. COROLLARIES. 1. BY way of Corollary it may be advertised, that this is the manner of arguing from any Range of a Piece, how much the same should be to shoot upwards by a perpendicular line; which shall be as much as the line AD found out by way of Calculation. 2. The same line AD, directs us from what Altitude it would be requisite to let fall a Cannon Bullet, that it may arrive at the Earth with the same Impetus that the Cannon itself conferreth, always allowing for the impediment which the Crassitude of the Air may occasion, which acknowledge must be sensible for to vary the demonstrated Propositions of Ranges, but much more for to obstruct this effect. PROBLEM. How with the sole Table of Sines we may know the greatest Altitude, to which the Ball hath attained passing through the Air in a Range, the Elevation and length of the said Range being given. projection elevation It is to be noted, that great Guns are not always used so as that the Ball goeth to determine in the same Horizontal plain from which it did departed, as Galileo's and our Tables do suppose. Therefore being to shoot upon the side of a Hills declivity or aclivity, as also being to shoot from the summity of a Rock upon the Horizontal plain that is below, there hath no man as yet reduced the measures of these Ranges to an Art. The Table of them might be calculated, but every one will perceive, that it being to be composed by every grave of the Pieces Elevation or Mounture, and by every grave of the Hills inclination, and by every pace of the Hills Altitude, the Multiplication would be almost infinite. We will therefore only give you the general Rule for calculating those Ranges when they shall occur. projection elevation projection elevation projection elevation projection elevation It is certain, that being to shoot from the top of a Rock, or of a Castle placed in the top of an Hill, or from any whatever high place above the Horizontal Plain of the Field that lieth below, the Ranges will prove much longer than those noted upon the Table of Amplitudes; and this difference shall be so much greater, by how much the situation of the Artillery shall be higher above that Horizontal plain in which the Balls are to hit, and the Ranges to determine. projection elevation By the Table of Amplitudes, we find the quantity of AB, and by the Table of Altitude, we find AC, the height of the Parabola. And for the working of the Computation, it may be performed sundry ways. Let the number of AB be squared, and divide that square by AC, and the Quotus shall be the right side of the Parabola FCB: Then multiply that Quotus by CD, and the square Root of the Product shall give DE. Or we may work thus: Draw the number DC into CA, and the square Root of the product shall be the mean proportional betwixt DC and CA Then say, as CA is to the Root, so is A B to another number. And this fourth number shall again be DE. Or lastly, in this manner: Say, as the number CA, the Altitude of the Parabola in the Table, is to the number CD, the Altitude of the Parabola and Range together, so is AB the Semi-Amplitude of the Parabola in the Table to another fourth number. Then take the number that is mean-proportional betwixt that last number and AB, for that mean-proportional shall give you the said DE. And for as much as DG, equal to AB is known, the whole line GE shall be known. projection elevation It shall suffice to have hinted this little for the Calculating of some varieties that may happen about these Ranges. Other cases may be put, like to these, and particularly those of their conversions; but from the knowledge of these, those may easily be deducted: and the Ingenuity of any Geometrician, applying himself thereto, shall find less difficulty in resolving many of these Problems of himself, than in undergoing the length and obscurity of our explanations. Therefore we will proceed to the making of the Quadrant, the which seemeth really appropriated, nay, made by Nature on purpose for to measure Scientifically and Geometrically the Ranges of Projects. Of the Quadrant. LEt us now come to practice; and by help of an Instrument, let us resolve some of the Propositions above demonstrated. We will make a Military Quadrant, which with invariable certainty showeth (at least to Geometrical Philosophers, if not to practical Gunners) what Mounture or Elevation ought to be given to any Piece, to the end that the length of the Range may prove to be of such a certain measure. We will also resolve, by help hereof, all Problems that can be framed about the shooting of Artillery, which were heretofore promised by Tartaglia, and reduced into Tables by Galileo, with something over and above. Military Industry did find that the use of a Machine so noble, and of so great consequence as the Canon, would be too much confined, and of too little benefit, if it could not be made use of save only at that small distance to which it carrieth a point blank, or in its level Range, without giving it with the Quadrant the advantageous assistance of some elevation. It was therefore enquired how a man might do that with the same Piece, which of itself did not carry more than 200 or 250 Geometrical paces, he might shoot 400 and also 600 paces, and more and more, until he come to the length of the greatest Range that can be made by that Piece. The Invention was thus: They began to help the Piece by Elevation, that is, they directed it not strait upon th' object which it was to hit, but, holding it in the very vertical of th' object, they elevated it above that right line which goeth from the Piece unto the object: and this they did sometimes more, and sometimes less, according as the force of the Shot was to be greater or lesser: An Artifice that from the very beginning of the world hath been known even to artless Boys. We see that when they with a Ball of Snow, or other matter, do aim to hit a mark that is very near, they throw it directly at the mark: but being at another time to aim at one which standeth farther off, or being to throw Stones at each other, they do not throw Horizontally, or directly at their Adversaries, but turning the cast half way into the Air, without having ever had any other consideration, they do all throw at the elevation of the fifth, and also of the sixth point of the Military Square to them unknown: But Gunners, in process of time, have found an Instrument, that doth with facility measure these Elevations. Nicolo Tartaglia of Brescia, a famous Mathematician, did invent a Square with unequal sides joined together with the Quadrant, which hath for more than a hundred years past, been generally used, and is still the only Regulator of Gunners, not only to manage great Guns, and to raise them to those Mountures which they call Randons', but also to levelly them in the Point-blank Ranges; Tartaglia divided that Quadrant into 12 equal parts, beginning the Numeration of them from the lesser [or shorter] sided; he also subdivided each of those into other 12 equal parts, naming those first Points, and these second Minutes of the Quadrant. We will insert the figure of the Quadrant, and show how it measureth the Elevation [Mounture or Randon] of the Piece. elevation measurement By the help of this Quadrant Gunners have with long observations composed such a Praxis, as that they know how many points they are to mount v. gr. a Culverin of 40 pound Ball to hit a mark distant; for example, 700 Geometrical paces, or at any other distance. But the truth is, the observations are so fallible, and the Gunners so few that have made them, and made them exactly, that the use of Artillery, taking from it the Range of Point Blank, must needs have very little of certainty in it. If one would collect some certain Science touching th' ordinary Quadrant, it would be necessary to make the Experiments not only with all sorts of Balls, and with all the varieties of Powder, but in all kind of Pieces, as also in all those that being the same in specie, are of different grandeur; and lastly, at all possible degrees of Elevation. A Multiplication that almost runs up into infinity. And we observe that these Experiments ought to be all made one by one; for it is not true, that by way of proportion one may from three or four Ranges of a Canon made at several elevations, argue to any others, no not of the same Canon, laden with the same Powder and Ball. That this is so, may be demonstrated by help of the Tables made by Signiore Galileo, and by us. For example, That Canon which being elevated at the sixth Point, curryeth its shot 4000 paces, elevated at one Point, aught to curry the sixth part, at two points the third, and at three points the half of that Range. But the thing falls out far otherwise: For being elevated to one point, it curryeth 1032 instead of 666, which is the sixth part of that same greatest Range 4000: at the second point (and note that with this Mounture, Pieces carry always the half of the greatest Range) in our case will curry 2000 in stead of 1333, which is the third part: At the third point it will curry 2824, instead of 2000, which is the half of the greatest Range: at the fourth point it will curry 3464 instead of 2666: At the fifth point it will curry 3860, in stead of 2333, which are 5 sixths of that greatest Range: See therefore how that increasing equally the Mountures of the Piece, that is shooting first at one point only, then at two, three, four, etc. unto the sixth, the increases of the lengths of the Ranges do not increase equally, that is with the same proportion wherewith the Or Mountures. Randons' increase. But the first point currying 1032, the second increaseth above it 968, the third increaseth 824, the fourth 640, the fifth 396, the sixth 140. Therefore to derive some rule from the Experiments, it were necessary to make them exactly, at all the Grades of Randons', in all sorts of Pieces, with all varieties of Powders, and different matters of Balls; and happily one might say, it were necessary also that every Gunner made them by himself. Things almost impossible to reduce unto Rules, from which any certainty might be gathered, if the Theoric and Geometry had not given us a manifest Science thereof, by means of that one sole Proposition of Galileo, in which first of all men he hath advertised and taught us, That Pro ects do all move in a Parabolical Line. Upon this supposition we will ground the Instrument promised: and though by the impediment of the medium the Parabola's become too deformed, or by many other accidents the Ranges prove very inconstant, yet it sufficeth us to have given indubitable satisfaction to the School of Mathematicians, if not to that of Gunners. Before we set down the making of our square, which consisteth only in describing one single Semicircle, we will divide the ordinary Quadrant into unequal points, so as they may not measure the Randons' of the Piece, but the lengths of the Ranges, which is that that serves to our purpose. Thus we shall be assured, that the Gun, if it shall be elevated to one point of the said Quadrant, shall carry to such a distance, whatever it be: and elevated to two points, shall precisely double that Range: and if to three, it shall carry three of those spaces; if to four and a half, it shall carry four and a half; if to five and a quarter, it shall carry five and a quarter; and thus until you come to the sixth point, shall the points of the Quadrant in the Instrument, and the spaces of the Ranges in the Field, always increase in the same manner, and with the same proportion, and from the sixth to the twelfth point, they shall go in the same manner decreasing. The construction and demonstration is Geometrically taken from the proposition which we have made the First of this our Book of Projects, which by the Amplitude given, teacheth us to find the Elevation. And it serveth in common for whatsoever sort of Artillery and Mortar Pieces, and for any sort of Ball or Powder. elevation measurement Now it is manifest by our I. Proposition, that if the line of the Of Mounture. direction, or of the elevation of the Piece shall be AO, or AP, the Amplitude or length of the Range shall be as the Quadruple of the SO; and if the direction shall be AM, or AN, the Range shall be as the Quadruple of RM: and if the elevation were according to the line AFD, the Range shall be as the Quadruple of QF: but the lines SO, RM, and QF, by our construction do equally exceed: And, therefore, likewise their Quadruples, or the Ranges aforesaid, shall equally exceed one the other. The use of the aforementioned Division made in the ordinary Quadrant. LEt there be propounded any Piece of Artillery, or Mortar-Piece; and with it let there be one single Experiment made, that is, let it be elevated to any point, as for example to the fifth. Let it off, and measure the length of the Range, and let it be found, verbi gratia, to be 2000 parts; this done we may know how far the same Piece will carry, being charged in the same manner, and elevated to any other Point or Minute: which shall be easy by the Rule of three, the points in this Instrument, as well as the length of the Ranges, being proportional. The Praxis is this; I desire to know how far the sixth point carrieth, I thus say, If five points give 2000 paces, how much shall six points give? and I find 2400 paces. I say then that the shot of that Piece at the sixth point, that is at the greatest Range, will curry 2400 of those parts, at which of the fifth point it curried 2000 And take notice by the way, that instead of performing this operation with the points 7, 8, 9, 10, 11, and 12, It may be done with their Compliments, which are 5, 4, 3, 2, 1, and 0. But if it were required (which importeth much more) that we should elevate the aforesaid Piece in such sort, that the length of the Range aught to be; for example, 1300 paces, we are to work thus. If 2000 paces were made by 5 points, or to say better, by 60 Minutes of the Quadrant, by how many points shall 1300 paces be made? the working will be 2000 60. 1300. 39, and we shall find that for to make the Range of 1300 paces, it would be necessary to give the Piece the Mounture of 39 Minutes of the Quadrant, or of three points and a quarter. The manner how to Compose our Square. BUt if we would frame an Instrument, which shall not only measure the length of the Ranges made at several Randons', but also the Altitude of the Parabola, the duration or time of the flight [or Range] the sublimity, and the other things demonstrated in the aforesaid Book of Projects, all this shall be performed with the sole and simple Semicircle of I. Proposition. But let us proceed to the making of it. semi-circle and square semi-circle and horizon That this is so, shall thus be demonstrated (having reference to the I. Proposition of Projects, and its Corollaries.) Let the line of the direction ABI be prolonged indefinitely, as also the perpendicular FBL; then by imagination take BL of such a length, that it may be really equal to half the greatest Range of our present Piece. And about the Diameter BL, let there be imaginarily drawn the great Semicircle BILL; cutting the Circumference BY in any point I; and draw the Horizontal line IN. It is manifest, by the Propos. I. of Projects, that the line MI shall be the real fourth part of the length of the Range; as also, that DM shall be the (not imiginary, but) real Altitude of the said Range; and so the other measures in the Semicircle BILL, shall be all true and real. Now observe, that the Triangle HBF is like to the Triangle BIM, as being rightangled, and having two angles at the Point B. Therefore the same Proposition shall be between all the small and imaginary measures of the square AC, as is between all the true measures in the imaginary and great Semicircle BILL; that is, the lines, AB, BF, FH and HB, shall be to one another in the same proportion respectively as LB, BIIM, and M B. Therefore, as to arguing in the proportions, we may without any error, as well make use of those feigned proportions upon the square, as of the true ones, imagined in the Amplitude of the Air. It remains now that we show how this Doctrine, which hath hitherto been a mere Speculation, may now be reduced to Manual practice, and that with facility. Every one seethe that for our obtaining knowledge of the quantity of the lines AB, BF, FH, and HB, and their proportions in the precedent Figure, it would be necessary that all the aforesaid lines were divided into most Minute parts with some common measure. To this purpose, therefore, we will divide the Diameter AB, and Semi-Diameter ED, into equal and very small parts, as appeareth in the following Figure; (upon which let us describe the imaginary square) and then let us give to each division of the circumference, its guide's parallel to those Diameters, that so in them the number and quantity of the lines which shall be Indices of the length and Altitudes of the Ranges, may be read or found: And in the point of the angle of Semicircle B, place the Thread and Plummet. As to the number of parts into which the Diameter AB is to be divided, it shall be left to the choice of every one; but yet it will be convenient to make choice of the number 2000, for that it will facilitate the Arithmetical operation. It is to be noted, that if any one will make a square, as hath been said, on purpose for one kind of Artillery only, he shall without the least trouble of Calculation, have the measures of all its Ranges. The Division of this square is to be made a posteriori, in this manner. Make an Experiment of the greatest Range of that same Piece to which you would have the square to be adapted, and let it be found v. gr. to be 3000. Then divide the Diameter of the square into 1500 parts, and the perpendicular Semi-diameter into 750 equal parts; that is, imagine that the Diameter AB 1500, is the half of the greatest Range 3000; as also, that the perpendicular Semi-diameter ED 750, is the fourth part of that greatest Range. And thus, every of the other Elevations being afterwards given, as soon as we shall apply this Square to the Muzzle of the Piece, we shall immediately see how many paces is the length, and how many the Altitude of the Range, etc. And this square made v. gr. for a Canon of 60 pound Ball, would be also good for every other Canon of 60 pound Ball, that should be the same in length, and other proportions, with that. It's true indeed, that if we would make the square universal, to serve indifferently for all Species and Magnitudes of Artillery, we must then do thus. Divide the Diameter AB in the precedent figure in 2000 equal parts: also let the Semi-Diameter ED be divided into 1000 equal parts, (we by reason of the smallness of the figure have divided it only into 100, taking the parts by ten and ten.) This done, let there be drawn by the Divisions of the Circumference, cut into equal degrees, as is usual, the guides parallel unto the Diameters, that so one may upon those Diameters read or find the quantity of the right lines, as they shall happen to be. shooting range If you desire the Altitudes, and not the lengths of Ranges, then make the same working as before, but not with the lines IO and ML, which give the lengths, but with HO and HL, which give the Altitudes. And if we would have the sublimities, it would be necessary to work with GO and GL. But, which more importeth, if any one after the previous Experiment hath been made, shall desire that the same Piece may make an assigned Range, in length, v. gr. 2200 paces, we are to find what elevation ought to be given to the Piece. Work thus: If the 1250 paces of the previous Experiment give IO numbered, what shall the 2200 paces give? and you shall find a number, which suppose for example, to be ascribed on the square unto the line ML. the Peice Therefore is to be raised to such a Random, that the thread may pass thorough the point M; and then the Range shall be 2200 paces. shooting range shooting range A Table which showeth how many Degrees and Minutes of the Ordinary Quadrant inserted Page 20. each Point of one Square, the Points of which are unequal, doth contain. Points unequal of the Square Degrees of the ordinary Quadrant half 02 23 I 04 48 half 07 15 TWO 09 44 half 12 19 III 15 00 half 17 50 IV 20 54 half 24 18 V 28 13 half 33 14 VI 45 00 half 56 46 VII 61 47 half 65 42 VIII 69 26 half 72 10 IX 75 00 half 77 41 X 80 16 half 82 45 XI 85 12 half 87 37 XII 90 00 For Example, It is demanded where the Division of the one seventh unequal point doth fall. Look upon the present Table, right against the number VII, and you find that it falleth upon gr. 61. and min. 47. of the ordinary Quadrant. BUt since we are fallen upon the consideration of the Motion and Impetus of Projects, we cannot balk th' occasion of adding something concerning the variety of their Forces in battering upon resisting Superficies, sometimes with greater, and sometimes with lesser Angles of Inclination. Galileo considereth th' Impetus of these Projects in every Point of their Parabola, and measureth how much it is in its self, that is, in respect of that Plane in which it doth perpendicularly hit. We presupposing that an Impetus, when it is upon the act of striking, is, as to itself, always the same, will consider and measure how much it is in respect of the resisting Plane, varied only by the diversity of th' Angles of Incidence. There is no Gunner so unskilful, but he knoweth that Cannon Bullets in hitting a Wall, have always lesser and lesser force (if all things else be alike) by how much the Angle of Incidence is more and more acute. So that if the said Cannon with sixty pounds of Iron, and forty of Powder, not only pierceth, but beateth down a Courtin, with its perpendicular Range, it shall scarce hurt it (though it have the same Charge, and the same distance) with the Projection of the Range, which they call Di ●●riscio. Grazing. The Problem, for any thing that I know, is unhandled. Therefore if we shall produce something that is less subsistent, and not purely Geometrical, either admit it till some others shall better handle the Doctrine, or wholly reject it, it matters not which. SUPPOSITIONS. ranges of guns 2. Let us suppose secondly, Galil. 2. de Motu aequabili. that the Forces or Impetus' of Projects are as the Spaces which they pass or curry in the same Time; that is, If the Spaces A, B and C shall be passed by the Movable in the same Time; the Impetus' or Forces in striking, shall be as the Spaces A, B and C respectively. 3. But if the same Space shall be passed by the Movable in divers Times, Galil. 3. de Motu aequabili. the Impetus' or Forces of the Movable in battering shall have the Proportion reciprocal of their Times. That is, if the same Space D shall be past one while in the Time E, and another while in the Time F; the Force of the first shall be as F, and of the second as E. ranges of guns ranges of guns Now observe, that of these two sorts of Impetus, one only is to the purpose, for increasing the Forces to make a breach in the Wall, and to drive the Ball into it; to wit, the Impetus of the perpendicular Lation AC. Th' other, although it were infinite, will never increase the force of the Project against the Resistance of the Wall, unless the perpendicular Lation be withal accelerated. Nay, if the Horizontal Motion were simple and alone, without any mixture with the perpendicular Motion, what other would the Ball do but run equi-distant unto the Wall, without ever touching it, so far would it be from breaking it, although it were a very thin Glass? When therefore, the Direction of any Projection being given, we shall know how much of this perpendicular Impetus entereth into the Composition of the Motion, we shall also know the Activity or Moment of the Project towards the Resistance of the opposite Wall. composition of motion Let us suppose, now, that the force of th' Evidence AB be as AC. To know the force of any other Incidence DB, let DB be taken equal to BASILIUS, and having drawn DE perpendicular unto the Plane, the force of this Incidence shall be as that same Line DE. For if AB and DB are equal, and are the Ranges of the same Piece, they shall be passed in the same Time. By Supposit. 2. Therefore AC and DE, are also past in the same Time: Therefore th' Impetus', as to the Wall, are as AC to AD. We will therefore infer, that, PROPOSITION. The Activities or Moment's of Ranges differently inclined, are as the Right Sins of th' Angles of Incidencies. COROLLARIES. 1. IT is deduced from hence as a Corollary, that the Perpendicular Incidence AB, hath greater Force than all others, the force of it being as the Whole Sine. And the parallel Projection shall have no force, its force being as the No-Sine. The Incidence DB at th' Angle of gr. 30. hath half of the total force, its Sine being the half of the Semi-diameter. The others, likewise, according as they shall have greater or lesser Right Sine, shall have greater or lesser force. 2. The Forces of Projections have reciprocally the same proportion that the Sides of the Triangle have, which shall be form upon the Plane by the Lines of the Incidencies. projection 3. Projects shall then have the same force in battering, when the Impetus' shall be as the Secants of the Compliment of the Incidencies. projection For if the Impetus' along AB and AC shall be as the Spaces AB and AC, the Movables shall, in the same Time, pass the two Lines AB and AC, that is, By Supposit. 2. the same perpendicular Approximation AB. Therefore they shall have the same force against the Wall. projection Yet let all this be spoken abstracting from a certain Effect of Pliancy or Refraction that Projects produce in passing with Inclination from the Rare Medium to the Dense, the Line incurvating contrary to that of the Refraction of Light, and visible Species. FINIS. TO THE INGENIOUS Student. IT being well known among the Learned, that the late famous Mersennus of France, a most diligent Collector and Publisher of the choicest Mathematical inventions of that time, hath among his Physico-mathematical Reflections, and Mechanics, divers material Experiments and Theories relating to the Art of Gunnery, it was thought fit for the Readers benefit to cause the same to be translated, and submitted to his censure. Moreover that Author giving all his distances in feet, or paces of three feet, or fathoms of six foot; It was thought likewise expedient to put the Reader into a capacity of reducing the same to our English measure, to which purpose there being an accurate experiment, made some time since by the most learned and Reverend Doctor John Wallis Savilian Professor of Geometry at Oxford, take an account thereof, as the Doctor communicated the same to a friend of his here, namely, that he hath formerly compared the French and English foot very exactly, both measures being as he was assured very exact to the Standards of each Nation, and he found the French foot to contain of ours 12⅘ Inches (not missing so much as 1/100 part of half an Inch.) OF THE Swiftness OF SOUND. The swiftness of Sound is greater than the swiftness of Bullets shot off, and finishes 230 fathoms in the space of one second minute. WHosoever would try the swiftness of Sounds by night, and by day, either in valleys, woods, or mountains, either with or against the wind, or when it is rainy or fair weather, shall find in all respects as I have tried it, that there will be always the same swiftness of Sound. But after that you have searched out a second by 230 fathoms, he that shoots off a lesser Gun, may again retire 230 fathoms, so that he may be gone back from you 460 fathoms, the same or the like Sound in passing over that way will spend two seconds; which when it shall be five times multiplied by us, that we should hear the Sound 1150 fathoms, the flash by night breaking forth from the mouth of the Gun is always seen at that distance before the Sound is heard five seconds of time. And seeing we make a French league to be 2500 fathoms, and the circuit of the Earth 7200 of such leagues, you may easily conclude in what time the sound does pass over one whole or several leagues, for the swiftness of the sound is not diminished by its debility, whenas the last part of the Sound that may be heard does emulate the swiftness of the first. The Sound of the Gun therefore will pass over a league in the space of 11 seconds, seeing a league contains 11 times 230 fathoms (the space passed over in a second minute) less only by 30 fathoms, which are here scarce worth consideration, because that they are passed over by the Sound in the seventh part of a second. From which many things may be gathered; first, that a Soldier attentive my decline or shun the shot of a Gun at one hundred fathoms, is he foresaw the flash of it; which I thus demonstrate: It is evident from observation, that a Bullet in flying 100 fathoms does at the least spend a second of time, and the Sound of it in passing of them does at the most spend but half a second. Therefore the Soldier from the fire seen (if Vision can be in an instant) hath a whole second wherein he my easily go three or four paces before that the bullet can fly so far; also there remains to him half a second from that point of time in which he hears the Sound, until the coming of the Bullet: although I would not advise any one to try that, unless he first fortify himself with a shield, helmet, and all other kind of Armour, that he may be out of all danger. But any one may try it behind a wall, to which the Sound will come before the Bullet. Secondly, from the Sound and fire observed, may be known how much the Guns are distant that are shot off against the besieged, or besiegers, even as to the ingenious Gunners there will not be wanting matter to promote their Art. Thirdly, by hearing the Sound of Thunder, and seeing the lightning go before may be known how far it is off, so that if the Thunder be not changed from the place where the lightning was seen; for how many seconds (whether measured by the pulse, which exactly continues a second, or by a Pendulum or any other Watch) there are between the Lightning and the Sound, so many 230 fathoms are to be reckoned; so that if you number five seconds it may be distant from you half a league; if ten seconds a whole league, whether the distance shall be upright, or sideways and obliqne, for it matters nothing. Fourthly, If by the turn and wind or Circles in the air a sound in the same manner may be considered, and caused, as we see circles extended in the water struck with the finger or a little stone, as all almost believe, and if from the swiftness of bodies in like manner moved we my guess at their crassitude, thickness and weight, we may say that water is 1380 times thicker and heavier than air; for as much as the Semidiameter of Circles of the Water in any manner struck, which is made in a second of time, scarce exceeds a foot, in which time the semidiamiter of Circles in the air, made also by any percussion is 1380 foot, that is 230 fathoms; which proportion of gravities come very near to observations by him mentioned. There is yet one thing that may cause some doubt, which is, that the Sound of greater Guns moves more slowly than of lesser, whereas our Geometer in the siege at Theodonis observed that their Sound was heard, from the fire seen, after thirteen or fourteen seconds of time, when yet he was scarce half a league distant from those Guns; And the Sound according to that which hath been before said, may pass over a whole league and more in that time: Wherefore the Sound of those Guns doth seem to be different from that of lesser Guns. The Author having by this discourse argued that the Sound of Guns is heard at the distance of above 16 miles a minute (which is almost as swift as the Copernicans suppose the Earth to move in its diurnal revolution about its Axis) it was thought fit to subjoin hereto the Author's latter thoughts of the same Argument, published three years after. OF THE SWIFTNESS OF SOUND, And force of Bullets shot out of Guns. WHen I have oftentimes considered that the Sound passes over 230 fathoms in the time of a 2d or sixtieth part of a minute; and that there seem to arise someed doubt, whether there should be that Swiftness of the Sound of greater Guns, as there is of lesser, with which I tried; at length it was observed that in the space of eleven seconds, the Sound of the greater Guns of the King's Armoury, have passed from the same Armoury, after the flash was seen, as far as our house, or the Vicennian Convent, whilst for obtaining the surrender of Pouploon the Guns were shot off by night. But when with a fathom I found that it was 3524 fathoms from Port Saint Anthony to the gate of the aforesaid Convent, where the ear was, and to the wall of the Vicennian Castle first meeting it, near 2500 fathoms, 'tis certain first that it is a just league of 2500 fathoms from the Garden walk of the Armoury, from whence the Guns are wont to be shot off, to that Castle: for if any thing in the passage must be diminished that distance will well enough equal it, whereby the corner of the Garden is more distant, or the walk by Sequana nearer from the Castle, than Port Saint Anthony. It is evident therefore that the Sound runs over more than 230 Fathoms in each second, to wit, 320 in every second, which make 1920 foot; which since any one can prove by his own experiments, I need not say more thereof. But some may imagine that hence perhaps must be concluded that greater Sounds pass more swiftly, which disagrees with divers observations. But when sometimes these experiments shall be repeated, that I may number the seconds, I shall advertise, for as much as I conjecture that there is no swiftness of sound greater than that, which I have proved of 230 fathoms for a second; for in these small matters I do not approve that common saying, He that acts by another, seems to act by himself; who want not opportunites may observe for their own satisfaction. But now we shall add some thing concerning the swiftness of Bullets shot out of Guns. When therefore at the marquis of Doraisons four leagues from the Sextian waters, I commanded a Brass Gun nine foot long, whose name was the Marchioness, commonly called lafoy Marquis, (whose Bullet was two pounds and an ounce, but quantity of Powder, such as is wont to be in the use of lesser Guns, the weight of one pound) to be leveled horizontally, with a plum line I found that the Bullet shot off Horizonitally, in the time of five seconds had passed over 630 fathoms or 3780 foot, and had reached the horizon, or fell to the ground, as was evident by the huge quantity of dust raised by the blow. Moreover that point of Earth which was first struck by the Bullet was depressed under the horizon of the Gun 27 fathoms, for otherwise the Range should not have been so great before its fall to the earth, which meets so much the more slowly by how much it is the more depressed under the Horizon of the Gun shot off, and I presume I have attributed a lesser swiftness to the Guns than is just, unless yet the Bullets of the greater Guns shot off with very fine powder, which we used, may exceed the swiftness of Bullets shot from Harquebusses; of which thing I do not yet pass judgement, till experiment, shall bring some further evidence: but I shall propound some things newly observed. Now therefore of the Bullet which I made trial of, I affirm that the swiftness was so great that, at least, in each second minute it could pass over 126 fathom: I said, at least, because the observers know that the force on the Bullet doth go before the excussion or flash of the powder, and the perceiving thereof; so that half a second may well be attributed to this time. Moreover in the first second the Bullet passes more swiftly, in which time I doubt not but it passes over 150 fathoms; Lastly, if by reason of that tarrying which happens between the smiting of the Earth until the dust is seen to rise, we should augment that swiftness by so many fathoms as it could pass over in half a minute, to wit 70, and that the swiftness be supposed almost equal for the time of five seconds, and in each second of that time that it passes over 140 fathoms, that is, if the point of the Earth first struck were 700 fathoms distant from the Gun, it would reach it in the time of five seconds. Then the swiftness of the Bullet may be determined from what hath been said, to be 130 fathoms, at least, in the time of a second: which also agrees with the experiments of Bullets shot from lesser Guns: to wit, they pass an hundred fathoms in the same time as the Sound of the Gun hath the same passage. For if, behind a wall that is to be struck by the Bullet, the ear be attentive, in the same instant the sound and the percussion of the Bullet is heard, as if the very Bullet had caused that Sound; which doubtless you shall find to be true as I did if you try: although it will be worth the labour to prove it, not only with that most refined powder, which they are wont to use who shoot at a mark for a wager, but also with the courser sort of Powder for great Guns, that it may be observed whether it causes any sensible difference of the swiftness. Whatsoever powder you use, the least swiftness of the Bullet, may be defined in the first second an hundred, the greatest 150 fathoms, if you put but so much Powder into the Gun as is necessary for a good shot; for if you put in but a few grains which can scarce shoot the Bullet off, another thing is to be said. I add that a Bullet shot vertically or Perpendicularly upright from the aforesaid Gun in its ascent and descent, spends 36 seconds: which if it spend so much time in its Rise as in its fall, and that a heavy body descending in the time of 18 seconds always keeps the same proportion in hastening its descent which it keeps in the four first seconds, the Vertical ascent shall be 648 fathoms, forasmuch as a Bullet of six pound Weight of that Gun, which the Illustrious Knight Hugenius caused to be shot off at the Hague upon my request, in its ascent in the time of 16 seconds passed over 512 fathoms, which falling, pierced three foot into the Earth. But two things there are which may lessen the space of the ascent; first, that perhaps the bullet may not spend so much time in its ascent as in its descent, because Arrows in ascending pass over the same way in three seconds of time that in descending they do in five seconds: furthermore should we imagine to shoot with the mouth of the Gun towards the Earth, the Bullet would pierce deeper into the Earth, than by its mere fall, as it happens in Arrows: whence there arises in me no small suspicion that the eyes in the ascent of the Bullet are deceived, to wit that the Bullet was even falling when it was yet esteemed to ascend: which also may be imagined of Arrows, which perhaps had begun to descend when they should seem to be inverted, that the point which went before ascending should likewise descending antecede: which you may conclude of from the small blow of the Bullet descending, unless you may contend that the stroke made by the Bullet shot upright from the mouth of the Gun and falling upon the Earth very near, is greater indeed than the stroke of the same Bullet shot from the greatest height, and that not by reason of the greater swiftness, but by reason of the air so unawares intercepted and oppressed, that it may much better turn over or bore through the Earth, than when it is prepared for the last motion by the Bullet falling slowly. Which indeed can be known by Rocks and Mountains 600 fathoms high, to wit, one standing on the top shall observe what time the Bullet that is shot off at the foot of the Mountain, shall spend in coming to the top or any other place of the Mountain, and a sign being given shall warn the leveller of the Gun of the time, or from it shall learn the time of the ascent and descent: from which cutting off the time of the ascent shall conclude how much shorter it shall be in the time of the descent; which also may be observed by an iron Bullet red-hot shot off in the night, whilst it can be seen light to the greatest height: however it is I think fit to add the observation of that Holland Gun, which being levelly or horizontally shot off, carried a Bullet of six pounds 398 paces, before it first touched the Earth, taking a pace for three foot; after this Space it made eight leaps, and at length it ceased at 1750 paces: we have here expressed the distance between each leap, as likewise the distance of each grazing from the Gun. Paces. The passage in the air was — 398 392 The first leap — 790 275 The second leap — 1065 179 The third leap — 1244 150 The fourth leap — 1394 81 The fifth leap — 1475 73 The sixth leap — 1548 73 The sixth leap — 1548 78 The seventh leap — 1626. 124 The eighth leap — 1750 Moreover a middle range of 45 degrees was 3225 paces, whose half if we take it for an upright or vertical shot, will be 3225 foot, or 537½ fathoms, for which before we counted only 512. Hence it comes to pass that we may judge that a vertical shot in the ascent doth not proceed by the same or equal and proportionable degrees of swiftness, by which it falls in its descent, for at least there are wanting 25 fathoms, by which 512 differ from 537, although that way of him that leveled the Gun, in counting by common paces, restrained to no rule, cannot be so certain, but that the other may differ from it, so that it cannot with undoubted certainty be reduced to our defined fathoms. Whoever therefore would certainly try, let him have a chain or wheel for counting of fathoms or any other determinate measures, as is done in the passage of the league of 2500 fathoms from the Bastilian Tower erected right over against Port Saint Anthony as for as the walls of the Vicennian Castle that first meet. There remains one thing that may diminish the upright height, to wit, that the Bullet spends more seconds in the descent than it ought, after it comes to the point of equality, after which it doth not any more augment its own swiftness: so that not only 16 seconds are to be reckoned for the descent of the Holland Bullet, but perhaps 20, and 12 are to be counted for the ascent. For although in moderate heights of 40 or 50 fathoms, the access to the point of equality, in leaden Bullets may not be sufficiently observed, it does not thence follow that it comes not to such a point, in greater heights of an hundred or more fathoms; yea experience proveth the Contrary. Let there be taken a Corken Bullet which is at least 70 times lighter than a leaden one, yet both them almost in the same time make a three foot space, although perhaps the Cork attains its point of equality within 50 foot. But whether a leaden Bullet 70 times heavier, can pass over a seventy fold space, that is, 3500 foot, before it comes to its point of equality, which little differs from the height to which Bullets arrive that are vertically shot out of Guns, although I cannot yet conclude, yet it seems probable enough to me. Moreover the force will never be augmented after the arrival at that point, if the greater force shall be argued from only the greater swiftness. But note, it hath been observed by a Noble man who related it to me, that a field Gun 18 foot long, and cut shorter foot by foot, did always curry its shot the further till it came to be eleven foot long, and then it began not to give so great a Range. To which may be added from the experience of some in small Guns, that if it be over charged with Powder, part of the Powder will blow out of the Gun without firing. Morever if the Bullet be not quite rammed home it will pierce the further, and the Gun recoil the more. Also that where the Gun is found most to fur with many shootings off with Powder, there it ought to be cut off, the remainder being the proper length requisite. It hath been related that a ship becalmed and tormented with the Cushee Piece of a Galley, that lay in a manner out of shot, was at the last reached by the industry of a Mariner, who wrapping up a much lesser sized Bullet than the Boar of the Gun made use of required, in a good Wad did shoot as far as the Galley, thereby retaliating the Injury received. Of the Depression of shot below the Mark. I Have often took care that a Gun should be shot off commonly called an Harquebuz, at the space of an hundred fathoms from the mark, that is, six hundred foot, which make three hundred common paces, and found that the Bullet was depressed under the mark-line eight or ten foot, which would scarce have made a greater space, if it had fallen perpendicularly down at the same moment of time it was left off. Again at the the Marquis of Doraisons, a Bullet shot off, in the space of five seconds of time fell 27 fathoms beneath its horizontal line or mark; and whereas perchance the rising of the dust, and the perceiving of it might make us lose a second of time, and that we retain only four seconds, then in each second the Bullet should be carried 157 ½ fathoms (surely not more) yet it ought to have descended 32 fathoms, if it descends so much horizontally shot off as it would naturally fall were it not shot off, and therefore it either loses some thing of its descent by reason of its being shot off, or in running 360 fathoms, it spends not so much as four whole seconds of time, but rather about 3 ¾. We add that something is by this means abated from the swiftness of the fall for the space of 27 fathoms which the Bullet in shooting off did descend, or fall below the mark: so that all things considered, I would not as yet start from that opinion, which holds that two heavy bodies, to wit, two Bullets, whereof one may fall perpendicularly from its place above the Horizon, Of this there is a controversy between Borellius who published a Treatise de vi percussionis, the which was writ against by Honorato Fabri in his Dialogues of Motion. and the other be forced horizontally, shall both in the same moment of time arrive at the ground or Horizon: for example, if the pit of the aforesaid Marquis be 27 fathoms deep, as indeed it is, if I rightly remember, or also a little deeper, 32. a Bullet shot into the fields enclosed between the Sextian waters, will hit the horizon, the same moment, that the like Bullet falling, shall the superior superfice of the aforesaid point of the water. There is another thing that I may suspect, whether or no the surveyour hath accurately enough measured the horizontal depression; however it be, you see with what difficulties experiments are hedged in, and how much natural knowledge is indebted to them, who are enriching the same with exact Observations. But note that the air that meets the bullet that is shot off does so much hinder or diminish its motion, as much as a wind of the same swiftness with the Ball, blowing continually against the same in a vacuum. For is it not the same impediment, or destruction of the same force, if the bullet beats the air or is beaten of it? But when I said it was known by experience, that water does so much the more descend, by how much the slower it moves horizontally, and the same may seem to be concluded of other projected heavy bodies; I advertise that observations are not yet made so exact as that any thing of this nature should be too positively asserted. Of the Impediment of the Air. IN regard that Bullets shot from Guns do about the end of their motion utter a more vehement noise or hissing than about the middle or onwards; there is no doubt to be made but that they move more slowly, and the force decreasing as the swiftness, Mersennus concludes that the Curved range line described by a Bullets motion cannot exactly describe a Parabola, but however the Theory is tolerable, admiting the first violence to move in the touch line of a Parobola, and it is likely the greater Mountures cause the greatest difference, because, there is so much the more Air beaten and removed by the passage of the shot. But yet it is most hard to find out, how much the Air hinders; for although it seems to hinder so much, as the wind agitating the air with the same swiftness, strikes upon the Bullet shot off; yet we are Ignorant of the force of that wind compared with the force of the Bullet shot off; unless we may appeal to our other experiments in which is shown that the air is at least a thousand times lighter than water: and seeing that a leaden Bullet is eleven times heavier than water of the same bulk, a leaden Bullet will exceed the weight of the air 11000 times; and therefore the air agitated by the same swiftness of the Bullet, meeting with the bullet, seems to take away the 1100 part of the swiftness from the Bullet shot off. Which impediment truly is so light, that in the description of the Parabole it scarce aught to be considered. Those things are very excellent which the famous Torricellius hath set forth in his approved Treatise, to which Mersennus refers his Reader. Experiments OF SHOOTING. Wherein is explained various observations concerning Guns; And what might happen to bullets shot off in a vacuity, divers ways compared with those which are obstructed in the Air. WHenas I made trial about the shooting of Bullets in Guns only of an indifferent bigness (which we commonly call Harquebusses) which in the ascent and descent together spend 22, 23 or 24 Seconds of time, Peter Petil a man most skilful and accurate in observations whilst he lived at Francopolis, found (at my request) the Range of a shot, out of a great gun, at the elevation of 22 degrees, whose iron Bullet weighed 33 pounds and ⅓, to be 1900 fathoms, which the Bullet flew or passed over in the space of 20, 21 or 22 seconds; the Gun being placed at 8 fathoms in the Castle above ground or Horizon; from which place a Bullet of 12 pounds which so many pounds of gunpowder shot off at the elevation of 16 degrees above the horizon, spent in the air 16 seconds. Besides, a Culverin of 12 foot long and horizontally leveled being 6 fathom high above the Horizon of the ocean and shot off, the Bullet, whose diameter was almost five Inches, continued 8 seconds of time in the air; when yet another Bullet whose diameter was 6 Inches and ½, also horizontally shot off out of an other Gun 12 ●●ot and ⅓ long, spent only 6 seconds in the air; another Gun shot off at the Elevation of 1● degrees, its Bullet spent 24 seconds in the Air. An Iron Culverin of 10 foot long, whose Bullet, had a diameter of almost four inches, horizontally leveled, and standing 9 fathoms above the surface or brim of the Sea, spent only three seconds, in its horizontal Range, after which grazing five times above the Ocean, spent four other seconds. Three days also before the taking of Theoud, Robervallus our Geometer observed, the Bullets of Guns shot off from the City against our Soldiers, for the most part to spend only 14 seconds of time in the air, after which there was a hissing increased more and more until the force and motion of the Bullet was almost quite extinguished, and that after the shot had flew almost half a league. Which being supposed it may be Theorically concluded, how great the shoots aught to be at whatsoever elevation above the horizon, if they be in such Proportion one to another, as shots in a Vacuity, no Medium hindering; that is, for example, if the range of 45 degrees be double the height of the Perpendicular or vertical shot in a space not hindering, so is the range of 45 in the air to the vertical in the air, and so of the rest; which observations only will teach; which yet are most difficult in the greater sort of Guns or Bows, especially the perpendicular, whose height we can scarce certainly know, unless some ●ock might be found high enough, to whose top, or some certain place, the Bullet or Arrow may come, the height of which top or place we may afterwards measure. No Towers surely are high enough; and by the time of the descent or fall of the Bullet, to conclude a place may be found to which bullets, darts, or other things that are cast upright or vertically ascending, do come, doth therefore fail, because they do not observe the same rule of swiftness in descending; as is evident from darts, to which seeing it happens in their ascent or rise of 50 fathoms to be slackened in their descent or fall, something like this may be also thought to happen to Bullets, to wit, when they descend from the height of a thousand fathoms. But you may avoid these difficulties: for if from that rock in the Dolphinate, whose height 'tis said is 600 fathoms or more, a stone or bullet of Iron or any other matter be let fall, Experiments of this kind the Reader will doubtless find, as also others about Pendulums in the Opuscula Posthuma of I. Bap. Batiani. the time of its falling being noted, as for example, if in the space of 18 seconds it fall from the height of 648 fathoms (as truly it should fall, if the spaces be in Duplicate ratio, or as the square of the times in the whole descent) than we have rightly judged before of the vertical altitude or perpendicular shot (which the Bullet of an indifferent Gun reaches) that is the height of 288 fathoms; which yet I cannot credit; otherwise the middle shot or range of 45 degrees of that Gun at least would be double to that perpendicular or vertical one, that is to say, it would be 576 fathoms, whenas I found it not 400 fathoms. Besides these observations I shall add those which the industrious Galeus an Engineer to divers Dukes in whose presence he made them, writ with his own hand and gave me, which that you may more easily understand, let the greater Gun K, which we commonly call a Cannon, be parallel to the Horizon, and let the eye be taking aim by the points I and O, the horizontal shot being supposed O P, or in the figure beneath, S X, or, T V, he says that the remainder of the rang which bends till it touches the horizon in the point λ, is almost equal to the horizontal shot, that is, that there is almost as much space made by the bullet from that point, from which it gins to bend towards the horizon, until it touch it, as it had made before the bending of it. cannon range But now let us suppose that horizontal shot OPEN, or TV, removed to the lower figure in which let AB be the horizontal plain, and let the the v horizontal shot be AI, Galeus contends that the middle range of 45 degrees, which is the longest of all, is eleven fold the length of the horizontal shot OPEN, or AI: And in those Guns which are half the weight of the foregoing greater Guns, to be in respect of AI, as 10 and ½ is to 1, and in lesser Guns as 10 to 1 that is our figure, as A B in respect of A I; in which the middle range is AGEB; for that is the middle range which passes through the middle of the quadrant φ 5, which they call the sixth point, because it is the middle part of the half circumference A, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, divided into 12 equal parts; which joined to the quadrant φ 5, may be useful for levelling the gun at any elevation above the horizon, if it shall be divided not only into 12 parts, but also into an 180 degrees. And hence he concludes that the dead or exact Horizontal Shot or range, that is in the figure, R λ I to be in Proportion to the middle range as 1 to 6; or in lesser Guns, as one to five; which dead Horizontal ranges is to the range of an Elevation of one degree, as five to six, or more exactly as 55 to 67, or as 14 to 17. But when the recoiling of the greater Gun is hindered, the dead Horizontal range will be greater by a seventh, eighth, ninth, or tenth part, than that range which is made with recoiling; in lesser Guns it will be a twelfth or a fifteenth part less. Moreover he asserts that the middle range A 6 E does proceed righton without arching by the line A G, which may be almost equal to A 5, that is, almost 5 fold or 4 ½ the Horizontal shot: than not only that it does ascend to the point D, so that the greatest height of the middle range may be fourfold the Horizontal, and be over the line AC sixfold the same which some affirm; but he by observation says is false against Tartaglia; affirming that the greatest altitude must be F E, answering the point 7, that is seven distances of Horizontal range from the gun A, that FE may be almost five fold the Horizontal range. Galeus did likewise well conjecture that the Curve for the middle range does come near to the Curve of an hyperbolical or parabolical line, and that not by force of reason, but only from observations. Moreover the greatest range at forty five degrees elevation he makes 16200 foot, that is 2700 of the French fathoms; who because he used feet less than ours, you might account it for 2500 fathoms, that the said range may answer to our league, and that the bullet might pass through the air in near half a minute, or 30 seconds of time: and because the dead Horizontal range may be 1/● of the utmost, it will be 2700 foot or 450 fathoms, which being supposed the Horizontal range will scarce exceed 200 fathoms. Mersennus in this place hath published a table of ranges made by the said Galeus, but it being apprehended that the same is not so near the truth as that of Torricellio, or another here published in English by the ancient well known Teacher of the Mathematics Mr. Henry Bond; that the same may be preserved and become more common in use we have inserted the same. Two Tables of RANGES According to Degrees of MOUNTURE. By H. Bond. The first Table. deg deg 1 8758 47 2113 2 7813 48 2150 3 7077 49 2189 4 6482 50 2230 5 5991 51 2272 6 5581 52 2317 7 5234 53 2363 8 4932 54 2412 9 4669 55 2463 10 4440 56 2516 11 4237 57 2572 12 4055 58 2633 13 3889 59 2695 14 3741 60 2762 15 3606 61 2832 16 3483 62 2908 17 3370 63 2989 18 3266 64 3075 19 3279 65 3168 20 3080 66 3268 21 2996 67 3376 22 2978 68 3493 23 2845 69 3621 24 2776 70 3762 25 2712 71 3916 26 2651 72 4086 27 2593 73 4276 28 2538 74 4489 29 2486 75 4732 30 2437 76 5006 31 2391 77 5303 32 2344 78 5690 33 2300 79 6263 34 2260 80 6641 35 2221 81 7274 36 2183 82 8059 37 2146 83 9061 38 2111 84 10430 39 2077 85 12330 40 2044 86 15140 41 2012 87 19850 42 1981 88 29250 43 1952 89 37480 44 2007 90 00000 45 2041 46 2076 Finis. The Second Table. deg deg 1 1.142 47 4.736 2 1.280 48 4.653 3 1.413 49 4.570 4 1.543 50 4.487 5 1.669 51 4.403 6 1.792 52 4.318 7 1.911 53 4.234 8 2.028 54 4.148 9 2.142 55 3.062 10 2.253 56 3.976 11 2.361 57 3.889 12 2.467 58 3.800 13 2.572 59 3.712 14 2.674 60 3.622 15 2.774 61 3.532 16 2.872 62 3.440 17 2.968 63 3.347 18 3.063 64 3.253 19 3.156 65 3.158 20 3.248 66 3.061 21 3.339 67 2.963 22 3.428 68 2.864 23 3.516 69 2.762 24 3.603 70 2.659 25 3.689 71 2.554 26 3.774 72 2.448 27 3.858 73 2.339 28 3.941 74 2.228 29 4.024 75 2.114 30 4.105 76 1.998 31 4.186 77 1.880 32 4.267 78 1.758 33 4.347 79 1.634 34 4.426 80 1.506 35 4.505 81 1.375 36 4.584 82 1.241 37 4.662 83 1.102 38 4.740 84 0.960 39 4.818 85 0.812 40 4.895 86 0.661 41 4.972 87 0.504 42 5.050 88 0.342 43 5.127 89 0.174 44 4.985 90 0.000 45 4.902 46 4.819 Finis. The use of the first Table, by Example. 1. Suppose a piece curry a shot 763. paces at 13. degrees of Mounture, What is the Horizontal Range? Multiply the Number against 13. degrees, which is 3889. by 763. and from the product cut off 2 figures towards the right hand, leaves the paces of the Horizontal Range desired. The use of the second Table, by Example. 2. Suppose a piece Curry a shot 374 paces at the Horizontal Range; How many paces shall it Curry at 16. degrees Mounture? Multiply the Number against 16. degrees, which is 2.872 of this second Table, by 374. and from the product cut off 3. figures towards the right hand, leaves the Number of paces desired. 3. Having the paces of any degree of Mounture to find how far that shall curry a shot at a greater degree of Mounture. Example. Suppose a piece Curry a shot 543 paces at 11. degrees Mounture; How may paces shall it curry at 19 degrees Mounture? First multiply the Number against 11. in the first Table, which is 4237, by 543. and Multiply that product again by the Number found in the second Table against 19 degrees, which is 3.156. And from the Last product cut off 7. figures towards the right hand, and the remainder are the Number of paces desired. 1. By the pieces Mounture, and the paces she curries a shot at that Mounture, to know how many she curries at level Range, by the direction aforesaid. 2. Having the level Range of a piece, to find how many paces that shall curry at a Mounture given, by the directions aforesaid. 3889 763 11667 23334 27223 296 (7307 2.872 374 11488 20104 8616 1074 (128 3. Having the paces that a piece Curries at one Mounture, to find how many paces it should curry at a greater Mounture, by the directions aforesaid. 4237 543 12711 16948 21185 2300691 2300691 3.156 13804146 11503455 2300691 6902073 726 (0980796 The Ranges of Spouts or Squirts compared with the Ranges of Bullets shot out of Guns. FOr as much as a Bullet spends a greater time in its fall than its rise, like darts; or the descent is not so swift, that it should always hasten in that degree whereby in three or four seconds, we have found its swiftness to be increased, which I suppose to be confirmed from this reason, because a bullet descending cannot have so great a power to smite, as it hath ascending, so that approaching the Earth it is not so swiftly moved, as when it comes from the mouth of the Gun, for when the swiftness of any thing projected is equal, it equally strikes. Therefore I account Spouts useful, seeing they bring us to the knowledge of shooting, of which otherwise we could not judge, by reason of the difficulty of trial which is most easily discerned in tubes: for because any one may compare in a little time what ever shot he pleases with another, to wit, Former Figure. a middle Range with a vertical, or Perpendicular one as to time and height, that this may be the better understood, in the following figure let the Cock be A above the Horizon A B, and let the altitude of the tube be A 12, whose vertical Squirt is A φ, Experience teacheth us that the length of the middle Squirt A B, is double to the Vertical A φ. But to what height the middle Squirt ranges, whether to D or E, which also you may understand of Bullets shot from Guns, there is none hitherto hath observed: but it is one half of the vertical φ A, wherefore the point D or E is higher than it ought to be, and whatever is said by the ingenious, may be corrected by spouts. There are other things also that want inquiry into; for example, how it can come to pass, that a bullet shot out of the mouth of a Gun from O to P comes right on, when in that time it flying along the line O P a hundred fathoms ought to fall towards the centre of the Earth 12 foot, if the horizontal motion of a thing violently projected hinders not its natural motion, as many imagine in a vacuity or place that does not impede. For although that can partly be explained by the diversity of the lines, which is found in Guns, to wit the line R X Y, which follows the outside of the Gun, and that which they call Linea animae S Z, which passes through the axis of the hollow M N to the aforesaid side, is in no wise parallel: because, to wit, the bullet K or H levelling at L may ascend to the side line I L, or the point S passing to Z may ascend to the point X of the side line R Y: yet another thing is to be added, when what is aforesaid is not true, when the eye of the shooter takes not aim by the line I L or R X but by the line M N or S X: for then the bullet K does not descend so much, as it would if it were left to itself in the air. Add, that the water out of the Cock fitted to the Horizontal Squirt doth not descend so much, as it would if left to itself; for it is manifest by Experience, that the Horizontal Squirt of 30 foot, which continues two seconds, descends not so much as eight foot, when according to the law of bodies of equal weight, it should be 48, or at least by reason of the resistance of the air breaking the water it ought to descend 30 foot. FINIS. men raising a wall VERSTERCKTE VESTING Uytgevonden In velerley voorvallen, en geobserveert in dese laeste Oorloogen, so in de VEREENIGDE NEDERLANDEN, als in VRANCKRYCK, DVYTS-LANT, ITALIEN, DALMATIEN, ALBANIEN, en die daer aengelegen landen, door HENRJCK RUSE, Ingenieur, en Capitein over e'en company voetknechten der Stadt Amsterdam. t' AMSTERDAM, By JOAN BLAEV. MDCLIIII. To the Honourable, etc. Dr FRANCIS BANNING KOCK, Knight of the Order of S. Michael, Lord of Purmerlandt, and Ilpendam, etc. CORNELIUS BICKER, Lord of SWIETEN, etc. JOHN HUYDEKOOPER, Knight, Lord of Maerseveen, etc. Dr NICHOLAS TULP: RULING BURGAMASTERS Of the City of AMSTERDAM. AS ALSO To the Honourable LORDS, CORNELIUS DE GRAFF, LORD of Zuydt-Polsbroeck, etc. NICHOLAS CORVER, Treasurers and old Burgamasters of the said City. AND ANTHONY OETGENS VAN WAVEREN Knight, Lord of Waveren, etc. Dr. GERARD Dr GERARD SCHAEP, Lord of Koerte-hoef, etc. Dr CORNELIUS WITSEN, JOHN VAN DE POLL; Old Burgamasters. MY LORDS, IF this little Treatise which I humbly present to your Lordships, may be favourably accepted as a pledge of my grateful Acknowledgements, and may beget in your Lordships a firm belief that my real intentions are to employ my best endeavours in the discharge of that Trust your Lordships have reposed in me, I have obtained the utmost of my desires; beseeching your Lordships to consider more the matter therein contained (which the greatest and wisest of men in all ages have esteemed as one of the most noble Sciences, and the most necessary for the settlement and preservation of a flourishing Commonwealth) than the rough and unpolished stile of the Writer, remembering that Soldiers and persons of my profession (as your Lordship's very well know) ought much rather to ponder their Actions, then to study the needless ornament of Words; as likewise to rest assured, that the continuation of your Lordship's affection towards me, will not only encourage me to a steadfast and unwearied perseverance in my zeal for your Service, but likewise to proceed to some other undertake of the like nature, for the good and benefit of your City, and of the whole Commonwealth. And so I remain, My Honourable, etc. Your Lordship's most devoted Servant, H. RUSE. THE AUTHOR TO THE READER. IN the year of our Lord 1639. (being the Fifteenth of my age) having a great inclination to the Wars, and my Genius leading me principally to the studies of Fortification, Artillery, Fireworks, Mines, and the like; I was first of all entertained in the service of the States, where I continued about four years; during which time I observed with great diligence the Manners and Customs used in these Countries, as well in the business of Encamping and Retrenching, as in Erecting their Fortifications. But hearing very much of the French and other Nations, for their marvellous Address and Dexterity in all Warlike Affairs, I was extremely desirous to be better acquainted with their ways, as promising myself to see wonders done by them: Wherefore I went with a Regiment of Walloons from Mastricht to France, in quality of a Lieutenant; which Regiment was joined to the Army of the Duke d' Enguin (who was then General of the French) and so they kept together till the Battle of Frybourg in Brisgow, 1644. where the said Regiment was wholly routed, and I with many other miserable Wretches shared together in our Misfortune; however with that Army we reduced the Palatinat by the Rhyne, Frankendal only excepted. Being since returned into France, I had the advantage of seeing there many places well Fortified, as also in Burgundy, Lorraine, and Germany, and did examine very curiously their Principles of War, together with the various Methods of Fortifying, attacking, defending, and embattailing their Armies, which often happened between the French and German, against the Imperialists and Bavarians, to which we were not altogether strangers. Thus having seen whatever I thought necessary in those Countries, I assisted at the Battle of Nortlingen, in and near the Village of Alderheym 1645. where the Duke d' Enguin was General of the French, V C. Tureyn of the Waymarians, and Merci of the Bavarians, which last was slain in the Fight. After this, having assisted in the Battle of Herbrausen near Mariedal, I resolved to seek my fortune in some other Country, to see what was there to be done, the French and Germane Customs and Warlike practices being sufficiently known to me already. Consequently in the year 1646. hearing that the Turks had invaded Candia, and declared War against the Venetians, I had great inclinations to follow that War, (besides the curiosity I had to see those Countries) as being against the most inveterate and irreconcilable enemy of Christendom. Whereupon I left the Germane Camp (for I was then come from the French to the Waymarians) where I had served for the space of three years, in divers employments, and endured many hard and tedious Marches, hazarded myself often in bloody Battles and famous Rencounters, with the loss of most of my Comrades and fellow-soldiers, who were either slain in fight, or otherwise lost their lives in the Service. From thence I first steered my course to Helvetia, and being arrived at Zurich, I met with the Venetian Ambassador, and other Germane Officers, with whom I made an agreement to levy Germane Soldiers, and to lead them over the Alps into Italy (Bergamo in Lombardy being the place appointed for our Rendezvouz) where having been a while, and observed the most eminent Fortifications on the Continent, we got Letters to go to Venice, from whence some of us were sent for Candia, others for Corfu, and I with some Germane Forces for Dalmatia, which was already invaded and taken by the Turks of Bosna, Macedonia, and the Grecians, who made great preparations to assault the Strong-Holds in those parts. Here, by the entreaty of Foscolo the Venetian Ambassador, I took upon me the employment of Engineer, and had many strange Adventures, too numerous to be here recited. About five years after, Lunardo Foscolo, than General in Dalmatia, was chosen Generalissimo in Candia, who desired me to accompany him thither. But when we came to Venice, his journey was retarded, and I employed my time in curing some Distempers I had gotten in the Wars, in the Paduan Baths; and afterwards returned to Venice, where I found the General, having got leave from the Senate, resolved to continue that summer at Venice. Whereupon being desirous to visit my friends and relations in my native Country, I took my leave, and went for Germany, and by the way had an opportunity of seeing some Fortifications of the Duke of Bavaria, and some others, which before I might not, because I served their enemies. Being in the Low-countrieses, I had an opportunity of offering my service to my Lords the Burgamasters of Amsterdam, in whose service I am at present employed, and hope, as occasion shall offer, I shall be able so to improve my talon, as to bring to light that which may be for the advantage of this great City, and the whole Country. In the mean time I shall begin with this small Treatise, the Subject whereof is the doctrine of Fortifications; not that I intent to discourse of the first Rudiments, but only to manifest unto those who understand this Science, the weakness of Modern Fortifications, and how the defects may be supplied, and the Works made incomparably stronger, as well the Royal Fortresses, as the Outworks, and all this with as small cost as ordinarily other Works are erected. Which expedients are no Chimaeras or idle Fancies, but such as have been sufficiently disputed of and throughly examined. For I have made it my business to observe very strictly the proper function of each distinct part of a Fortification, and that not in a Closet, but abroad, and in the Field, together with the manifold ways of improving them; and have discoursed and debated the same with the most excellent Engineers of this our age. I do not mean with such who attack Cities by a fireside or in a chimney-corner, but with such who have been trained up among the Canons and Muskets: nor do I mean with our ordinary Mathematicians, who think that Wars, and all affairs of this world ought to be regulated unchangeably after their rules. Neither do I hereby in any wise despise or under value Mathematical Learning; for on the contrary, I lay that for my foundation and groundwork, having for my own particular studied it with great affection and delight. But because I have found by experience, that the Principles of War are not always limited to Mathematical Rules, therefore I do not begin this Treatise with Demonstrations, but declare my opinion to the lovers of this kind of learning as plainly and as briefly as I can; not thinking it necessary to show how to erect a Fortification, but only to point at some general Amendments, which will, I doubt not, be very grateful to all ingenious Students. And in case there be any thing found which they cannot approve of, they will highly oblige me whenever they please to declare the same, and to propound expedients for the reforming of whatever is amiss. But forasmuch as I do not doubt but that this little Treatise will find acceptance, I shall God willing communicate unto the world my particular reflections and observations, for Attacking, Defending, Artillery, Mines, Countermines, with all other things relating thereto, as likewise for the ordering and forming of Battles; all which have been found to be practicable, and of great use in the late Wars. THE STRENGTHENING of STRONG-HOLDS: INVENTED On several Occasions, and practised during the late WARS, as well in the United Provinces, as in France, Germany, Italy, Dalmatia, Albania, and the Neighbouring Countries. By HENRY RUSE, Engineer, and Captain of a Foot-Company belonging to the City of AMSTERDAM. Translated out of the Low-Dutch-Copy, by His Majesty's Command. In the Savoy, Printed by the Assigns of John Bill and Christopher Barker, Printers to the Kings most Excellent Majesty. 1668. THE STRENGTHENING OF STRONG-HOLDS: INVENTED On several Occasions, and practised in the late Wars, as well in Holland, as in France, Germany, Italy, Dalmatia, Albania, And the Neighbouring Countries; BY HENRY RUSE. AFter I had throughly considered the best Methods of Fortification practised in the Countries before mentioned, I found that none of them had made better use of Situations (as to the Artificial part) than the United Provinces. Forasmuch as they have not only very well designed and contrived their Fortresses, but have also placed them so advantageously, that by the overflowing of Waters (which they can by the opening of Sluices let in or out as they please) they have rendered the greatest part of the Works impregnable. I do not say but that in other Countries are also found very sufficient Fortresses, and well contrived; but there hath been a necessity in these Provinces (where they have had to deal with so potent an Enemy) to use greater caution and circumspection then elsewhere, and to make choice of the best Fortifications, and yet with no great charge, being made of Earth only, which of all Materials I hold to be the best for this purpose; whereas in other countries', especially in Italy, they are of opinion, that the outsides of their Works ought to be altogether of Stone, and afterwards cut or pared, which cannot be done without excessive charge. And yet notwithstanding all their endeavours, they have not been able so to contrive their Strong-Holds, but that the best of them, if accessible, are taken in a short time, being hardly tenable for three Months, to the astonishment of the World, as examples do abundantly testify. This hath been the cause why many Military Architects have tried all ways and means to supply those Defects, of which I have seen many Conceits, but in my judgement altogether impracticable; which has encouraged me to improve my own Observations in all Occurrences, and earnestly to mind each part of the Fortification, of what use it might be, and whether it were able to perform that, for which it was ordained and intended. And having discovered very many Errors, especially in the Modern Flanques and Outworks, I did debate my Observations very particulary with many Engineers of the greatest Practice and Renown; but never met with any whose judgement I so well approved, as that of a certain noble Italian, who having had several Employments, as well in Germany and the Low-countrieses, as likewise in the French Wars, had carefully improved all opportunities and advantages of gaining Knowledge and Experience. With this Gentleman I therefore made a particular Acquaintance and Friendship, and we did mutually communicate and compare together our Observations, till such time as we had found out, and agreed upon such a Method, as seemed to us to be of all other the safest, and yet practicable with the least expense; according to which Method, almost all considerable Fortifications might without difficulty be redressed. The truth is, this Method is something near that which shall hereafter be discoursed of: For having looked yet more narrowly into this matter, and examined it with greater diligence and curiosity, I did only (as I found cause) altar something of that our first design. I do not here undertake to make Accessible places impregnable, since all that is made by man, may by man be again destroyed; for the Attacques being carried on upon a sure foot, and the Approaches being managed with skill and judgement, if in the mean time no relief come, even the strongest places must at length yield up to the Besiegers. My intention is only so to contrive Works, that they may resist much longer then ordinarily they do, that so the Besiegers may be wasted and consumed, either by ill weather or some other accidents. (For by lengthening of time, opportunity is given to the Besieged to get relief; or in the mean while to Attaque some other places in the Enemy's custody, and so to make him quit his design;) which will be a sufficient recompense for the pains and charge, which I conceive to be but little more than ordinary, in case the Work be managed by an experienced Artist, as will sufficiently appear by what hereafter follows. In the mean time I shall propound some general Rules or Principles of Fortifications, approved and owned by many skilful Captains and Engineers. The Maxims or general Rules which are observed in the Modern Fortifications. 1. There aught to be no point of the whole Fortification undiscovered or unflanqued, and that from several places of Defence. 2. The Lines defending aught to be longer than the Lines defended, or at least as long. 3. A Regular Fortification is very much stronger than an Irregular. 4. The more Bastions a Regular place hath, the greater is its Strength and Defence. 5. A Fortress ought to command all places whatsoever round about. 6. Those parts of a Fortress which are nearest to the Centre, aught to command those that are more remote. 7. Those parts of a Fortification which are at greatest distance from the Centre, ought always to be Commanded by those that are nearest the Centre. 8. The Line of Defence Fichante, ought not to be much longer than 60 Rods, that being the distance ordinarily allowed for the Port of a Musket. 9 The larger the Flanques and Gorges are, the better and stronger they are, provided the other parts are not prejudiced thereby. 10. Of second Flanques, and Courtine-Flanques, the larger is the better, in case it cause no disproportion in the other parts of the Fortification. 11. As for the Linea Stringens, (or Line of Defence Secant, which is continued from the Face to the Courtine) the shorter it is, the better, if the Flanques be not too much lessened by it. 12. That opening of the Angle of a Bastion is the best, which gives a right length to the Flanque, second Flanque, and Gorge. 13. The Angle of a Bastion ought not to be less than 60 degrees, nor greater than a Right Angle, or 90 degrees. 14. The Angle of the Poligone ought not to be less than 90 degrees. 15. The Angle of the Face and Flanque ought to be at least 150 degrees. 16. The Angle of the Courtine and Flanque ought to be evermore 90 degrees, or a Right Angle. 17. The outward Angle of Defence (or Angle Flanquant) cannot well be too Acute. 18. The inward Angle of Defence ought not to be less than 25 degrees. 19 The proportion between the Courtine and the Face ought to be as 3 to 2, or as 36 to 24. 20. The Faces should never be longer than the Courtine, nor shorter than one half of the Courtine. These are the Maxims and Rules for the structure of most of the Modern Fortifications, which I hold to be exceeding good and necessary, all but the 16th, which says, That the Angle of the Flanque and Courtine must always be a Right Angle. As for the reason of that Position, we shall see more hereafter. For I do assert the contrary, and say, That it ought always to exceed 90 degrees: which Angle is the only thing that makes the difference in the form of my Ground-Lines from those now in use; besides that, I take greater Parts, and other Profiles. The truth is, the Flanques are the most considerable parts of a Fortification, and those wherein lies its chiefest Strength, and therefore the Structure of those is of so much the greater consequence. But now the reasons of those who would have the Flanque evermore perpendicular to the Courtine, are these that follow, viz. Because all Shots coming from thence fly parallel to the Courtine; and that by night all parts of the Courtine may be better defended; and that when it is very dark, the Soldiers holding their Muskets in a right Angle to their Breasts, must needs hinder the Enemy from approaching the Courtine, as may be seen in Fig. 1. These reasons being well scanned and examined, appear so weak, that they are scarce worth the answering; nevertheless I shall briefly refute them. The first reason is, because the Shots fly all parallel with the Courtine: whereupon I say, whether the Flanque be perpendicular to the Courtine or no, the Shots may for all that fly parallel with the Courtine; for the Soldiers know not how to make a Right Angle in setting their Muskets. I do also affirm, That only one Musqueteer can with one Shot clear the whole Courtine at once, and all the rest must incline to it; for if they do fly parallel, than those who give the Assaults must have Wings likewise, that so they may be shot in the Air, in case those within are to defend the upper part of the Wall, or else the Shots must fly only the height of four or five foot above the Horizon (as out of the Fausse-bray) that so they may keep parallel to the Horizon; whereas contrariwise; the Flanques in these Fortifications are eighteen or twenty foot high, and all Shots go downwards, and therefore hit the Horizon in one place only. The principal duty of a Musqueteer is, that by nighttime he turn himself with his Musket towards the place where he heareth a noise, or seethe fire, or something else; to which neither the Perpendicularity nor the Obliquity of Flanques can give any advantage, or become the least hindrance. And these parallel-shots are only Imaginary, found out upon the Ground-Lines, which in the Profile come far otherwise, as Fig. 1. Num. 1. showeth. The Musquetteer A standing upon the Flanque, which is Perpendicular to the Courtine, cleareth the upper part of it: in case the Musquetteer B do the same, and Shooteth parallel with A; but then his Bullet flieth so far from the Wall, as he himself standeth off from his fellow; and so likewise all the rest that stand along in the same Line. Whence it followeth, That those who assault, must be upon the Wing, or in the Air, or else are not to be hit by these parallel-shots: but let the others without the Point A, as C, D, etc. not Shoot parallel with A, than their Shots cannot hit either the Courtine or Moat, or Bridge, but in one place only; which in an Obliqne Flanque of an equal height, will be the same. Now as for my Flanques, I order them after another Method, and therefore they are of far greater Advantage than the former, or any other that were ever yet in use, which any Artist may easily conceive, when he vieweth only the Figure, although no Explanation or Animadversion were made upon it, in case he will but declare his judgement without partiality, according to right reason, and the practice of War. The Flanques or Defending-Lines are the chiefest part of the Fortification, and aught therefore to be considered in the first place. They have been altered several times already, but never with any advantage comparable to what is obtained by these; which advantage is distributed and has an influence upon all the parts of the Fortification. The Flanques with Casematts are odious in the United Provinces, because their orillon's could not stand, unless they were Walled up with Stone, which is too chargeable; as likewise by their Cutting and Retiring of the Flanques mounted with Canon, the entrance of the Bulworks came to be too little, which in my Work is otherwise. Those who view my Bulworks, and do not understand the Profiles, may also imagine, that they are made with Casematts; but it is very far from that, and there is something else in it, which hereafter shall be sufficiently declared and explained: only let no man flatter himself with an opinion, that forasmuch as so many brave Captains and Engineers have employed the best of their understandings and endeavours to arrive at the utmost perfection of this Art of Fortification, it cannot be, but that they have attained unto it: Whereas in the late Wars it hath been observed, and is daily seen, that the best Fortresses, made after the manner aforesaid, can scarce resist so much as two Months; and it is altogether needless to produce Examples of that which so many Histories do attest. Besides all this, we are to know, that the bravest Captains and Engineers of this Age knew very well the imperfection of the Modern Flanques, and therefore they have made it their business to think of it, and the truth is, many have conferred with me about it; but I did not find the Inventions propounded by them, practicable in all places: and in this Country it hath not been minded, because the Spanish did seldom or never Attack any place of consequence with an industrious force; but being Besieged in any of their own places, did easily Surrender it, without troubling themselves much with the knowledge of Engineership. But I shall leave this Subject, and come to my purpose, which is not to teach the Grounds or first Rudiments of Fortification, but only to Instruct the Ingenious Lovers of that Art, how to reform those errors which in these late furious and industrious Wars have been rightly discovered in the Modern Fortifications. I style them furious and industrious, because no History gives a relation of any War that was carried on with greater fury, or of any Cities that were taken with greater industry. In the sequel of this Discourse, I shall manifest the Errors of Modern Fortification, and in order thereunto, I shall begin first from the Ground-Lines, and propound a part of a Regular Fortress of Eleven Bulworks, according to the practice of Friday and other Modern Mathematicians, whose Method I esteem to be much better than those of former Ages. But before I proceed, the Enemies of Strong-Holds aught in the first place to be known, which are Sappes, Spades, Pikes, Canon, Mines, and Muskets, managed by Soldiers, and Commanded by skilful Captains and Engineers: And forasmuch as the very same things are to be made use of for Defence, it is necessary that the Fortresses, to the end they may be convenient for use, should be prepared for it long before. Now this cannot be practised in small Works, where after the springing of one Mine, all is lost. It is also necessary, that the Works should outwardly be defended, as well with Canon as with Muskets, by a greater number of men, and from more places of Defence, then can be done by the Enemy conveniently in his Attacques; And herein consisteth the virtue of a Fortification: For if the Enemy do find place to make a Battery of six or eight Pieces, to break the Flanques; we ought to have a commodious place to plant Twenty eight or Thirty pieces in Contra-Battery, which will soon ruin the Enemy's Battery, being greater in number, and standing already in advantageous places; whereas the Enemy must first raise his Battery under the danger of those Canon-shots. All which being premised and well considered, let us now inquire whether our Modern Fortresses have this conveniency; and if not, where the difference lies. For example, see Fig. 2. Num. 2. which is part of a Work of eleven Bastions, and Fortified after the best Modern Method and Practice, (being Fryday's second Way) and according to the measure of these following Lines. A B Polygone exterior 78.13 Long. F G Polygone interior 64.93 Long. F E Demy-Gorge 14.19 Long. A G Capital-Line 24.40 Long. A C Face 24.00 Long. C D Flanque 11.91 Long. D E Courtine 36.00 Long. A E Line of Defence Fichante 61.68 Long. A H Line of Defence Secant 48.85 Long. graph of wall fortifications Fig 11 The Modern Engineers refer themselves much to the strength of their Outworks, whereof some nevertheless are very Murthering-Holes, more troublesome than useful; as I shall prove in due time: but for the present shall only show, how the faults of Modern Fortifications may be Rectified according to my Method. It is notorious to every one, who understands Fortifications, according to the Maxims , that the longer the Defending Lines are, the better they are; and that according to Axiom 9 the longer Flanques and Gorges, are much the stronger; always provided, they may be made without prejudice to other parts, or that they be weakened thereby: As also, that the great Bulworks are better than the little ones, because Retrenchments and Countermines may be made within them; and because more Pieces of Canon and Musqueteers may be placed there, for the defence of the next Bulwark; and because it is fit for all other Warlike actions. It is also notorious, that the longest Polygones and Regular Fortresses contain most room, and therefore aught to be preferred before the shorter, in case the Lines of Defence in the Fortification do not exceed the reach of a Musket, that is, 60 or 70 Rods; for after this manner more space is included with fewer Bulworks, and therefore with less charges. The other Maxims are also very strictly observed in my Fortifications. Now to obtain all these Advantages, I describe in Fig. 2. Num. 2. the Ground-Lines of part of an Eleven-angled Work, according to Friday, as also part of an Eleven-angled Work, according to my own practice, both of them Fortified after our second Methods of Fortifying. Which is the most commodious, and the fittest for Cities of an ordinary extent: but to Fortify very great Towns, it will be better to make use of the third Method. I shall therefore show first the difference of Lines in our two Methods, and afterwards the manner of applying the whole Work unto practice. See Num. 2. Fig. 2. The Length of Lines in an Eleven-angled work Fortified after Fryday's second Method. A B Exterior Polygone 78.13 F G Interior Polygone 64.38 .. .. The little Semi-diameter 114.26 F E The Gorge 14.19 A G The Capital-Line 24.40 A C The Face 24.00 C D The Flanque or Shoulder 11.91 D E The Courtine 36.00 A E Line of Defence Fichante 61.68 A H Line of Defence Secant 48.85 E H Second Flanque 14.19 The Length of Lines, according to my second Method, in a Figure of Eleven Angles. A B 90.00 F G 74.03 ... 131.36 F E 24.00 A G 28.32 A C 27.69 C D 16.00 D E 27.00 A E 64.50 A H 54.00 E H 12.00 Here the difference of Lines is clearly seen; and that my Figure of eleven Angles containeth in the Circuit of its exterior Polygones, 130. 57 ① more than that of Fryday's; for his eleven Polygones are 859.43 ① in length, and my eleven 990 ⓪, and my Line of Defence is no more than 2.72 ① longer than his, which is little or no difference; my Flanques, Gorges, and consequently whole Bulworks are much larger, and more convenient. My Bulworks-Angle, (or Angle Flanqued) is equal to his; as also the Angle of the Polygone, and the Angle of the Tenaille, and the Faces are as long as the Courtines. My Flanques defend the next Bulworks, Faces and Moats, at right Angles: So that all parts do mutually defend themselves with great conveniency. Here it is to be observed, That I do include very near as much space with nine of my Bulworks, as Friday doth with eleven of his, keeping very near the same Line of Defence; which easeth the Charges very considerably, besides the great Symmetry of the Work. And this is all that concerns the Ground-Lines; the virtue of this Work will be seen by that which follows. I shall proceed now to the Structure of these Fortifications, and how the proportions of Lines are to be found. I doubt not, but there be many Theorici, which understand the use of Fortifications not otherwise than upon the Paper, who will imagine, that this Work cannot be good, seeing the Flanques do not (according to the profound Error before mentioned) stand Perpendicular to the Courtines; not considering what strength the Bulworks have by this Obliquity, not only those that are next, but also those that are situated on the other side. For hereby the Bulworks gain at the entrance upon each Gorge, the length D I, being 8 ⓪ twice, which is 16 Rods gained upon both the Gorges, so that the entrance of the Bulwark cometh to be 48 Rods. This affordeth place enough to Lodge upon the Flanques the supposed Artillery and Soldiers, which I esteem necessary. It affordeth also room for the making of Retrenchments, and the Flanques come to be much longer after this manner, as is proved by the 47 of the first of Euclid. It maketh also the great Line of Defence to keep its due measure, not surpassing the length of 64 ⓪, which is the true reach of a Musket. Although my Polygones be considerably longer, yet the Lines of Defence are not sensibly longer than those of Fryday's, and others. I am also of opinion, That the Modern Flanques are more for an imaginary beauty, than to make good the Defence, which notwithstanding is the main end for which they are made, and wherein consisteth the strength of Fortresses. The Calculation of my great Fortifications, consisting in the little, mean, and great Royal. TO do this, I state first my exterior Polygones, after which I regulate the proportions of the whole Work. For the exterior Polygone of the little Royal, I take 80 ⓪, for that of mean Royal 90 ⓪, and for the exterior Polygone of the great Royal 100 ⓪; and I follow the same proportions in the Calculating of my Lines, which Friday hath, that is, making the Courtine to the Face, as 36 to 24, or as 3 to 2; but the difference is, that I take my parts greater, and redress them, after the first Position is done. This Calculation is done only by the Rule of Three, thus: Admit there is a place to be Fortified with a Regular Fortification of four, five, six, or more Angles, and that after the first, second, or third of my Methods; I take then the Lines of such a Polygone, as the Fortress should be, that I intent to make, out of Fryday's Tables. For example, I would make a Square after my first Method; I take then out of the Tables the length of the Lines; as 24 ⓪ for the Faces; 36 the Courtines; for the George's 9.23 ②; for the Capital 19.73 ②; for the Flanque 7.74 ②; and so for all the Lines: these Lines I lay before me, and say, by the Rule of Three, If the exterior Polygone of a Square of Fryday's, being 82.36 ②, giveth me the Courtine 36 ⓪, what does my exterior Polygone of 80 ⓪ after the first Method in the great Royal, give me for my Courtine? and the answer is, 34.97 ②. Item, the exterior Polygone giveth for the Face, according to Friday, 82.36 ②— 24 ⓪. What giveth the Polygone of 90 ⓪?— Answer. It giveth 23.31 ② graph of wall fortifications Fig. 11. And so observing the same Rule for a Square, whose exterior Polygone is 80 Rods (as in the Figure of Numb. 1.) there will arise the following proportions of the Lines, viz. H G The Courtine 34.97 ① A I The Face 23.31 ① C H The Gorge 8.96 ① C A The Capital-Line 19.16 ① H I The Flanque 7.52 ① H L The second Flanque 6.77 ① C D The interior Polygone 52.88 ① H B The great Line of Defence 59.05 ① D M The little Semi-diameter 39.37 ① N. B. He who is disposed to Calculate, or who has not these Tables at hand, he may find out himself, by Calculation, the chief Angles of every Figure, and afterwards by the Tables of Sines, or Trigonometry, the length of the Lines, etc. These Lines and others that may be required, being found by the foregoing Rules, I delineated the Figure (whether it be a Fortress of five, ten, eleven or more Angles) according to Art, as here in the Figure Numb. 1. the Square, which I hold to be the first Figure capable of being Fortified. This being drawn according to the Modern Practice, I redress the Ground-Lines according to my Method, very easily thus: I lengthen the Faces at pleasure, as here A I, N C, of which I N, is the Line of Defence Secant. Upon this C A, I let fall a Perpendicular-line, touching the extremity of the Face B K, in K, and I take the Line F K, for the Flanque; and thus I do round about the whole Fortification; and this from a Square, to a Figure of twelve sides inclusive. In such Fortresses, as have more than twelve Polygones, I keep always the same Courtines. And so the form of a Square with its Ground-Lines is sufficiently seen in Numb. 1. and the Structure of it shown before. From this alteration arise these Advantages; First, That the Gorges are lengthened by F G, and H E, and therefore the Bulworks at their entrance become wider and fit for Retrenchments, and the use of necessary Artillery; as may be seen in the Profile of the Flanques. But the Gorges remaining at the length of D G, the said Artillery cannot be duly Lodged. This lengthening of the Gorges maketh also the Flanques E I, F K, longer than the former Flanques K G, and I H, were: This Obliquity of Flanques causeth also the Faces A I, and K B, together with the Moats lying before them, to be Defended at Right-angles, and that the Lines of Defence F A, and E B, become shorter. And lastly, This manner of Structure giveth sufficient room for the Cutting or Retiring of the Flanques. And concerning the Angle-flanqued, or Angle of the Bulwark, which in a Square is 60 degrees; he who desires to have it greater, let him draw a Line from the Point, where the Flanque and Courtine meet together, by the extremity of the opposite Flanque; as by 5 to Q, which is the Line D 5 Q, and so at th'other side. Thus the Faces become something shorter, and the Angle something greater, according to the 21 of the first of Euclid. But the Second Flanque is lost, which in a Square signifieth but little. And this in my opinion, is sufficient as to the alteration of the Ground-Lines, and the finding of them; and the more Bulworks in any Figure keep their just distance, the more considerable will be the advantage gained by their Alteration. Of the Fausse-bray. THe Modern Engineers draw the Fausse-bray parallel, round about the foot of the Wall, at such a distance, that between the Parapet of the Fausse-bray and the Wall is left a hidden way of between 15 and 25 Foot. This Parapet is made to defend the Moat, when the Enemy is passed the Counter-scarp, and intendeth to carry over the Gallery. I make also Fausse-brays, but after another manner than the Modern, viz. thus: I draw a Parallel-Line with the Flanques, as in Numb. 1. X W, parallel with the Flanque 6 V, at the distance of five Rods; so that the place may be capable to hold Canon; afterwards I lengthen the Faces of the Bulwark, as B V, till they cut the parallel X, W; this done, I draw a parallel with the Courtine, at the distance of 3 or 4 ⓪, as X Y; so that the Lines V, W, X, Y, 2, 3, make the Fausse-bray; and this I do round about the Fortress, only before the Flanque and Courtine, and not before the Faces. The reasons hereof are these: First, It is found by experience, that the Fausse-brays are more hurtful than advantageous before the Faces; because they are not of service, before the Enemy cometh to Lodge upon the Esplanade or Parapet of the hidden way, and then they are to oppose him, which they cannot possibly do: And this so much the less, because the Enemy may plant his Canon there for the Destroying and Dismounting of them. Which is easily done, seeing it is but a bare Parapet, which is soon thrown down; so that in this part before the Faces, which are Attacked, no body can remain for Defence, by reason of the playing of the great Guns from the Batteries, which may be made as need requireth; as here Fig. 11. Numb. 1. is intimated by the Letters A, B, and C; where from the Battery A, the Face of the Bulwark D, and its Fausse-bray is pierced Perpendicularly, and from the Battery B Obliquely; but the Battery C cutteth and cleareth the Earth away, which is shaken by the two others; so that by these Batteries and Musquet-shots, coming from the Lines and Cors de Guards, the Faces, as well of the Fausse-bray, as of the great Wall, are soon ruined and left without Defence, so that no body may be seen upon these Lines without being hit; whence it followeth, That they cannot hinder the coming over of the Gallery, but it must of necessity be done from the opposite Flanque. Item, That so soon as this part of the Fausse-bray, lying before the Face, is discovered, it is presently made useless to the Defenders; and not only so, but it does them this hurt and disadvantage, that so soon as the Gallery cometh over, the Miners are able to Undermine the Faces of the Bulwark, where they please, and at several places together. The Mines being blown up, the Enemy may set Footing upon the space where the Fausse-bray lies, not only to Assault the Breach, but he may run along the Foot of the Wall through the Fausse-bray, to fall on at more places at the same time. To this it might be replied, That the Fausse-bray aught to be Cut with Trenches, to hinder this running about. But every one who has experience in these Actions, knows very well, what slender Opposition these Trenches are able to make, especially, when the Earth, which is raised by the Mine, falls down, and sometimes buries the Defenders alive. This place is also of Advantage for the Enemy, when the Breach is Retrenched, and he will make new Attacques upon it, and by that means will lodge himself conveniently in the Fausse-bray, and further in the Breach; whereas otherwise, where there is no Fausse-bray before the Faces, he findeth very inconvenient Lodging against the slooping of the Wall, seeing no other place is found to fix upon. The Miners are forced to make their Mines about the place, where the Gallery cometh on; besides that the Faces, which are surrounded with these Fausse-brays, being Attacked by Canon and Mines, all the Ruins of them remain lying in the same, and afford an easier Ascent unto the Enemy; whereas otherwise, where they are not, the Ruins roll down into the Moat, and the Breach remaineth clear, and the Enemy findeth little Earth to Retrench himself. By all which it is easy to understand, That this part bringeth more advantage than hurt unto the Enemy. To what end is it then, to be at such Charges to our Prejudice, and to cumber the Moat before the Bulworks with this needless Parapet? Therefore to conclude, I say, That the Faces of a Bulwark being Attacked, can make little Opposition of their own; but aught to be Defended from the Flanques and parts of the Courtine; and the more even and neatly the Faces lie, the better may they be Flanqued. That part of the Flanque of the Fausse-bray D, hinders also, that the Face a G from being defended at the bottom from the opposite Flanque. Some Engineers are of opinion, That the Fausse-brays aught to run out after the shape of Ravelins in the middle, before the Courtine. I think this needless, where the Lines of Defence are of a just length, not much exceeding 60 Rods; but where they be longer, this must be practised. At Breda, it is done before some long Courtines. And this is enough as to what concerns the Ground-Lines of the Fausse-bray, in the Profiles: I shall show hereafter, how the Work is to be raised. It remaineth now, that I speak of the Ground-Lines of the Counter-scarp and hidden way, and how it may be made, that it may defend itself with great Advantage, without the great Wall; and that these Counter-scarps are as strong, yea stronger, than the Modern Fortresses themselves. N. B. In those Fortresses, where the exterior Flanquing-angle (or, as the French call it, Angle de Tenaille) comes to be less than 120 degrees, (but it is never made less than 90 degrees) the Faces may be lengthened upon the Ground-Lines, till they meet together; and in such Figures the Fausse-bray may be made upon these Lines, that is, upon the Line of Defence Secant, without running parallel with the Flanque, as may be seen in Numb. II. by the three Figures 5, 6, 7. But when it happeneth, that the Lines of Defence Secant meet one another within the Courtine, or just before it; then a Parallel-Line is to be drawn before the Courtine at the distance of three Rods, to have a Communication; as the understanding Reader will easily perceive, and is seen in the Figure of Numb. TWO, etc. Of the Counter-scarp, or hidden Way. THe Modern Engineers do strengthen the outward Brink of the Moat (or Counter-scarp in Italian,) with Ravelins and Halfmoons, leaving a hidden way with a Ditch about it, and without this hidden way they make sometimes another, without a Ditch; as may be seen at Breda: Which latter I hold to be very good, because not only great Defence may be made from thence, but they are also very convenient for Sallying out, both on Foot and on Horseback; for the Moat doth not hinder it, and the Enemy doth not know from what side he must expect the Sally: Those who thus Sallyout, being driven back, may always retire hither, and presently be in a posture of Defence again behind this Parapet; whereas otherwise they are many times driven into the Ditch of the hidden way, with great loss and disorder. This hidden Way (or Esplanade) costeth little, for in places where the ground is something dry, it is cut in above half its height under the Horizon, that is, three or four Foot, that it may be the better flanqued from the first Esplanade which is behind it; as also, that the Shots may fly more Horizontally, etc. I do Fortify my Moat with another kind of Work, and I shall show first the manner how I do it, and afterwards give reasons why it is so much better than the Modern Works. And at the same time I shall discover the Defects, which the Modern Works are subject unto. See Fig. 4. Numb. 3. which is part of a Regular Seven-angled Figure after my little Royal, where the exterior Polygone is 80 ⓪ long: Now to draw my Counter-Guards (for so I call them instead of Counter-Scarps, this name being improper) about it, and to give them such a form, as may fit them for that service I expect from them; I lengthen the Half-diameter K, O to A, or further at pleasure; then I measure upon the lengthened Half-diameter from the brink of the Moat O to I, thirty Rod or more, according as I would have the Flanques N 5 and 4 R short or long. Then I draw from ⅓ of the Face, as from K the Line K, G 5, as also on th'other side the Line L, R, M, from the Point where these two Lines meet, which should be before the middle of the Courtine; as here from G, I draw the Perpendicular G H, which is the Capital-Line of the Ravelin W, G, P, H; then I measure from N to L, as also from G to P, upon the Lines K, G, on th'other side L, G, such a distance as I need for my retired Flanques: from these Points, viz. from N and 4, I draw N 5 Perpendicular to L, M, and 4 R, Perpendicular to K 5, as is clearly seen in the Figure, and wanteth no further explanation as to the Delineation of it. I make further upon the Line 5 R an equilateral Triangle, as 5 R, R, which giveth a Ravelin, whose Angle at the Point R is 60 degrees: He who desireth the Angle to be greater, may make it so, without prejudice to th'other Work. About this Work I draw a Parallel-Line at the distance of five Rods, viz. M R G 5 2; which is the Ditch about the Counter-Guard, so that the Ravelins lying before, become little Islands. At the brink of this Ditch I make a hidden way or Esplanade, whose sloping is regulated according to the Wall of the Counter-Guard, without Ditches, with small cost, which becomes a great benefit. This I continue about the whole Fortress; and all is clearly seen in the Figure, how the Work must lie according to the scale and measures. These are all the Outworks, which I look upon as necessary for a good Defence; and I make no Hornworks, etc. unless extreme necessity do require it, when perhaps there is some height; and then I make them after another manner than the Modern, as the nature of the place does require. Of the Virtues and Defects of the Modern Outworks. THe Modern Outworks are Ravelins, Halfmoons, hidden Ways, Crownworks, Hornworks, Tongues, Kettles, etc. and are made about the Fortresses, as Fig. 5. Num. 3. showeth; where the Figures marked with C are called Halfmoons, those with B Ravelins, D is a Crownwork, such as are laid before the Courtines, before which there lieth a single Tongue; E is a Crownwork lying before a Bulwark, being strengthened with a double Tongue, and at the side of it there is represented the form of a Hornwork. This Figure is part of a Regular Seven-angled Work, according to the most Modern practice, as well the Outworks as the Royal Work. The Virtues and Defects of the Royal Work are in part manifested already. But now I shall show those of the Outworks; and first Of Ravelins. THe Ravelins, marked with B, I count very necessary, seeing they multiply very much the Defence, especially of the Outworks: But because they do in a manner stand instead of a Royal Work in Modern Fortresses, they have this Defect, that their Flanqued Angles are too small, and the Points may be easily broken, as also the Faces, as may be seen in Fig. 5. where the Ravelin B being Attacked from the Batteries A, A, is easily made useless. There may be more Batteries placed to Attack these Ravelins, as it is required, because it is seen from the whole Field I A L. These Works being Attacked, it is very difficult to secure them, and no less difficult for the Defenders to retire when it is taken; and being once taken, it becomes, as it were, a Knife to cut the Throat of the whole Fortress. Of the Modern Halfmoons. THese Halfmoons marked Fig. 5. Numb. 3. with C, I look upon as Works of little use, because they can make but poor Defence, and are Defended but weakly; since they have no other Flanque, than from the Faces of the next situated Ravelins; which Defence being broken (which is easily done, as I have showed by the Ravelins, and appeareth by the Figure) they remain to the use of the Enemy, to make in it the Battery H, whereby the opposite Flanques of the Bulworks are ruined, and the Galleries are brought over with surety; all which is clearly showed. N. B. The Faces of the Halfmoons cannot be seen from the Flanque of the great Wall, the Ravelins being in the way; ergo, they cannot be Flanqued from thence, etc. Of the Modern hidden Way, or Counter-scarp, as they call it. THese hidden Ways are very advantageous before Fortresses; for lying low by the Horizon, they make all the Shots that come from thence, to Mow and Clear the Horizon: neither can they well be broken by the Canon, but must for the most part be taken by storm, and they are commanded from the great Wall: This is a work which covereth much the defects of the Modern Fortifications. They favour also the Sallying out, when they have no Ditches; but here in these United Provinces they have almost all of them their Ditches; which fault being discovered, it hath been remedied by another hidden Way, running about the Ditch of the first, and being cut in, part of it, according to the nature of the ground, under the Horizon, and the surface of the Parapet of this hidden Way, loseth itself, sloping into the Field, without a Ditch. Of Crown-works, and Horn-works. IT is many times necessary to make these or the like Works to take in any heights or suburbs, according as the place requireth it. They are made after the manner and practice of the great Fortresses, and according to the same proportion, excepting only, that their parts are smaller, and they have but half-Bulworks on either side, which are very weak; and yet their strength may be much increased by an understanding Engineer. They ought, in my judgement, to be made so, that they need not to rely upon the Defence of the great Wall; but that they be sufficient to defend themselves, especially those that lie before the Courtines, as in Fig. 5. may be seen by the Crownwork D, whose Wings have a very weak and obliqne defence from the Faces of the Bulworks, and being Attacked by night, the Lines E E cannot be well defended from the Faces of the Bulworks. Yea, in such occasions the Defence of the great Wall is but troublesome to these or the like Works; for the Musqueteers of the great Wall, shooting by night only upon the Alarm of the Assaulters of the Outworks, do hit as well within as without, and wound as well the Defenders as the Adversaries. They ought nevertheless to lie open towards the City; and to be made so, that being taken, they may be little able to hurt it. Of single and double Tongues. THese are very slight Works, and never ought to have other Profiles, than those of ordinary Trenches; for else, if the Wall should be high, they were not able to defend their own Front. Neither are they but seldom made otherwise than Trenches, or to hinder the Approaches; as also the Kettles marked with H. Hence it may be seen, wherein the strength of the Outworks now in use doth consist, which the Modern Engineers make such boast of. Let us now examine the Outworks according to my Practice. OF OUTWORKS, ACCORDING To the latest METHOD and PRACTICE. First of the Counter-Guard. OF these Outworks it might be said, That they take in much place, which is a truth; but when we shall have showed what benefit cometh by them, I doubt not but that will outweigh any inconvenience that shall be occasioned be the great space and place which these Works take in more than other Works usually do. Neither is the difference so very great: For admit, that about the Modern Seven-angled Work Fig. 5. Numb. III. there should be made another hidden Way about that which is there already, or that it should be strengthened with two hidden ways; the Semi-diameter of my Heptagone Fig. 4. is but five Rod longer than that of th'other. In recompense whereof it is to be considered, That my exterior Polygones of the Heptagone are 80 Rods; whereas those of th'other (or Modern) Heptagone are but 70 Rod long, which in the whole maketh 70 Rod difference, which is an entire Polygone. Wherefore to include the place of my Heptagone after the Modern manner, there would be required eight Bulworks; so that I do include and Fortify more place with fewer Bulworks than now is usual, which understanding men will easily conceive, by comparing the one with th' other. To show then, what good this Counter-guard doth, let us suppose, That the Fortress Fig. 4. is also Attacked by the Approaches O O. Now skilful Artists know, That it is best for the Enemy to Attack the Point D, and after he hath gained the Counter-scarp, to pass the Ditch of the Counter-guards of 5 Rods. To do this, it is needful for him to render first the Flanque of this Work D, and the Face of the Ravelin F uncapable of Defence: but if he would break the Flanque of the Counter-guard D, he findeth no other place for his Battery than by the letter C, where but five Pieces can be placed, graph of wall fortifications Fig 4 Fig 5 to Dismount the lowest Flanque; and further in the Field about G there might be planted 3 or 4, to throw down the uppermost Parapets of the Retired Flanques, so that nine Pieces of Canon may be used; whereas those of the Retired Flanques may bring 17 or 18 Pieces in Counterbattery, and from the part H, 4 or 5 Pieces, for the Defence of the Face of the Counter-guard; therefore the Defenders are able with more ease to break the Battery of the Assaulters, than they to break the Flanques of the Defenders. That which hinders, that no greater place is found for the Battery of the Assaulters, is the Ravelin F, and the Angle of the Flanque of the Counter-guard I. Let us see, whether there be not where else a place to make a Battery, to break the Retired Flanques withal, and to Dismount the Canon standing upon the same. Suppose there be a Battery by B, from thence with the Line B one might boar in between the Ravelin F, and the Angle I, but not so, as to touch the lowest and first Flanque; yet this shot (which cannot be done by more than one Piece of Canon) would come obliquely against the last Shooting-hole of the second Retired Flanque, and cannot Dismount the Canon that standeth there, because the shot hitteth the Parapet obliquely in the forepart. No more can it be done from the Battery A, against which Batteries upon the Line D E, every where Counter-batteries may be made. Put the case, That the Enemy not regarding all these difficulties, do with great loss pass the Ditch by D, and undermine the Point of the Counter-guard, (which would also be very hard to do, seeing the Walls are made so, that one cannot well put a Spade into the Ground without being discovered) and make a Breach. In this case, I can first with small labour cut off this Point by the Retrenchments 1 and 2, till the great Retrenchments by 3 and 4 be finished, which are duly defended from the Flanques 6 and 7, as also from the Bulworks-point 8; besides that they secure and defend one another. And in case the Besiegers mean to pass between the Retrenchments towards the Bulworks-point, without gaining before the two Lines marked with 3 and 4, they will find hot work. But suppose they force one of these Lines, than there is within, two or three Rods after them, another ready, and those that lie before are Undermined, which Mines are blown up, when the Enemy once thinks to lodge there; and this is a thing that may be done with great advantage. There needs not one Rod of ground be lost, but what is gained with abundance of blood, and also with great toil and labour. Being forced, we have always a free retirement into the Ravelins marked with K and L. And in case there be but men within a Fortification made after my Method, who understand the Work, it seems impossible to gain it any other way, than by length of time, and with the loss of many men. This Work helpeth itself, nothing being in the way that hindereth; and all parts are so contrived, that they are provided against all inconveniencies. Hence the understanding Reader may easily conceive, what advantage these Outworks have before the Modern. They are Flanqued within and without with Canon and Muskets from the great Wall; there may be made in haste, and with small pains, as many Retrenchments as is desired, which are all enfiled within and without from the great Wall; and the more obstacles are cast in the way, the more the strength of these Works is discovered. This is enough as to the form and advantage of my Outworks, which each according to his judgement and place may apply: In my opinion, it would be needless to propound these things in a plainer manner, seeing all particularities may be observed by the Figures. It might be said, That these Outworks would cost more, than those that are now in use: the contrary of which is true; for the Parapet of the Modern hidden Way having a Base of 60 or 70 Foot, costeth as much as my Counter-guards-wall, whose Profile I do make so, that it is just Canon-proof. I shall not add here the charges of the Modern Crownworks, Hornworks, etc. but I put my two Ravelins against the Modern Halfmoon and Ravelin; the Counter-guard against the Counter-scarp now in use, my outward hidden Way without Ditches (which is made with small charges) against the Modern second hidden Way, being also without Ditches. And although this Work should cost much more, yet the charge is sufficiently balanced by the benefit that is had thereby: For the Fortresses made after this manner, have quite another Defence, and are, besides their Out and In-works, provided against all Occurrences, with 2, 3, a 4, double Flanques, made as well for Canon, as for Muskets. If any body thinketh, that I propound new and strange things, as doubtless those will do, who are possessed with the Modern practice of Fortifying, and never did search after more convenient means, or examine the strength of every part of it distinctly; or what may be the cause, why Strong-Holds are lost so soon, neither understand the force of the Maxims of War now in use: To those I reply, That if they will consider these new things judiciously, they will find, that the practices of War now in use, aught to be preferred before those old things; and that the Work is very proper and capable of making a good Defence; and that these things were not practised conjecturally in a Closet, but in occasions of Besieging, or being Besieged; and that in several countries and grounds, and in such places where indeed flew swift Bullets, not Sugar-plums, or roasted Capons. Many things may be projected upon Paper; but we ought to look, whether they be practicable in the open Fields, The Latin proverb, Facile est inventis addere, might be applied here, I do confess, but it hath not been done as yet by others. I have been about this a long time; but always observing more and more, whether any thing might hinder it, which perhaps I had not considered of; and possibly there may be some such thing, but whatever it be, it may with ease be rectified by time and practice. All things devised by men, do not immediately come to perfection. Let them who please to use this way, first consider the Work well; and if there be any thing that they do not like, let them practise the Latin proverb abovesaid. There are yet many Particularities in this Work, which I do not describe here, but keep them for my use, and propound only the Generals. It is true, That the Art of Fortifying is highly improved in these United Provinces, by reason of the continual exercise in it: But here have been but few alterations or diversities of Attacques, seeing they are almost all of them made after the same manner; as also the Defences of the Spaniards, who were furnished most commonly with ignorant Engineers, and their places ill Fortified; so that being Besieged, and much pressed, they wanted many things that were most necessary. Here in these parts they have been a while at a stand, without practising any thing at all, which might serve to rectify their Errors; although understanding men saw well enough, that there was something wanting, and that the Work did want another Form; and this proceeds chief from the impression which many had, and still have, that the Fortifications were at perfection, contrary to experience and matter of Fact in the late Wars. In this opinion they were confirmed by the curious searches, experiences and amendments, made by His Excellency Prince Maurice, and His Highness Friderick Henrick, Princes of Orange, of glorious Memory: These indeed did in those days reform many things exceeding well; but the manner of Attacking being much altered since, the Fortifications ought also to be strengthened against them. The Practitioners have only joined to the first Inventions, those things which serve to establish Fortifications upon sure Rules, according to the Mathematics, to which we ought not to be tied too close; however it is necessary to take their assistance in this Science. The question is not, Whether the Fortifications do lie exactly according to the Rules of Mathematics; but whether the Lines be well Flanqued, and all things ordered for most conveniency. I confine myself indeed to these Rules and Calculations, for so much as the first Ground-Lines do require; but upon these I make my Observations afterwards: so that my Work receives no small benefit from thence, by reason of the firm and well-contrived Flanques, and the giving of little advantage and place to the Enemy to erect his Batteries against them. Many places (though well Fortified) are also lost in a short time, for want of skilful Officers and Governors. For although a man had the best Sword he could wish for, and yet did not know how to use it for his advantage, the worst would be as good for him as the best. Let the best Fortress be defended by a Governor, who knows it not, that Fortress shall be gained sooner than a mean place Commanded by an experienced Officer. This hath been sufficiently made good in these late Wars, which also Histories do testify abundantly. For, Retrenchments, Cuts, Counter-approaches, Countermines, besides the ordering of Sallies at due times; as also the managing of Fireworks, contrived by an expert person and skilful Architect, are all very advantageous for Places, and detain the Enemy long. And yet they cannot well be known, before there is Attack made; and then they may easily be so ordered, as to be made more advantageous for the Enemy, then for the Place itself: Hereof there are examples enough, and these Works cannot have a good success, unless they be directed by a skilful Architect, who has not only a perfect knowledge in Fortification, but understands also the power of Artillery and Fireworks, as also the manner of managing them, and how Mines ought to be made upon all occasions. And this I think sufficient for the designing of Ground-lines, and have described only three Figures more of three Regular Hexagones' Fortified; see Num. FOUR one of them, after the great Royal, whose exterior Polygone is 100 ⓪; another after the mean Royal, whose exterior Polygone is 90 ⓪; and a third after the little Royal, the exterior Polygone being 80 ⓪. NOTE. No body is confined to these lengths of Polygones, but they may be taken shorter or longer; only care must be had, that the Lines of Defence be not too long. The lengths of the Lines of these three Demy-Hexagones are of several Quantities; viz. the first, whose outward Polygone is 80.35 ①, and is equal to the Modern Polygones of an Hexagone, according to Friday: the second is of 90 ⓪: the exterior Polygones of the third are of 100 Rods, and the proportion of the Courtines to the Faces (which is to be understood in the first design, which afterwards is altered) Sesquialter, or as 3 to 2. Lengths of the Lines according to the first Calculation. Lengths of the Lines after the first manner, where the outward Polygone C D is always 80.35 Rod in length, in a Regular Hexagone. Lengths of Lines after the second manner, where the out ward Polygone is always 90 Rods long, in a Regular Hexagone. The outward Polygone being 100 Rod, in a Hexagone. Lengths of the Lines, after my alteration, in an Hexagone, as followeth: The I. The II. The III. manner. The Courtine F I 36.00 40.44 44.82 29 30 33 Face C M 24.00 26.88 29.86 the same. Gorge G F 11.36 12.72 14.43 14 17 19 Capital G C 21.26 24.20 26.89 the same. Flanque F M 9.54 10.68 11.87 11 12 13.5 Second Flanque F N 12.98 14.53 16.16 8.5 10 10 Line of Defence Fichante CI 61.11 68.44 76.05 58 63.5 69 Interior Polygone G L 58.73 65.89 73.09 the same. Distance of Polygones F E 18.72 20.96 23.29 the same. The Intelligent Reader will see all things better in the three Figures, Numb. I I I I. and may measure it by the Scale that is joined to them, by which all three of them are made; and it is to be observed, that these Lines serve only for an Hexagone. But if any one would Fortify another Figure, he must first calculate the Lines, and afterwards alter the work according to the directions heretofore mentioned. By the first Figure are showed three several manners of Counter-guards, being all three very good and commodious, and may be very fitly applied to places, that are already Fortified; as also the Royal Work, and the great Wall may be redressed in such places, with little charge, after this way. The second and third manner of Counter-guards I count better, when the place and occasion permitteth it, to make them so large, for they are extraordinary Advantageous; but for brevity sake, I shall not rehearse here all their Advantages and Conveniencies. Some will say perhaps, That the Ground which these Outworks take in, being so large, the same would cost very much to buy it from the owners, in such places where it is required. To these I answer, That in this case there is not graph of wall fortifications me health, till I bring to light the other parts (viz. of Attacques and Defence, of Undermining, Counter-mining, Fireworks and Artillery, when it may be done most conveniently) than the advantages of this manner of Fortifying will be better conceived and understood; for the quality of every part of a Fortification shall there be declared one by one separately and distinctly. Of Irregular Fortresses. I Shall say only this, That it would be too long to show here particularly the manner of working, which I esteem as needless, seeing that Irregular Fortresses are made up out of parts of Regular ones: The calculation thereof may be done after the Modern practice, and the parts afterwards reform according to my way; as hath been showed in the Regular. There are many Engineers, who think it an Art to Fortify any places altogether Irregular, although they might well enough alter them. I do not glory in this; but am very well content, when I meet with such an unfit Figure, to reform it after the Regular, as near as the place will permit. A Regular place, besides that it hath its Defence more equal, is also the fit, and taketh in with the same Lines more space, which I prove thus: Let there be a Rightangled Square, each of whose sides is 12 Rod, and the four together 48 Rod, whose content is 144 square Rod: Let there be another Irregular Square or Rhomboides, having also four straight Lines each of 12 Rod, that is, the four of 48 Rod; let this Rhomboides be made of two Equilateral Triangles, than the shortest Diameter is 12 Rod, and the longest 20 Rod, and 8 foot, whose content is therefore 124 square Rods, and 8 square Feet; From whence it appeareth, That the Rhomboides containeth 19 Rod, and 2 square Feet less than the Quadrat; and the more the Rhomboide recedeth from Regularity, the less is the content of it, etc. But this is true of Irregular Fortifications, That the Rules and Maxims of the Regular being known, the good or bad Form, as also the strength or weakness dependeth wholly on the knowledge and experience of the Engineers, etc. SOME QUESTIONS That might be moved concerning this manner of Fortifying; together with the Answers to the same: by which the use of this Work may be the better understood. I. Question. FOr what are the Flanques not drawn Perpendicular or Rightangled upon the Courtine or inward Polygone, in this Way of Fortifying; but Rightangled upon the Line of Defence Secant: For it is esteemed more graceful after this manner, and the Ground-lines may be found more easily by Calculation; it being also believed, that being thus made, they defend the Outworks the better? Answer. I Give this Obliquity to the Flanques for the Reasons following. See Numb. II. the Figure being Calculated and stated after the foregoing manner and proportion, or being measured in the Fields, the longest Defence-line would exceed a Musquet-shot; whereas now the said Line by this Obliquity is brought to its due length; whereby I reap this advantage, that with fewer Bulworks than the Modern do use, I can include a far greater space. Examples have been before alleged. And with an Octogone of my great Fortification I do include as much place, wanting only about half a Polygone, as the Modern do with an Hendecagone, or Fortress of Modern Bulworks; whereby so much charge is saved, and the Lines of Defence remain within Musquet-shot. Item, By this Delineation, the George's gain on each side in length 8 Rods in an Hendecagone, whereby the Bulworks get the desired opening at their entrance, which maketh place for the Retired Flanques, and affordeth conveniency for the making Retrenchments speedily and easily. By this Obliquity the Flanques do likewise become also longer, and therefore fit to lodge a competent number of Canon and Musqueteers upon them. This Obliquity causeth also the Gun-holes not to stand Obliquely, and that the Moats are Rightangled and defended from the Flanques. And whereas they say, that the Perpendicular Flanques defend the Outworks the better, this doth not stand to reason; but it is known, that the Obliqne ones do it better, seeing they come more flat against them, and the Outworks are better seen from the Obliqne Flanques, when they are made after this manner, etc. II. Question. FOr what are there three Flanques and the great Wall, set at the top of one another, and yet below a Fausse-bray's Flanque; whereas nevertheless the Canon being placed thus above one another, the uppermost cannot be discharged conveniently, without prejudice to those that are in the lower Batteries. Besides that, the flame coming out of the upper Canon, and falling upon the lower, might give Fire to them also sooner than would be desired? Answer. THese three or four Flanques, I make at the top of one another, not to plant them all full of Canon; but to fit the uppermost with Musqueteers and Falconets, as occasion requireth. But if need should require, that I must have a strong Counterbattery upon the Flanques, or that much Canon must be there, to hinder the coming over of the Galleries: then put the case, that all four Flanques are filled with Canon; what should hinder me from using them at pleasure, without endamaging the lower, or giving fire to the lower Canon before the due time, if I go to work after the manner following? At one side of these Retired Flanques, I place a skilful person, either an Officer of the Artillery, or some other. This Officer, when they are upon Discharging, commandeth the men in the lower Flanques, to retire themselves at the side of the Battery into the Way, by which the Canon is let into the Flanques, till such time as the uppermost have Discharged; which Shooting beginneth from the last Retired Flanque, where the longest and heaviest Canon may most conveniently be used. When these have Discharged, they Charge presently again, and then those of the second Retired Flanque give Fire; which being done, they also Charge again with all possible expedition: For those that have Discharged (beginning from the hindermost) cannot be prejudiced by the following Canonadoes; and this continueth, till the Flanque of the Fausse-brays (being the last to give Fire) hath also done. In this time the hindermost can have almost Charged and Leveled; so that after this manner one may orderly Charge and Discharge the Canon, as if it were a Band of Musqueteers, without hindering or prejudicing another. These Canon-shots are alternatively favoured by Musquet-shots, coming from the second Flanques; (where I would Lodge no Canon, except there were great need, for the reasons before mentioned) as also from the second Flanque of the Fausse-bray, and also from the half of the great Walls Flanque and Faces, etc. Concerning what is objected, That the lower Canon might be kindled by the upper before its time; for this, no other remedy needs to be used, but to cover the Holes with a Plate of Lead, as they do in Ships. Now it may be considered, Whether it be easy or no, to bring a Gallery over a Moat, that is seconded by such a Hail of Canon and Musquet-shot. III. Question. SInce here is mention of so many Canons, there must be great number of them, to furnish one of these Fortresses with Artillery: For besides that the great Wall (or Royal Work) requireth much Canon, the Outwork ought to have part of it too, seeing it defendeth itself, as well as the great Work, with Artillery and Muskets; and according to the number of Gun-holes, there must upon the four heightened Flanques on each side of every Bulwark be at least 20 Pieces, which is 40 Pieces for each Bulwark; which in a Fortress of seven Bulworks amounts to 208 Pieces, for the entire Fortress only. Now in the Outworks there is by the joining Halfmoons of the Counter-guard, on each side place for 12, 13, or 14 Pieces: If it be 14, it is for every Courtine 28, which for the Counter-guard of an Heptagone comes to 196 Pieces of Artillery, and so the whole Work to 476; to which Ammunition being added proportionally, all other things necessary, the charge would be extraordinary. Answer. IN this my Fortification I want no more, or at least very few more Canon, than in the Modern; which I prove thus: In a Modern Heptagone there must be at least eight Pieces for every Bulwark, when a Siege is expected; namely 3 upon every Flanque, and two upon the Bulworks Point, that is 4 Demy-Canons, two Pelicans shooting a Bullet from 3 to 8 pound, and two half or whole Dragons as occasion requireth. Whereunto are commonly joined 4 or 6 whole Canon, to be used upon Counter-Batteries; these being reckoned together make up 56. It is an old custom, to keep in Fortresses that are considerable, twice as many Pieces in the Arsenal, as are upon the Wall, to fill up the places of those that shall happen to be Dismounted or to crack, or to become useless by any other accident; as also to be used upon the Crown, and Hornworks: This number is in all 188; which the Modern Engineers appoint in their Works. These I distribute in my Fortification, when there is no Siege, after this manner: Upon every middle Flanque of the great Wall two, and upon every Bulworks-point two, which is 6 for every Bulwark, and so for the Royal Work 42: In the Counter-guard none are required, but however, in case one would Plant them there, there might be set near every joining Halfmoon, two, which maketh 4 for every Courtine, that is 28 for seven Courtines, in all 70 Pieces; and then the place is furnished round about with Artillery, as well for the Inworks as Outworks. But instead of lodging these 28 Pieces upon the Flanques of the Counter-guards, I think it more convenient to use them upon the next Ravelin, because I keep there the outward Sentries, or Cors de Guards, which do Flanque the Counter-guards from within, and hit the Enemy from behind, in case he should undertake to pass the great Moat. But in time of Siege, I distribute my Canon quite otherwise, and do as follows. At the first coming on or surrounding, I take my lightest Canon and place them upon the points of the Counter-guards, to keep off the Enemy's Quarters, as far as it is possible; yet, the Quarters being closed, and I perceiving whereabout they open their Approaches, whether they bring on 2 or 3, although they make seldom more than two, and have sometimes a third, only for diversions sake: Admit, they carry on two Approaches, by which they intent to Attack two Bulworks; to promote these Approaches, it is needful for the Besiegers to raise Batteries, under whose favour they may make their Labourers work with more surety. Against these Batteries I raise Counter-batteries (that is, when they come near, within 150 or 200 Rod,) these Counter-batteries I can raise every where, as well in the outmost Ravelin before the Counter-guard, as upon the Faces of the Counter-guards themselves, whereto I use some heavy Pieces: upon the other Bulworks or Outworks there is then little need of any Pieces, but only of Falconets, or other small Guns. Now the Besiegers being after all difficulties, come so far with their Approaches, that they are ready to pass the Ditch of the Counter-guards, than I use not where any Pieces more to defend the Outworks, but only upon the Flanques of the Counter-guards, where in Fortresses according to the great Royal, might be used 14. Yet in case two Bulworks be Attacked at once, the Ditches and Faces may also be defended by two opposite Flanques, upon which two there must then be 28 Pieces. If three Bulworks be Attacked, there must be 42. These Pieces I can always retire again from the Flanques into the joining Ravelin, and from thence into the Fausse-bray of the great Wall, and further upon the Flanques of the great Wall, which are opposite to the Faces Attacked; and upon all occasions there need be no more upon these Flanques than 14, seeing the Enemy cannot place any more against them with advantage, but 10, unless they come to stand one in another's way. Suppose one would have 18 upon every Shoulder or Flanque, this would make 54 Canons for three Flanques, which being also trebled, the whole number amounts to 162. Whence it appeareth, That in my Fortification no more Canon is required than in the Modern; and one might in time of need very well make shift with a third part, that is with 54, in a Fortress of seven Bulworks, if a skilful Governor had the management of it: But for want of such men, the best Strong-Holds are soon lost; For let a place be Fortified with as much providence as it will, in case he who Commands it, has no skill, it signifieth nothing. iv Question. WHat may this way of Fortifying cost more than the Modern, seeing they are far larger in their parts; and much more is spent for the retired Flanques, than for the simple ones, as well to make the Shooting-holes, as also the paved Batteries: The Wall of the great Work, or of the Fortress must also needs be something higher, than that of the Modern, so it may command the better over the Wall of the Counter-guard; and with these Counter-guards much Field is also taken in, which is chargeable, in places where it must be bought from the Commonalty or Owners? Answer. THis Work being well considered, it will be found, that the charges differ little from the Modern: For I with my Pentagone take in as much or more place than the Modern with an Hexagone; my Line of Defence Fichante remaining still within Musquet-shot, whereby the charges of one whole Courtine and a Bulwark in a Pentagone are saved. Concerning the charges of the retired Flanques, against them I put the two Faces of the Modern Fausse-brays, which I do not make; as also the charges that are required for the digging of the Moat before the Courtine, where in my Fortification out of that part of the Moat nothing near so much Earth is taken. N. B. It is not necessary, that these Flanques should be brought presently into this order round about the Fortress, when they are made. One may make up the first paved Flanque of the great Wall, which falleth upon the Ground-line, something higher then usually, and lay 2 or 3 Benches behind the Parapet, and putting Palisadoes at the top of the Parapet, which come to be so high as the great Wall; and being Besieged, whilst the Outworks are disputed, there is time enough to bring all things into order. Concerning the great compass of the Counter-guards, the charges bestowed that way are little, seeing in time of Peace, (as is said before,) the enclosed Land and Wall, and all may serve for civil uses as well, as if these Walls were not there at all: Besides, that these being compared with the Modern Outworks, as Halfmoons, Horn and Crown-works, etc. as are about many Strong-Holds, it will be found, that these my Counter-guards do not enclose so much place, nor do not cost so much. It might be further said, that these my Fortresses would require more men for Defence than the Modern: In order whereunto, it is to be considered, How the Garrisons ought to be ordered in time of an Attacque? I shall only answer this, That the Outworks ought first to be Defended well; and to do that well in my Fortifications, no more men are required, than in one of the Modern, having but one Bulwark more than one of mine; for by my Method, I include more place with fewer Bulworks. I shall only tender this, That the Flanques being well furnished, the Fronts are easily defended; for herein consisteth the strength of Fortresses: which may be compared with a man that hath strong and long arms; it is evident, that such a one can better defend himself, than another who hath short and stiff arms. Thus I conclude this little Work, hoping that it will be acceptable to the Lovers; and stir them up, in case it do not please them, to bring to light something better. TO please those who desire to study Engineership, I have added an Abridgement, which shows how all Calculations necessary for this Science may be made with little pains, only by Decimals, without being subject to the intricacies of Fractions; as also the most usual manners of Working with ease, by Compasses, etc. Arithmetic in Decimals. THis Calculation doth not differ from the ordinary Method, only in the understanding of the Signs of the Fractions, and how to place them rightly, which is as follows: First take a Rod, (which is the usual measure of the Country where you are,) or what measure you please, and call that an Integer; this divide into ten equal parts, and take one part for a Foot; this Foot divide again into ten parts, and one of them take for an Inch; the Inch divide again into ten parts, and call one of them a Grain; the Grain divide again into ten, one of which call a first Scruple; and that divide again into ten, and let one of those parts be called a second Scruple; and so on to the tenth Scruple; which tenth Scruple is 1/10000000000 part of a Rod, and is so small, that it cannot be comprehended otherwise, than by understanding the following Signs: A Rod, or Integer, Foot, Inch, Grain, First Scruple, Second Scruple, ⓪ ① ② ③ ④ ⑤ Third Scruple, Fourth Scruple, Fifth Scruple, Sixth Scruple, ⑥ ⑦ ⑧ ⑨ and so on to the Ninth Scruple. Addition in Decimals. OBserve here the same manner, as in the Addition of Integers; but have a care, that the Signs of the Fractions of one sort, do stand under one another; as Rods under Rods, Inches under Inches, etc. Example. THere are to be added Rods, Feet, Inches, Grains, Scrup′. Scrup″. Scrup‴. ⓪ ① ② ③ ④ ⑤ ⑥ 2 3 4 7 0 2 3 to Rods; ⓪ ① ② ③ 89 2 3 4 I place then Rods under Rods, as 2 ⓪; under 89 ⓪, and the other Signs also under one anoother; as may be seen and where the Signs want, fill up the places with 0, and put the last Signs of the Fractions behind them in a crooked or round stroke; which showeth, how many places or kinds of Decimals there be, as is seen in the Example, and the Sum is 91. 581023 ⑥, that is, 91 Rods, 5 Foot, 8 Inches, 1 Grain, 0 First Scruple, 2 Second Scruple, etc. and the Sign of the Fractions being ⑥, therefore six Figures are to be counted from the last towards the left hand; and so many kinds of Decimals there be. Substraction in Decimals. PUt here also the Signs of one sort under one another; and where they fail, fill up the place with 0. Example. There are 56. 32 ② to be substracted from 982. 345 ③, therefore put 982. 345 ③, and 56. 32 ② underneath, so that 56.320 ③ Rods come to stand under Rods; so the remainder is 926. 025 ③, and so forth in all cases, fill the places of the Signs with 0, where they are not. Multiplication in Decimals. HEre follows also the common rule; but you must add the Signs of the Fractions together. Example. 53. 26 ② 4.3 21 ③ 53 26 10652 15978 21044 231 13646 ⑤ Division in Decimals. THis is also done the ordinary way; but here the Sigh of the Divisor must be substracted from the Signs of the Dividend, or the Number to be divided: and in case the Number to be divided, be less than that by which it must be divided, join so many 0 to it, till it come to be equal to it. Example. THere are 5.76 ② to be divided by 3482 ④; here the Divisor is greater than the Dividend; therefore add so many 0 to it, till it come to be as great or greater; as here 0000 Ciphers, and there will be 5. 670000 ⑥, this divide by 3482 ④, as is usual in common Divisions; and put the Signs as here is seen, & the Quotient is 165 ②; Now to know what kind of parts they be, subtract the Signs of the Fractions, as 4 from 6, and there remaineth 2, and this 2 is the Sign of the Quotient, as may be seen; and this is a general way: There remain yet 772, of which if you desire to have yet smaller parts; then put so many Ciphers behind it as you desire. N O T A. If you put one 0 behind it, or Multiply it by 10, that is all one; and by so doing it is brought to 10 lesser parts, etc. The Rule of Three in Decimals. THis is performed after the same manner, as in the Integers: and forasmuch as it consisteth of Multiplying and Dividing, observe the foregoing Rules. Example. The proof make thus: Say 7 ② giveth 116 ⓪, what then does 3 ④ give? There ariseth by Multiplication 348, to which adding 2 which remained, the whole is 350 ④ these divided by 7 ②, the Quotient 50 ②, and putting away the 0, as signifying nothing, there remaineth the sign ①, and then the Quotient is as above 5 ①, and the Work is right. To extract the Square Root in Decimals. TO find the Root of a Number given, even in its smaller parts, put after the Number given towards the right hand, as often two Ciphers, or 0 0, as you desire parts, and half the Number of the Ciphers is the Sign of the Fractions that belongs to the Root; as may be seen in the Example. Example. 20345, Out of this Number I desire to have the Square Root, to the second Scruple, or nearer; therefore I put as often two Ciphers to it, as I desire to have parts, as here 4; wherefore I join eight Ciphers to it, and work, as is usual in Integers; as may be seen here beneath. 1 28 0 1 10 68 67 31 1 7 81 24 31 78 19 2 03 48 00 00 00 00 ⑧ 1 4 2 6 3 5 9 ④ 22 88 48 22 67 0 22 88 55 2 22 8 The Root is 142 Rod, 6 Foot, 3 Inches, 5 Grains, and 9 First Scruples or tenth parts of Grains; the Signs of the joined Ciphers, or their Number is 8, the half of 8 is 4, which is the sign of the Fractions, and is written thus 142. 6359 ④, here remain yet 3119 parts: if you desire to have the Root still nearer, add again two Ciphers, as often as you desire to have smaller parts, etc. geometric figures To extract the Cube-root in Decimals, or Fractions. OPerate in the same manner, as in Integers, and look how many Fractions you desire, so often put 3 Ciphers behind it; and this wanteth no further declaration, etc. Having thus shown the Arithmetic in Decimals, I proceed to show some Draughts and Operations with the Compasses, which any one may use at pleasure. How a given Circle is to be divided into equal parts, and the Polygones of all Regular Figures, necessary for Fortification, are to be inscribed within it. LEt the given Circle be A, B, F, E, Numb. VIII. Fig. 1. through which draw the Diameter AB; and where it toucheth the Circumference, as in A and B, put one foot of the Compasses, and make the two Intersections, C and D; and from the Points, where they cut, draw a straight Line CD, falling Perpendicular upon the Diameter A, B: these two Lines A, B and C, D divide the Circle into four equally, and A, E is a side of a Square. Taking F for the Centre, and drawing at the distance F, G an Ark H, G, I, and then a right Line from H to I; where this Ark cutteth the Circumference, as H, I, this is a side of an Equilateral Triangle, which may be inscribed within this Circle. The half of this Line, as H, K, is a Polygone of an Heptagone, and the distance IB is the side of a Dodecagone; Take K for the Centre, and at the distance A, K describe the Ark A, L, the Line drawn from the Section L to A is a side of a Pentagone, the Line G, L is the side of a Decagone; G, N of an Hexagone; E and B are the Centres of the Arks G, M, which Line divideth the fourth part of the Circumference into two, and N, B is the side of an Octogone; divide the Ark H, F, I into three equal parts, and one third, as H, O is the side of an Enneagone; from L to P is the side of an Hendecagone; E, L is the Polygone of a Figure of 16 sides. Another way to find the Sides of every Regular Figure, that may be inscribed within a Circle. THis is done thus; Divide the Circumference into four equal parts, and then one fourth part of the Circle into so many equal parts, as the Figure should have sides; and take four of those parts, and that will be the length of the Polygone of such a Figure as you seek. Example. THe Circle Q, P, V, R, in the Plate Numb. VIII. Fig. 2. is first divided into four equal parts by the two Diameters Q, V, and P, R; ¼ part Q, P is divided into ten equal parts, four of those parts is the side of a Decagone, viz. the length K, P, which being set off ten times about the Circumference, describeth a Regular Decagone; after the same manner do with all other Figures, dividing always ¼ of the Circle into so many parts, as you desire sides; and four of these parts being taken with the Compasses, make up the side. This manner may be also proved by Arithmetic. N. B. In the making of Geometrical Figures, the Compasses ought always to be set perfectly upon the Lines, and marks made softly with the feet, to do the work with more perfection. There are many other ways, which we pass over for brevity sake. To divide a Line with the first opening of the Compasses, into as many parts as you desire. LEt the given Line be D, E, which you desire to divide into ten equal parts; therefore draw an undetermined Line B, H, and open the Compasses at pleasure, and with that opening set off as many parts upon the Line as you desire, (as here ten from B, to H;) so the tenth part reacheth to H; upon this Line B, H make an equilateral Triangle B, A, H, and from A draw the Lines AI, AK, ALL, AM, etc. Thus you have by the parts of the Line B, H, a Triangle, which is divided proportionally: then take with the Compasses the given Line D, E, and set it off from A to G, and also from A to P, and draw the Line P, G, equal to D, E, which by the intersecting Lines is divided into 10 equal parts; as also the Line F, G, if it be required, and so with all other Lines whatsoever. To let fall a Perpendicular upon a given Line. THe given Line is G, F, and upon the point G we let fall the Perpendicular G, H; therefore set one foot of the Compasses in G, and open th'other at pleasure, as here to I; from thence make the Circumference H, G, F; and where this cutteth the Line G, F, (as in F) from thence draw a Line just by the Centre, till it touch the Circumference in H, and from the Point H draw the Line H, G, which standeth rightangled or Perpendicular to G, F. There are many other ways, which I here omit for brevity sake. From a given Point in a Line, to raise a Perpendicular. THe given point is A, and the Line B, C, in Fig. 5. Set one foot of the Compasses in the point A, making with th'other the Ark B, C; upon these Points set one foot of the Compasses, opening th'other at pleasure, as to D, and make from these Points the intersection of the Arks in D, at the distance D, C, and draw a Line from the intersection by the given point A, to the Line B, C, which is Perpendicular to B, G. To make an Equilateral Triangle. UPon the Line B, H, in Fig. 6. set one foot of the Compasses in B, and with th'other take the distance B, H, and with that make an Ark about A; as also out of H: where these Arks intersect one another, there is the third Point of the Triangle; and draw from thence the Lines A B, and A H, and so the Triangle is made. To make a Triangle of three right Lines given, whatever they be, provided that two of them be longer than the third. THe Lines are AB, CD, OF; take with the Compasses the length of one of the three, which you would have to be the Base, (which is here A, B) and mark two Points, one in H, and th'other in L; from the Point L describe the length of the Line C, D with an Ark in K, and from H the length of the Line E, F, and cut the former Ark in K, and there is the third Point: from K draw the Line K, H, equal to E, F; K, L, equal to C, D; and L, H, equal to A, B, etc. Three Points being given, and not standing in a right Line, to draw a Circumference, which shall pass through all three. THe Points are O, P, Q; make the equal sections on both sides of the Centre, as from P and also from Q, which is done in V; as likewise from O, which falleth in 5, Perpendicular upon Q, P, and P, O. Where these touch one another, there is the Centre (as is seen in Fig. 7. Numb. VIII.) of the Circular Ark O, P, Q, which being drawn, etc. The same manner observe in the finding of the Centre of a Circular Ark, or a whole Circle. To divide a given Circle into 360 degrees, and to make an instrument from it which Geomemetricians call a Theodolit, or Astrolab. THis Instrument is of great use in the Mathematics; for by the same all inaccessible distances, heights and depths are measured, the use of which I shall declare in its own place in the following parts, and it is divided thus: The Circle A, B, C, D being first divided into four equal parts by the two Diameters A, B and C, D, take with your Compasses the exact length of the half Diameter; as A, E or E D, by which the Circle is divided into six equal parts, and after the manner following into 12; with this opening of the Compasses set one foot in C, and with th'other make upon the Circumference marks on both sides in F and G, likewise from D in H and L, etc. Thus the Circumference is divided exactly into 12 equal parts. The part D, A, or a quarter of a Circle, containeth 90 degrees, as a quarter of 360 degrees; F, C being a sixth part, 60 degrees; and D H as a twelfth part, 30 degrees; then divide a twelfth part, as D, H or D L into two, as in O and P, and such a part holdeth 15 degrees; then divide one of these parts into 3, and one of them will hold 5 degrees, of which one being exactly divided into 5, one of these is a degree, of which 360 make up the whole Circumference of every Circle, whether it be great or small, and are always proportional, viz. the least Circle that can be made, to the greatest Circle of the Sun, or any other Astronomical Circle: For if you draw several Circles out of one Centre, and from the same Centre several Semidiameters to the utmost Circle, the Arks intercepted in the innermost Circles contain as many degrees, as those in the outmost, etc. Each degree containeth 60 Minutes, a Minute 60 Seconds, a Second 60 Thirds, a Third 60 Fourths, and so on; and they are written thus, 4. ° 5. ′ 6. ″ 7. ‴ 8. ' ' ' ' which is as much, as 4 Degrees, 5 Min. 6 Seconds, 7 Thirds, 8 Fourths. How all kind of Ovals may be drawn by the Compasses, is to be seen by the marks 1, 2, 3, 4, 5, and needeth in my opinion no further declaration, seeing the manner of working appeareth enough by the Figures. By 6 is an Oval, which can be made by a Cord and 2 or 3 Nails: This manner is of much use in Architectura civili, to make obliqne Vaults. By 7 and 8 are seen two sorts of spiral Lines, whose structure may also be perceived by the Figures. And thus I have showed the principal Draughts with Compasses, serving for Geometrical use. END. For the Bookbinder, To place the Prints of the Copper-Plates. Numb. after Fol. II. 8 I. 12 III. 22 IU. 28 V. 30 VI. 34 VII. 36 VIII. 48 TABULA Numerorum QVADRATORVM Decies millium, unà cum ipsorum Lateribus ab Unitate incipientibus & ordine naturali usque ad 10000 progredientibus. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. Quadratus fit numero aliquo in se multiplicato, qui numerus Latus quadrati vocatur. DIOPHANTUS Lib. 1. Defin. 1. A TABLE Of Ten thousand SQUARE NUMBERS, Namely, Of all the Square Numbers between 0 and 100 Millions; And of their SIDES or ROOTS, Which are all the whole Numbers between 0 and Ten thousand. LONDON, Printed by Thomas Ratcliff, and Nath. Thompson, and are to be sold by Moses Pitt at the White Hart in Little Britain, 1672. A Table of whole Numbers, and their Squares. 0.. 1.. 2.. 3.. 4.. 5.. 6.. 7.. 8.. 9. 00 0 1 0000 4 0000 9 0000 16 0000 25 0000 36 0000 49 0000 64 0000 81 0000 01 1 1 0201 4 0401 9 0601 16 0801 25 1001 36 1201 49 1401 64 1601 81 1801 02 4 1 0404 4 0804 9 1204 16 1604 25 2004 36 2404 49 2804 64 3204 81 3604 03 9 1 0609 4 1209 9 1809 16 2409 25 3009 36 3609 49 4209 64 4809 81 5409 04 16 1 0816 4 1616 9 2416 16 3216 25 4016 36 4816 49 5616 64 6416 81 7216 05 25 1 1025 4 2025 9 3025 16 4025 25 5025 36 6025 49 7025 64 8025 81 9025 06 36 1 1236 4 2436 9 3636 16 4836 25 6036 36 7236 49 8436 64 9636 82 0836 07 49 1 1449 4 2849 9 4249 16 5649 25 7049 36 8449 49 9849 65 1249 82 2649 08 64 1 1664 4 3264 9 4864 16 6464 25 8064 36 9664 50 1264 65 2864 82 4464 09 81 1 1881 4 3681 9 5481 16 7281 25 9081 37 0881 50 2681 65 4481 82 6281 10 100 1 2100 4 4100 9 6100 16 8100 26 0100 37 2100 50 4100 65 6100 82 8100 11 121 1 2321 4 4521 9 6721 16 8921 26 1121 37 3321 50 5521 65 7721 82 9921 12 144 1 2544 4 4944 9 7344 16 9744 26 2144 37 4544 50 6944 65 9344 83 1744 13 169 1 2769 4 5369 9 7969 17 0569 26 3169 37 5769 50 8369 66 0969 83 3569 14 196 1 2996 4 5796 9 8596 17 1396 26 4196 37 6996 50 9796 66 2596 83 5396 15 225 1 3225 4 6225 9 9225 17 2225 26 5225 37 8225 51 1225 66 4925 83 7225 16 256 1 3456 4 6656 9 9856 17 3056 26 6256 37 9456 51 2656 66 5856 83 9056 17 289 1 3689 4 7089 10 0489 17 3889 26 7289 38 0689 51 4089 66 7489 84 0889 18 324 1 3924 4 7524 10 1124 17 4724 26 8324 38 1924 51 5524 66 9124 84 2724 19 361 1 4161 4 7961 10 1761 17 5561 26 9361 38 3161 51 6961 67 0761 84 4561 20 400 1 4400 4 8400 10 2400 17 6400 27 0400 38 4400 51 8400 67 2400 84 6400 21 441 1 4641 4 8841 10 3041 17 7241 27 1441 38 5641 51 9841 67 4041 84 8241 22 484 1 4884 4 9284 10 3684 17 8084 27 2484 38 6884 52 1284 67 5●●4 85 0084 23 529 1 5129 4 9729 10 4329 17 8929 27 3529 38 8129 52 2729 67 7●●9 85 1929 24 576 1 5376 5 0176 10 4976 17 9776 27 4576 38 9376 52 4176 67 8976 85 3776 25 625 1 5625 5 0625 10 5625 18 0625 27 5625 39 0625 52 5625 68 0625 85 5625 26 676 1 5876 5 1076 10 6276 18 1476 27 6676 39 1876 52 7076 68 2276 85 7476 27 729 1 6129 5 1529 10 6929 18 2329 27 7729 39 3129 52 8529 68 3929 85 9329 28 784 1 6384 5 1984 10 7584 18 3184 27 8784 39 4384 52 9984 68 5584 86 1184 29 841 1 6641 5 2441 10 8241 18 4041 27 9841 39 5641 53 1441 68 7241 86 3041 30 900 1 6900 5 2900 10 8900 18 4900 28 0900 39 6900 53 2900 68 8900 86 4900 31 961 1 7161 5 3361 10 9561 18 5761 28 1961 39 8161 53 4361 69 0561 86 6761 32 1024 1 7424 5 3824 11 0224 18 6624 28 3024 39 9424 53 5824 69 2224 86 8624 33 1089 1 7689 5 4289 11 0889 18 7489 28 4089 40 0689 53 7289 69 3889 87 0489 34 1156 1 7956 5 4756 11 1556 18 8356 28 5156 40 1956 53 8756 69 5556 87 2356 35 1225 1 8225 5 5225 11 2225 18 9225 28 6225 40 3225 54 0225 69 7225 87 4225 36 1296 1 8496 5 5696 11 2896 19 0096 28 7296 40 4496 54 1696 69 8896 87 6096 37 1369 1 8769 5 6169 11 3569 19 0969 28 8369 40 5769 54 3169 70 0569 87 7969 38 1444 1 9044 5 6644 11 4244 19 1844 28 9444 40 7044 54 4644 70 2244 87 9844 39 1521 1 9321 5 7121 11 4921 19 2721 29 0521 40 8321 54 6121 70 3921 88 1721 40 1600 1 9600 5 7600 11 5600 19 3600 29 1600 40 9600 54 7600 70 5600 88 3600 41 1681 1 9881 5 8081 11 6281 19 4481 29 2681 41 0881 54 9081 70 7281 88 5481 42 1764 2 0164 5 8564 11 6964 19 5364 29 3764 41 2164 55 0564 70 8964 88 7364 43 1849 2 0449 5 9049 11 7649 19 6249 29 4849 41 3449 55 2049 71 0649 88 9249 44 1936 2 07●6 5 9536 11 8336 19 7136 29 5936 41 4736 55 3536 71 2336 89 1136 45 2025 2 1025 6 0025 11 9025 19 8025 29 7025 41 6025 55 5025 71 4025 89 3025 46 2116 2 1316 6 0516 11 9716 19 8916 29 8116 41 7316 55 6516 71 5716 89 4916 47 2209 2 1609 6 1009 12 0409 19 9809 29 9209 41 8609 55 8009 71 7409 89 6809 48 2304 2 1904 6 1504 12 1104 20 0704 30 0304 41 9904 55 9504 71 9104 89 8704 49 2401 2 2201 6 2001 12 ●801 20 1601 30 1401 42 1201 56 1001 72 0801 90 0601 50 2500 2 2500 6 2500 12 2500 20 2500 30 2500 42 2500 56 2500 72 2500 90 2500 51 2601 2 2801 6 3001 12 3201 20 3401 30 3601 42 3801 56 4001 72 4201 90 4401 52 2704 2 3104 6 3504 12 3904 20 4304 30 4704 42 5104 56 5504 72 5904 90 6304 53 2809 2 3409 6 4009 12 4609 20 5209 30 5809 42 6409 56 7009 72 7609 90 8209 54 2916 2 3716 6 4516 12 5316 20 6116 30 6916 42 7716 56 8516 72 9316 91 0116 55 3025 2 4025 6 5025 12 6025 20 7025 30 8025 42 9025 57 0025 73 1025 91 2025 56 3136 2 4336 6 5536 12 6736 20 7936 30 9136 43 0336 57 1536 73 2736 91 3936 57 3249 2 4649 6 6049 12 7449 20 8849 31 0249 43 1649 57 3049 73 4449 91 5849 58 3364 2 4964 6 6564 12 8164 20 9764 31 1364 43 2964 57 4564 73 6164 91 7764 59 3481 2 5281 6 7081 12 8881 21 0681 31 2481 43 4281 57 6081 73 7881 91 9681 60 3600 2 5600 6 7600 12 9600 21 1600 31 3600 43 5600 57 7600 73 9600 92 1600 61 3721 2 5921 6 8121 13 0321 21 2521 31 4721 43 6921 57 9121 74 1321 92 3521 62 3844 2 6244 6 8644 13 1044 21 3444 31 5844 43 8244 58 0644 74 3044 92 5444 63 3969 2 6569 6 9169 13 1769 21 4369 31 6969 43 9569 58 2169 74 4769 92 7369 64 4096 2 6896 6 9696 13 2496 21 5296 31 8096 44 0896 58 3696 74 6496 92 9296 65 4225 2 7225 7 0225 13 3225 21 6225 31 9225 44 2225 58 5225 74 8225 93 1225 66 4356 2 7556 7 0756 13 3956 21 7156 32 0356 44 3556 58 6756 74 9956 93 3156 67 4489 2 7889 7 1289 13 4689 21 8089 32 1489 44 4889 58 8289 75 1689 93 5089 68 4624 2 8224 7 1824 13 5424 21 9024 32 2624 44 6224 58 9824 75 3424 93 7024 69 4761 2 8561 7 2361 13 6161 21 9961 32 3761 44 7561 59 1361 75 5161 93 8961 70 4900 2 8900 7 2900 13 6900 22 0900 32 4900 44 8900 59 2900 75 6900 94 0900 71 5041 2 9241 7 3441 13 7641 22 1841 32 6041 45 0241 59 4441 75 8641 94 2841 72 5184 2 9584 7 3984 13 8384 22 2784 32 7184 45 1584. 59 5984 76 0384 94 4784 73 5329 2 9929 7 4529 13 9129 22 3729 32 8329 45 2929 59 7529 76 2129 94 6729 74 5476 3 0276 7 5076 13 9876 22 4676 32 9476 45 4276 59 9076 76 3876 94 8676 75 5625 3 0625 7 5625 14 0625 22 5625 33 0625 45 5625 60 0625 76 5625 95 0625 76 5776 3 0976 7 6176 14 1376 22 6576 33 1776 45 6976 60 2176 76 7376 95 2576 77 5929 3 1329 7 6729 14 2129 22 7529 33 2929 45 8329 60 3729 76 9129 95 4529 78 6084 3 1684 7 7284 14 2884 22 8484 33 4084 45 9684 60 5284 77 0884 95 6484 79 6241 3 2041 7 7841 14 3641 22 9441 33 5241 46 1041 60 6841 77 2641 95 8441 80 6400 3 2400 7 8400 14 4400 23 0400 33 6400 46 2400 60 8400 77 4400 96 0400 81 6561 3 2761 7 8961 14 5161 23 1361 33 7561 46 3761 60 9961 77 6161 96 2361 82 6724 3 3124 7 9524 14 5924 23 2324 33 8724 46 5124 61 1524 77 7924 96 4324 83 6889 3 3489 8 0089 14 6689 23 3289 33 9889 46 6489 61 3089 77 9689 96 6289 84 7056 3 3856 8 0656 14 7456 23 4256 34 1056 46 7856 61 4656 78 1456 96 8256 85 7225 3 4225 8 1225 14 8225 23 5225 34 2225 46 9225 61 6225 78 3225 97 0225 86 7396 3 4596 8 1796 14 8996 23 6196 34 3396 47 0596 61 7796 78 4996 97 2196 87 7569 3 4969 8 2369 15 9769 23 7169 34 4569 47 1969 61 9369 78 6769 97 4169 88 7744 3 5344 8 2944 15 0544 23 8144 34 5744 47 3344 62 0944 78 8544 97 6144 89 7921 3 5721 8 3521 15 1321 23 9121 34 6921 47 4721 62 2521 79 0321 97 8121 90 8100 3 6100 8 4100 15 2100 24 0100 34 8100 47 6100 62 4100 79 2100 98 0100 91 8281 3 6481 8 4681 15 2881 24 1081 34 9281 47 7481 62 5681 79 3881 98 2081 92 8464 3 6864 8 5264 15 3664 24 2064 35 0464 47 8864 62 7264 79 5664 98 4064 93 8649 3 7249 8 5849 15 4449 24 3049 35 1649 48 0249 62 8849 79 7449 98 6049 94 8836 3 7636 8 6436 15 5236 24 4036 35 2836 48 1636 63 0436 79 9236 98 8036 95 9025 3 8025 8 7025 15 6025 24 5025 35 4025 48 3025 63 2025 80 1025 99 0025 96 9216 3 8416 8 7616 15 6816 24 6016 35 5216 48 4416 63 3616 80 2816 99 2016 97 9409 3 8809 8 8209 15 7609 24 7009 35 6409 48 5809 63 5209 80 4609 99 4009 98 9604 3 9204 8 8804 15 8404 24 8004 35 7604 48 7204 63 6804 80 6404 99 6004 99 9801 3 9601 8 9401 15 9201 24 9001 35 8801 48 8601 63 8401 80 8201 99 8001 10.. 11.. 12.. 13.. 14.. 15.. 16.. 17.. 00 100 0000 121 0000 144 0000 169 0000 196 0000 225 0000 256 0000 289 000 01 100 2001 121 2201 144 2401 169 2601 196 2801 225 3001 256 3201 289 3401 02 100 4004 121 4404 144 4804 169 5204 196 5604 225 6004 256 6404 289 6804 03 100 6009 121 6609 144 7209 169 7809 196 8409 225 9009 256 9609 290 0209 04 100 8016 121 8816 144 9616 170 0416 197 1216 226 2016 257 2816 290 3616 05 101 0025 122 1025 145 2025 170 3025 197 4025 226 5025 257 6025 290 7025 06 101 2036 122 3236 145 4436 170 5636 197 6836 226 8036 257 9236 291 0436 07 101 4049 122 5449 145 6849 170 8249 197 9649 227 1049 258 2449 291 3849 08 101 6064 122 7664 145 9264 171 0864 198 2464 227 4064 258 5664 291 7264 09 101 8081 122 9881 146 1681 171 3481 198 5281 227 7081 258 8881 292 0681 10 102 0100 123 2100 146 4100 171 6100 198 8100 228 0100 259 2100 292 4100 11 102 2121 123 4321 146 6521 171 8721 199 0921 228 3121 259 5321 292 7521 12 102 4144 123 6544 146 8944 172 1344 199 3744 228 6144 259 8544 293 0944 13 102 6169 123 8769 147 1369 172 3969 199 6569 228 9169 260 1769 293 4369 14 102 8196 124 0996 147 3796 172 6596 199 9396 229 2196 260 4996 293 7796 15 103 0225 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6556 1409 6719 0809 98 5772 9604 5925 9204 6080 8804 6237 8404 6396 8004 6557 7604 6720 7204 99 5774 4801 5927 4601 6082 4401 6239 4201 6398 4001 6559 3801 6722 3601 82.. 83.. 84.. 85.. 86.. 87.. 88. 00 6724 0000 6889 0000 7056 0000 7225 0000 7396 0000 7569 0000 7744 0000 01 6725 6401 6890 6601 7057 6801 7226 7001 7397 7201 7570 7401 7745 7601 02 6727 2804 6892 3204 7059 3604 7228 4004 7399 4404 7572 4804 7747 5204 03 6728 9209 6893 9809 7061 0409 7230 1009 7401 1609 7574 2209 7749 2809 04 6730 5616 6895 6416 7062 7216 7231 8016 7402 8816 7575 9616 7751 0416 05 6732 2025 6897 3025 7064 4025 7233 5025 7404 6025 7577 7025 7752 8025 06 6733 8436 6898 9636 7066 0836 7235 2036 7406 3236 7579 4436 7754 5636 07 6735 4849 6900 6249 7067 7649 7236 9049 7408 0449 7581 1849 7756 3249 08 6737 1264 6902 2864 7069 4464 7238 6064 7409 7664 7582 9264 7758 0864 09 6738 7681 6903 9481 7071 1281 7240 3081 7411 4881 7584 6681 7759 8481 10 6740 4100 6905 6100 7072 8100 7242 0100 7413 2100 7586 4100 7761 6100 11 6742 0521 6907 2721 7074 4921 7243 7121 7414 9321 7588 1521 7763 3721 12 6743 6944 6908 9344 7076 1744 7245 4144 7416 6544 7589 8944 7765 1344 13 6745 3369 6910 5969 7077 8569 7247 1169 7418 3769 7591 6369 7766 8969 14 6746 9796 6912 2596 7079 5396 7248 8196 7420 0996 7593 3796 7768 6596 15 6748 6225 6913 9225 7081 2225 7250 5225 7421 8225 7595 1225 7770 4225 16 6750 2656 6915 5856 7082 9056 7252 2256 7423 5456 7596 8656 7772 1856 17 6751 9089 6917 2489 7084 5889 7253 9289 7425 2689 7598 6089 7773 9489 18 6753 5524 6918 9124 7086 2724 7255 6324 7426 9924 7600 3524 7775 7124 19 6755 1961 6920 5761 7087 9561 7257 3361 7428 7161 7602 0961 7777 4761 20 6756 8400 6922 2400 7089 6400 7259 0400 7430 4400 7603 8400 7779 2400 21 6758 4841 6923 9041 7091 3241 7260 7441 7432 1641 7605 5841 7781 0041 22 6760 1284 6925 5684 7093 0084 7262 4484 7433 8884 7607 3284 7782 7684 23 6761 7729 6927 2329 7094 6929 7264 1529 7435 6129 7609 0729 7784 5329 24 6763 4176 6928 8976 7096 3776 7265 8576 7437 3376 7610 8176 7786 2976 25 6765 0625 6930 5625 7098 0625 7267 5625 7439 0625 7612 5625 7788 0625 26 6766 7076 6932 2276 7099 7476 7269 2676 7440 7876 7614 3076 7789 8276 27 6768 3529 6933 8929 7101 4329 7270 9729 7442 5129 7616 0529 7791 5929 28 6769 9984 6935 5584 7103 1184 7272 6784 7444 2384 7617 7984 7793 3584 29 6771 6441 6037 2241 7104 8041 7274 3841 7445 9641 7619 5441 7795 1241 30 6773 2900 6938 8900 7106 4900 7276 0900 7447 6900 7621 2900 7796 8900 31 6774 9361 6940 5561 7108 1761 7277 7961 7449 4161 7623 0361 7798 6561 32 6776 5824 6942 2224 7109 8624 7279 5024 7451 1424 7624 7824 7800 4224 33 6778 2289 6943 8889 7111 5489 7281 2089 7452 8689 7626 5289 7802 1889 34 6779 8756 6945 5556 7113 2356 7282 9156 7454 5956 7628 2756 7803 9556 35 6781 5225 6947 2225 7114 9225 7284 6225 7456 3225 7630 0225 7805 7225 36 6783 1696 6948 8896 7116 6096 7286 3296 7458 0496 7631 7696 7807 4896 37 6784 8169 6950 5569 7118 2969 7288 0369 7459 7769 7633 5169 7809 2569 38 6786 4644 6952 2244 7119 9844 7289 7444 7461 5044 7635 2644 7811 0244 39 6788 1121 6953 8921 7121 6721 7291 4521 7463 2321 7637 0121 7812 7921 40 6789 7600 6955 5600 7123 3600 7293 1600 7464 9600 7638 7600 7814 5600 41 6791 4081 6957 2281 7125 0481 7294 8681 7466 6881 7640 5081 7816 3281 42 6793 0564 6958 8964 7126 7364 7296 5764 7468 4164 7642 2564 7818 0964 43 6794 7049 6960 5649 7128 4249 7298 2849 7470 1449 7644 0049 7819 8649 44 6796 3536 6962 2336 7130 1136 7299 9936 7471 8736 7645 7536 7821 6336 45 6798 0025 6963 9025 7131 8025 7301 7025 7473 6025 7647 5025 7823 4025 46 6799 6516 6965 5716 7133 4916 7303 4116 7475 3316 7649 2516 7825 1716 47 6801 3009 6967 2409 7135 1809 7305 1209 7477 0609 7651 0009 7826 9409 48 6802 9504 6968 9104 7136 8704 7306 8304 7478 7904 7652 7504 7828 7104 49 6804 6001 6970 5801 7138 5601 7308 5401 7480 5201 7654 5001 7830 4801 50 6806 2500 6972 2500 7140 2500 7310 2500 7482 2500 7656 2500 7832 2500 51 6807 9001 6973 9201 7141 9401 7311 9601 7483 9801 7658 0001 7834 0201 52 6809 5504 6975 5904 7143 6304 7313 6704 7485 7104 7659 7504 7835 7904 53 6811 2009 6977 2609 7145 3209 7315 3809 7487 4409 7661 5009 7837 5609 54 6812 8516 6978 9316 7147 0116 7317 0916 7789 1716 7663 2516 7839 3316 55 6814 5025 6980 6025 7148 7025 7318 8025 7490 9025 7665 0025 7841 1025 56 6816 1536 6982 2736 7150 3936 7320 5136 7492 6336 7666 7536 7842 8736 57 6817 8049 6983 9449 7152 0849 7322 2249 7494 3649 7668 5049 7844 6449 58 6819 4564 6985 6164 7153 7764 7323 9364 7496 0964 7670 2564 7846 4164 59 6821 1081 6987 2881 7155 4681 7325 6481 7497 8281 7672 0081 7848 1881 60 6822 7600 6988 9600 7157 1600 7327 3600 7499 5600 7673 7600 7849 9600 61 6824 4121 6990 6321 7158 8521 7329 0721 7501 2921 7675 5121 7851 7321 62 6826 0644 6992 3044 7160 5444 7330 7844 7503 0244 7677 2644 7853 5044 63 6827 7169 6993 9769 7162 2369 7332 4969 7504 7569 7679 0169 7855 2769 64 6829 3696 6995 6496 7163 9296 7334 2096 7506 4896 7680 7696 7857 0496 65 6831 0225 6997 3225 7165 6225 7335 9225 7508 2225 7682 5225 7858 8225 66 6832 6756 6998 9956 7167 3156 7337 6356 7509 9556 7684 2756 7860 5956 67 6834 3289 7000 6689 7169 0089 7339 3489 7511 6889 7686 0289 7862 3689 68 6835 9824 7002 3424 7170 7024 7341 0624 7513 4224 7687 7824 7864 1424 69 6837 6361 7004 0161 7172 3961 7342 7761 7515 1561 7689 5361 7865 9161 70 6839 2900 7005 6900 7174 0900 7344 4900 7516 8900 7691 2900 7867 6900 71 6840 9441 7007 3641 7175 7841 7346 2041 7518 6241 7693 0441 7869 4641 72 6842 5984 7009 0384 7177 4784 7347 9184 7520 3584 7694 7984 7871 2384 73 6844 2529 7010 7129 7179 1729 7349 6329 7522 0929 7696 5529 7873 0129 74 6845 9076 7012 3876 7180 8676 7351 3476 7523 8276 7698 3076 7874 7876 75 6847 5625 7014 0625 7182 5625 7353 0625 7525 5625 7700 0625 7876 5025 76 6849 2176 7015 7376 7184 2576 7354 7776 7527 2976 7701 8176 7878 3376 77 6850 8729 7017 4129 7185 9529 7356 4929 7529 0329 7703 5729 7880 1129 78 6852 5284 7019 0884 7187 6484 7358 2084 7530 7684 7705 3284 7881 8884 79 6854 1841 7020 7641 7189 3441 7359 9241 7532 5041 7707 0841 7883 6641 80 6855 8400 7022 4400 7191 0400 7361 6400 7534 2400 7708 8400 7885 4400 81 6857 4961 7024 1161 7192 7361 7363 3561 7535 9761 7710 5961 7887 2161 82 6859 1524 7025 7924 7194 4324 7365 0724 7537 7124 7712 3524 7888 9924 83 6860 8089 7027 4689 7196 1289 7366 7889 7539 4489 7714 1089 7890 7689 84 6862 4656 7029 1456 7197 8256 7368 5056 7541 1856 7715 8656 7892 5456 85 6864 1225 7030 8225 7199 5225 7370 2225 7542 9225 7717 6225 7894 3225 86 6865 7796 7032 4996 7201 2196 7371 9396 7544 6596 7719 3796 7896 0996 87 6867 4369 7034 1769 7202 9169 7373 6569 7546 3969 7721 1369 7897 8769 88 6869 0944 7035 8544 7204 6144 7375 3744 7548 1344 7722 8944 7899 6544 89 6870 7521 7037 5321 7206 3121 7377 0921 7549 8●21 7724 6521 7901 4321 90 6872 4100 7039 2100 7208 0100 7378 8100 7551 6100 7726 4100 7903 2100 91 6874 0681 7070 8881 7209 7081 7380 5281 7553 3481 7728 1681 7904 9881 92 6875 7264 7042 5664 7211 4064 7382 2464 7555 0864 7729 9264 7906 7664 93 6877 3849 7044 2449 7213 1049 7383 9649 7556 8249 7731 6849 7908 5449 94 6879 0436 7045 9236 7214 8036 7385 6836 7558 5636 7733 4436 7910 3236 95 6880 7025 7047 6025 7216 5025 7387 4025 7560 3025 7735 2025 7912 1025 96 6882 3616 7049 2816 7218 2016 7389 1216 7562 0416 7736 9616 7913 8816 97 6884 0209 7050 9609 7219 9009 7390 8409 7563 7809 7738 7209 7915 6609 98 6885 6804 7052 6404 7221 6004 7392 5604 7565 5204 7740 4804 7917 4404 99 6887 3401 7054 3201 7223 3001 7394 2801 7567 2601 7742 2401 7919 2201 89.. 90.. 91.. 92.. 93.. 94.. 95.. 00 7921 0000 8100 0000 8281 0000 8464 0000 8649 0000 8836 0000 9025 0000 01 7922 7801 8101 8001 8282 8201 8465 8401 8650 8601 8837 8801 9026 9001 02 7924 5604 8103 6004 8284 6404 8467 6804 8652 7204 8839 7604 9028 8004 03 7926 3409 8105 4009 8286 4609 8469 5209 8654 5809 8841 6409 9030 7009 04 7928 1216 8107 2016 8288 2816 8471 3616 8656 4416 8843 5216 9032 6016 05 7929 9025 8109 0025 8290 1025 8473 2025 8658 3025 8845 4025 9034 5025 06 7931 6836 8110 8036 8291 9236 8475 0436 8660 1636 8847 2836 9036 4036 07 7933 4649 8112 6049 8293 7449 8476 8849 8662 0249 8849 1649 9038 3049 08 7935 2464 8114 4064 8295 5664 8478 7264 8663 8864 8851 0464 9040 2064 09 7937 0281 8116 2081 8297 3881 8480 5681 8665 7481 8852 9281 9042 1081 10 7938 8100 8118 0100 8299 2100 8482 4100 8667 6100 8854 8100 9044 0100 11 7940 5921 8119 8121 8301 0321 8484 2521 8669 4721 8856 6921 9045 9121 12 7942 3744 8121 6144 8302 8544 8486 0944 8671 3344 8858 5744 9047 8144 13 7944 1569 8123 4169 8304 6769 8487 9369 8673 1969 8860 4569 9049 7169 14 7945 9396 8125 2196 8306 4996 8489 7796 8675 0596 8862 3396 9051 6196 15 7947 7225 8127 0225 8308 3225 8491 6225 8676 9225 8864 2225 9053 5225 16 7949 5056 8128 8256 8310 1456 8493 4656 8678 7856 8866 1056 9055 4256 17 7951 2889 8130 6289 8311 9689 8495 3089 8680 6489 8867 9889 9057 3289 18 7953 0724 8132 4324 8313 7924 8497 1524 8682 5124 8869 8724 9059 2324 19 7954 8561 8134 2361 8315 6161 8498 9961 8684 3761 8871 7561 9061 1361 20 7956 6400 8136 0400 8317 4400 8500 8400 8686 2400 8873 6400 9063 0400 21 7958 4241 8137 8441 8319 2641 8502 6841 8688 1041 8875 5241 9064 9441 22 7960 2084 8139 6484 8321 0884 8504 5284 8689 9684 8877 4084 9066 8484 23 7961 9929 8141 4529 8322 9129 8506 3729 8691 8329 8879 2929 9068 7529 24 7963 7776 8143 2576 8324 7376 8508 2176 8693 6976 8881 1776 9070 6576 25 7965 5625 8145 0625 8326 5625 8510 0625 8695 5625 8883 0625 9072 5625 26 7967 3476 8146 8676 8328 3876 8511 9076 8697 4276 8884 9476 9074 4676 27 7969 1329 8148 6729 8330 2129 8513 7529 8699 2929 8886 8329 9076 3729 28 7970 9184 8150 4784 8332 0384 8515 5984 8701 1584. 8888 7184 9078 2784 29 7972 7041 8152 2841 8333 8641 8517 4441 8703 0241 8890 6041 9080 1841 30 7974 4900 8154 0900 8335 6900 8519 2900 8704 8900 8892 4900 9082 0900 31 7976 2761 8155 8961 8337 5161 8521 1361 8706 7561 8894 3761 9083 9961 32 7978 0624 8157 7024 8339 3424 8522 9824 8708 6224 8896 2624 9085 9024 33 7979 8489 8159 5089 8341 1689 8524 8289 8710 4889 8898 1489 9087 8089 34 7981 6356 8161 3156 8342 9956 8526 6756 8712 3556 8900 0356 9089 7156 35 7983 4225 8163 1225 8344 8225 8528 5225 8714 2225 8901 9225 9091 6225 36 7985 2096 8164 9296 8346 6496 8530 3696 8716 0896 8903 8096 9093 5296 37 7986 9969 8166 7369 8348 4769 8532 2169 8717 9569 8905 6969 9095 4369 38 7988 7844 8168 5444 8350 3044 8534 0644 8719 8244 8907 5844 9097 3444 39 7990 5721 8170 3521 8352 1321 8535 9121 8721 6921 8909 4721 9099 2521 40 7992 3600 8172 1600 8353 9600 8537 7600 8723 5600 8911 3600 9101 1600 41 7994 1481 8173 9681 8355 7881 8539 6081 8725 4281 8913 2481 9103 0681 42 7995 9364 8175 7764 8357 6164 8541 4564 8727 2964 8915 1364 9104 9764 43 7997 7249 8177 5849 8359 4449 8543 3049 8729 1649 8917 0249 9106 8849 44 7999 5136 8179 3936 8361 2736 8545 1536 8731 0336 8918 9136 9108 7936 45 8001 3025 8181 2025 8363 1025 8547 0025 8732 9025 8920 8025 9110 7025 46 8003 0916 8183 0116 8364 9316 8548 8516 8734 7716 8922 6916 9112 6116 47 8004 8809 8184 8209 8366 7609 8550 7009 8736 6409 8924 5809 9114 5209 48 8006 6704 8186 6304 8368 5904 8552 5504 8738 5104 8926 4704 9116 4304 49 8008 4601 8188 4401 8370 4201 8554 4001 8740 3801 8928 3601 9118 3401 50 8010 2500 8190 2500 8372 2500 8556 2500 8742 2500 8930 2500 9120 2500 51 8012 0401 8192 0601 8374 0801 8558 1001 8744 1201 8932 1401 9122 1601 52 8013 8304 8193 8704 8375 9104 8559 9504 8745 9904 8934 0304 9124 0704 53 8015 6209 8195 6809 8377 7409 8561 8009 8747 8609 8935 9209 9125 9809 54 8017 4116 8197 4916 8379 5716 8563 6516 8749 7316 8937 8116 9127 8916 55 8019 2025 8199 3025 8381 4025 8565 5025 8751 6025 8939 7025 9129 8025 56 8020 9936 8201 1136 8383 2336 8567 3536 8753 4736 8941 5936 9131 7136 57 8022 7849 8202 9249 8385 0649 8569 2049 8755 3449 8943 4849 9133 6249 58 8024 5764 8204 7364 8386 8964 8571 0564 8757 2164 8945 3764 9135 5364 59 8026 3681 8206 5481 8388 7281 8572 9081 8759 0881 8947 2681 9137 4481 60 8028 1600 8208 3600 8390 5600 8574 7600 8760 9600 8949 1600 9139 3600 61 8029 9521 8210 1721 8392 3921 8576 6121 8762 8321 8951 0521 9141 2721 62 8031 7444 8211 9844 8394 2244 8578 4644 8764 7044 8952 9444 9143 1844 63 8033 5369 8213 7969 8396 0569 8580 3169 8766 5769 8954 8369 9145 0969 64 8035 3296 8215 6096 8397 8896 8582 1696 8768 4496 8956 7296 9147 0096 65 8037 1225 8217 4225 8399 7225 8584 0225 8770 3225 8958 6225 9148 9225 66 8038 9156 8219 2356 8401 5556 8585 8756 8772 1956 8960 5156 9150 8356 67 8040 7089 8221 0489 8403 3889 8587 7289 8774 0689 8962 4089 9152 7489 68 8042 5024 8222 8624 8405 2224 8589 5824 8775 9424 8964 3024 9154 6624 69 8044 2961 8224 6761 8407 0561 8591 4361 8777 8161 8966 1961 9156 5761 70 8046 0900 8226 4900 8408 8900 8593 2900 8779 6900 8968 0900 9158 4900 71 8047 8841 8228 3041 8410 7241 8595 1441 8781 5641 8969 9841 9160 4041 72 8049 6784 8230 1184 8412 5584 8596 9984 8783 4384 8971 8784 9162 3184 73 8051 4729 8231 9329 8414 3929 8598 8529 8785 3129 8973 7729 9164 2329 74 8053 2676 8233 7476 8416 2276 8600 7076 8787 1876 8975 6676 9166 1476 75 8055 0625 8235 5625 8418 0625 8602 5625 8789 0625 8977 5625 9168 0625 76 8056 8576 8237 3776 8419 8976 8604 4176 8790 9376 8979 4576 9169 9776 77 8058 6529 8239 1929 8421 7329 8606 2729 8792 8129 8981 3529 9171 8929 78 8060 4484 8241 0084 8423 5684 8608 1284 8794 6884 8983 2484 9173 8084 79 8062 2441 8242 8241 8425 4041 8609 9841 8796 5641 8985 1441 9175 7241 80 8064 0400 8244 6400 8427 2400 8611 8400 8798 4400 8987 0400 9177 6400 81 8065 8361 8246 4561 8429 0761 8613 6961 8800 3161 8988 9361 9179 5561 82 8067 6324 8248 2724 8430 9124 8615 5524 8802 1924 8990 8324 9181 4724 83 8069 4289 8250 0889 8432 7489 8617 4089 8804 0689 8992 7289 9183 3889 84 8071 2256 8251 9056 8434 5856 8619 2656 8805 9456 8994 6256 9185 3056 85 8073 0225 8253 7225 8436 4225 8621 1225 8807 8225 8996 5225 9187 2225 86 8074 8196 8255 5396 8438 2596 8622 9796 8809 6996 8998 4196 9189 1396 87 8076 6169 8257 3569 8440 0969 8624 8369 8811 5769 9000 3169 9191 0569 88 8078 4144 8259 1744 8441 9344 8626 6944 8813 4544 9002 2144 9192 9744 89 8080 2121 8260 9921 8443 7721 8628 5521 8815 3321 9004 1121 9194 8921 90 8082 0100 8262 8100 8445 6100 8630 4100 8817 2100 9006 0100 9196 8100 91 8083 8081 8264 6281 8447 4481 8632 2681 8819 0881 9007 9081 9198 7281 92 8085 6064 8266 4464 8449 2864 8634 1264 8820 9664 9009 8064 9200 6464 93 8087 4049 8268 2649 8451 1249 8635 9849 8822 8449 9011 7049 9202 5649 94 8089 2036 8270 0836 8452 9636 8637 8436 8824 7236 9013 6036 9204 4836 95 8091 0025 8271 9025 8454 8025 8639 7025 8826 6025 9015 5025 9206 4025 96 8092 8016 8273 7216 8456 6416 8641 5616 8828 4816 9017 4016 9208 3216 97 8094 6009 8275 5409 8458 4809 8643 4209 8830 3609 9019 3009 9210 2409 98 8096 4004 8277 3604 8460 3204 8645 2804 8832 2404 9021 2004 9212 1604 99 8098 2001 8279 1801 8462 1601 8647 1401 8834 1201 9023 1001 9214 ●801 96.. 97.. 98.. 99. In this Table, To find the Square of any Whole Number less than Ten Thousand. 2. To find the Side of any Square Number less than 100 Millions Imitate these following Examples. I desire the Square of 9738; That is, of 9700 and 38. (For so every Side in this Table is parted into two Portions.) A Column bearing 97.. on the head of it, is found only in this 28. Page, and another in the 29. In the Margin of this 28. pag. I find 38. A right Line running from this 38, crosseth the column marked 97.. at the number 94828644. This 94828644 is the Square of 9738. But the Square of 9756 is not found in this pag. because 56 more than 49. In the margin of pag. 29, I find 56. A right line, running from this 56, showeth you the number 95179536, in the column on whofe top stands 97.. This 95179536 is the Square of 9756. Thus in p. 24, you see 67551961 in the right Line running from the Marg. 19, to the column whose Vertical is 82.. Then say, 67551961 is the Square of 8219. And so I find 70829056 to be the Square of 8416. In pag. 9 you have 7080921 the Square of 2661. And in pag. 2, you have 675684 the Square of 822. As in pag. 3, you find 70756 the Square of 266. That First opening, in Pag. 2. & Pag. 3, contains all Square Numbers less than a Million, and all Sides less than 1000 And the first Column of those two Pages [2 and 3] hath the Square of every Number less than 100; That is to say, It hath all square numbers less than 10000 Wherefore the Square number 62821476 being given, and its Side being sought, you may cut off the two last Figures [76] and may find all the rest of the Figures in that First Opening; thus, Pag. 2. 62 is the Square of 7 and more. Pag. 3. 6282 is the Square of 79 † Pag. 3. 628214. is the Square of 792 † This sends you to seek a Column, whose head bears 79 which is in Pag. 22. and 23. In Pag. 22. you may find the entire number 62821476. to be the Square of 7926. 00 9216 0000 9409 0000 9604 0000 9801 0000 01 9217 9201 9410 9401 9605 9601 9802 9801 02 9219 8404 9412 8804 9607 9204 9804 9604 03 9221 7609 9414 8209 9609 8809 9806 9409 04 9223 6816 9416 7616 9611 8416 9808 9216 05 9225 6025 9418 7025 9613 8025 9810 9025 06 9227 5236 9420 6436 9615 7636 9812 8836 07 9229 4449 9422 5849 9617 7249 9814 8649 08 9231 3664 9424 5264 9619 6864 9816 8464 09 9233 2881 9426 4681 9621 6481 9818 8281 10 9235 2100 9428 4100 9623 6100 9820 8100 11 9237 1321 9430 3521 9625 5721 9822 7921 12 9239 0544 9432 2944 9627 5344 9824 7744 13 9240 9769 9434 2309 9629 4969 9826 7569 14 9242 8996 9436 1796 9631 4596 9828 7396 15 9244 8225 9438 1225 9633 4225 9830 7225 16 9246 7456 9440 0656 9635 3856 9832 7056 17 9248 6689 9442 0089 9637 3489 9834 6889 18 9250 5924 9443 9524 9639 3124 9836 6724 19 9252 5161 9445 8961 9641 2761 9838 6561 20 9254 4400 9447 8400 9643 2400 9840 6400 21 9256 3641 9449 7841 9645 2041 9842 6241 22 9258 2884 9451 7284 9647 1684 9844 6084 23 9260 2129 9453 6729 9649 1329 9846 5929 24 9262 1376 9455 6176 9651 0976 9848 5776 25 9264 0625 9457 5625 9653 0625 9850 5625 26 9265 9876 9459 5076 9655 0276 9852 5476 27 9267 9129 9461 4529 9656 9929 9854 5329 28 9269 8384 9463 3984 9658 9584 9856 5184 29 9271 7641 9465 3441 9660 9241 9858 5041 30 9273 6900 9467 2900 9662 8900 9860 4900 31 9275 6161 9469 2361 9664 8561 9862 4761 32 9277 5424 9471 1824 9666 8224 9864 4624 33 9279 4689 9473 1289 9668 7889 9866 4489 34 9281 3956 9475 0756 9670 7556 9868 4356 35 9283 3225 9477 0225 9672 7225 9870 4225 36 9285 2496 9478 9696 9674 6896 9872 4096 37 9287 1769 9480 9169 9676 6569 9874 3969 38 9289 1044 9482 8644 9678 6244 9876 3844 39 9291 0321 9484 8121 9680 5921 9878 3721 40 9292 9600 9486 7600 9682 5600 9880 3600 41 9294 8881 9488 7081 9684 5281 9882 3481 42 9296 8164 9490 6564 9686 4964 9884 3364 43 9298 7449 9492 6049 9688 4649 9886 3249 44 9300 6736 9494 5536 9690 4336 9888 3136 45 9302 6025 9496 5025 9692 4025 9890 3025 46 9304 5316 9498 4516 9694 3716 9892 2916 47 9306 4609 9500 4009 9696 3409 9894 2809 48 9308 3904 9502 3504 9698 3104 9896 2704 49 9310 3201 9504 3001 9700 2801 9898 2601 50 9312 2500 9506 2500 9702 2500 9900 2500 This table of Sides and Squares may be continued by Addition of all the Odd numbers greater than 19 997. Thus. When the difference of two Sides is an Unite, The difference of their Squares is the sum of those Sides. Sides. Squares. 9999 99980001 19999 10000 100000000 20001 10001 100020001 20003 10002 100040004 etc. etc. If it be continued to the Square of 100000, it may be printed like the foregoing Table. Every page may have six columns; then 300 pages will hold 90000 Squares. And so the whole Table of 100 thousand Squares may end in pag. 329. A Book of 168 leaves is not an inch thick. But without such a Book, the numbers in these 29 pages, may be made use of. 1. To find the Square of any whole number less than 100 thousand. Thus, A 2 9947 9 4706 B 2 9940 9 4700 C 5 9887 18 9406 D 7 6 E 41 9209 113 6436 F 89640 3600 89 6809 0000 G 89682 2809 89 6922 6436 A The given Number: Of 5 figures D The fifth or last figure of A. B Remainder, after subtract. D from A. C The Sum of A and B E C multiplied by D F The Square of B. 00 after a Tabular G The Sum of E and F. The Square of A. 2. To find the Side of any Square number, of more than 8 figures. From the end of the given number, Cut off as many pairs of figures as may leave 7 or 8 figures. From these subtract as great a Tabular number as you can. Note the 4 figures of the Side of that Tabular square, etc. As 2 9 9 4 7 9 4 7 0 6 8 9682 2809 89 6922 6436 8 9640 36 89 6809 00 41 9209 113 6436 5 9887 18 9406 41 9209 113 6436 0 0 51 9314 1801 9508 2001 9704 2201 9902 2401 52 9316 1104 9510 1504 9706 1904 9904 2304 53 9318 0409 9512 1009 9708 1609 9906 2209 54 9319 9716 9514 0516 9710 1316 9908 2116 55 9321 9025 9516 0025 9712 1025 9910 2025 56 9323 8336 9517 9536 9714 0736 9912 1936 57 9325 7649 9519 9049 9716 0449 9914 1849 58 9327 6964 9521 8564 9718 0164 9916 1764 59 9329 6281 9523 8081 9719 9881 9918 1681 60 9331 5600 9525 7600 9721 9600 9920 1600 61 9333 4921 9527 7121 9723 9321 9922 1521 62 9335 4244 9529 6644 9725 9044 9924 1444 63 9337 3569 9531 6169 9727 8769 9926 1369 64 9339 2896 9533 5696 9729 8496 9928 1296 65 9341 2225 9535 5225 9731 8225 9930 1225 66 9343 1556 9537 4756 9733 7956 9932 1156 67 9345 0889 9539 4289 9735 7689 9934 1089 68 9347 0224 9541 3824 9737 7424 9936 1024 69 9348 9561 9543 3361 9739 7161 9938 0961 70 9350 8900 9545 2900 9741 6900 9940 0900 71 9352 8241 9547 2441 9743 6641 9942 0841 72 9354 7584 9549 1984 9745 6384 9944 0784 73 9356 6929 9551 1529 9747 6129 9946 0729 74 9358 6276 9553 1076 9749 5876 9948 0676 75 9360 5625 9555 0625 9751 5625 9950 0625 76 9362 4976 9557 0176 9753 5376 9952 0576 77 9364 4329 9558 9729 9755 5129 9954 0529 78 9366 3684 9560 9284 9757 4884 9956 0484 79 9368 3041 9562 8841 9759 4641 9958 0441 80 9370 2400 9564 8400 9761 4400 9960 0400 81 9372 1761 9566 7961 9763 4161 9962 0361 82 9374 1124 9568 7524 9765 3924 9964 0324 83 9376 0489 9570 7089 9767 3689 9966 0289 84 9377 9856 9572 6656 9769 3456 9968 0256 85 9379 9225 9574 6225 9771 3225 9970 0225 86 9381 8596 9576 5796 9773 2●96 9972 0196 87 9383 7969 9578 5369 9775 2769 9974 0169 88 9385 7344 9580 4944 9777 2544 9976 0144 89 9387 6721 9582 4521 9779 2321 9978 0121 90 9389 6100 9584 4100 9781 2100 9980 0100 91 9391 5481 9586 3681 9783 1881 9982 0081 92 9393 4864 9588 3264 9785 1664 9984 0064 93 9395 4249 9590 2849 9787 1449 9986 0049 94 9397 3636 9592 2436 9789 1236 9988 0036 95 9399 3025 9594 2025 9791 1025 9990 0025 96 9401 2416 9596 1616 6793 0816 9992 0016 97 9403 1809 9598 1209 9795 0609 9994 0009 98 9405 1204 9600 0804 9797 0404 9996 0004 99 9407 0601 9602 0401 9799 0201 9998 0001 Omnis Quadrati numeri Nota postrema esto, 1, 4, 5, 6, vel 9 Posteriores binas, ternas, quaternas exhibent haec tria Cribra Synoptica. 22 End of Square numbers in 2 figures. 0 1 4 5 6 9 159 End of Square numbers in 3 figures. 00 01 04 09 16 21 24 25 29 36 41 44 49 56 61 64 69 76 81 89 96 9 9 0.1.2.3.4.5.6.7.8.9. 0.1.2.3.4.5.6 7.8 9 9 0 1.2.3.4.5 6.7 8.9 9 0.1.2.3.4.5.6.7.8.9 0.1.2.3.4.5.6.7.8.9 0.1.2.3.4.5.6.7.8.9 9 0.1.2.3.4.5.6.7.8.9 9 0.1.2.3.4.5.6.7.8.9 0.1.2.3.4.5.6.7.8.9 0 1.2.3.4.5.6.7 8.9 8 8 8 8 8 8 8 8 8 7 7 7 6 6 6 6 6 4.5.6 6 6 6 6 6 6 6 5 5 5 5 5 4 4 4 4 4 4 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1 0.1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1044 End of Square Numbers in 4 Figures. 0 000 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 241 0 2 4 6 8 496 1 3 5 7 9 744 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 001 0 2 4 6 8 244 2 500 0 2 4 6 8 756 0 2 4 6 8 004 0. 1. 2. 3. 4. 5. 6. 7 8 9 249 1 3 5 7 9 504 0. 1. 2. 3. 4 5. 6. 7. 8. 9 761 0.1.2.3.4.5.6.7.8.9 009 0 2 4 6 8 256 0 2 4 6 8 516 1 3 5 7 9 764 0 2 4 6 8 016 1 3 5 7 9 264 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 521 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 769 1 3 5 7 9 024 0 2 4 6 8 276 1 3 5 7 9 524 1 3 5 7 9 776 0.1 2.3.4 5 6 7.8.9 025 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 281 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 529 0 2 4 6 8 784 0 2 4 6 8 036 1 3 5 7 9 284 1 3 5 7 9 536 1 3 5 7 9 796 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 041 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 289 0 2 4 6 8 544 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 801 1 3 5 7 9 044 1 3 5 7 9 296 1 3 5 7 9 556 0 2 4 6 8 804 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 049 0 2 4 6 8 304 0. 1. 2. 3. 4. 5 6. 7. 8. 9 561 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 809 1 3 5 7 9 056 1 3 5 7 9 316 0 2 4 6 8 564 0 2 4 6 8 816 0 2 4 6 8 064 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 321 0. 1. 2. 3. 4. 5. 6. 7. 8 9 569 1 3 5 7 9 824 1 3 5 7 9 076 0 2 4 6 8 324 0 2 4 6 8 576 0 2 4 6 8 836 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 081 0.1.2.3 4.5.6.7 8.9 329 1 3 5 7 9 584 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 841 0 2 4 6 8 084 0 2 4 6 8 336 0 2 4 6 8 596 1 3 5 7 9 844 0. 1. 2 3. 4. 5. 6. 7. 8. 9 089 1 3 5 7 9 344 1 3 5 7 9 600 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 849 0 2 4 6 8 096 0 2 4 6 8 356 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 601 1 3 5 7 9 856 0 2 4 6 8 100 0.1.2.3 4 5.6.7.8.9 361 1 3 5 7 9 604 0 2 4 6 8 864 1 3 5 7 9 104 1 3 5 7 9 364 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 609 1 3 5 7 9 876 0 2 4 6 8 116 0.1.2.3.4.5.6.7.8 9 369 1 3 5 7 9 616 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 881 0.1.2.3.4.5 6.7.8.9 121 1 3 5 7 9 376 0 2 4 6 8 624 0 2 4 6 8 884 1 3 5 7 9 124 0 2 4 6 8 384 0 5 625 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 889 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 129 1 3 5 7 9 396 1 3 5 7 9 636 0 2 4 6 8 896 1 3 5 7 9 136 0 2 4 6 8 400 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 641 0 2 4 6 8 900 0 2 4 6 8 144 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 401 0 2 4 6 8 644 1 3 5 7 9 904 1 3 5 7 9 156 0 2 4 6 8 404 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 649 0 2 4 6 8 916 0. 1. 2. 3. 4. 5. 6. 7. 8 9 161 0 1. 2. 3. 4. 5. 6. 7. 8. 9 409 0 2 4 6 8 656 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 921 0 2 4 6 8 164 0 2 4 6 8 416 1 3 5 7 9 664 1 3 5 7 9 924 0.1.2 3.4.5.6.7.8.9 169 1 3 5 7 9 424 0 2 4 6 8 676 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 929 0 2 4 6 8 176 0 2 4 6 8 436 0.1.2.3.4.5.6.7.8 9 681 1 3 5 7 9 936 1 3 5 7 9 184 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 441 1 3 5 7 9 684 0 2 4 6 8 944 0 2 4 6 8 196 1 3 5 7 9 444 0.1.2.3 4.5.6.7.8.9 689 1 3 5 7 9 956 0.1.2.3.4.5 6.7.8.9 201 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 449 1 3 5 7 9 696 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 961 1 3 5 7 9 204 1 3 5 7 9 456 0 2 4 6 8 704 0 2 4 6 8 964 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 209 0 2 4 6 8 464 1 3 5 7 9 716 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 969 1 3 5 7 9 216 1 3 5 7 9 476 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 721 0 2 4 6 8 976 0 2 4 6 8 224 0.1 2.3 4.5.6.7.8 9 481 0 2 4 6 8 724 1 3 5 7 9 984 0. 1. 2. 3. 4. 5. 6. 7. 8 9 225 0 2 4 6 8 484 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 729 0 2 4 6 8 996 1 3 5 7 9 236 0 1. 2. 3. 4. 5. 6. 7. 8. 9 489 0 2 4 6 8 736 This Synopsis may seem too short. See them all at large in the next leaf. Every Square Number endeth in 0.1.4.5.6 or 9 None endeth in 2. 3. 7 or 8. Every Square number hath one of these two and twenty end 00. 01. 04. 09. 16. 21. 24. 25. 29. 36. 41. 44. 49. 56. 61. 64. 69. 76. 81. 84. 89. 96. Every Square number hath one of these 159 End. 000 044 100 161 216 276 329 396 444 500 561 609 664 724 784 844 900 961 001 049 104 164 224 281 336 400 449 504 564 616 676 729 796 849 904 964 004 056 116 169 225 284 344 401 456 516 569 624 681 736 801 856 916 969 009 064 121 176 236 289 356 404 464 521 576 625 684 744 804 864 921 976 016 076 124 184 241 296 361 409 476 524 584 636 689 756 809 876 924 984 024 081 129 196 244 304 364 416 481 529 596 641 696 761 816 881 929 996 025 084 136 20● 249 316 369 424 484 536 600 644 704 764 824 884 936 036 089 144 2●4 256 321 376 436 489 544 601 649 716 769 836 889 944 041 096 156 26● 264 324 384 441 496 556 604 656 721 776 841 896 956 Every Square number hath one of these 1044 End. 0000 0304 0641 0969 1296 1641 2001 2321 2644 2976 3316 3649 4004 4324 0001 0321 0644 0976 1316 1649 2004 2324 2649 2996 3321 3664 4009 4329 0004 0324 0649 0996 1321 1664 2009 2329 2656 3001 3329 3681 4016 4336 0009 0329 0656 1001 1329 1681 2016 2336 2676 3009 3344 3684 4025 4356 0016 0336 0676 1009 1344 1684 2025 2356 2681 3024 3361 3689 4036 4361 0025 0356 0681 1024 1361 1689 2036 2361 2689 3025 3364 3696 4041 4369 0036 0361 0689 1025 1364 1696 2041 2369 2704 3041 3369 3716 4049 4384 0041 0369 0704 1041 1369 1716 2049 2384 2721 3044 3376 3721 4064 4400 0049 0384 0721 1044 1376 1721 2064 2400 2724 3049 3396 3729 4081 4401 0064 0400 0724 1049 1396 1729 2081 2401 2729 3056 3401 3744 4084 4404 0081 0401 0729 1056 1401 1744 2084 2404 2736 3076 3409 3761 4089 4409 0084 0404 0736 1076 1409 1761 2089 2409 2756 3081 3424 3764 4096 4416 0089 0409 0756 1081 1424 1764 2096 2416 2761 3089 3441 3769 4100 4436 0096 0416 0761 1089 1441 1769 2100 2436 2769 3104 3444 3776 4116 4441 0100 0436 0769 1104 1444 1776 2116 2441 2784 3121 3449 3796 4121 4449 0116 0441 0784 1121 1449 1796 2121 2449 2801 3124 3456 3801 4129 4464 0121 0449 0801 1124 1456 1801 2129 2464 2804 3129 3476 3809 4144 4481 0129 0464 0804 1129 1476 1809 2144 2481 2809 3136 3481 3824 4161 4484 0144 0481 0809 1136 1481 1824 2161 2484 2816 3156 3489 3841 4164 4489 0161 0484 0816 1156 1489 1841 2164 2489 2836 3161 3504 3844 4169 4496 0164 0489 0836 1161 1504 1844 2169 2496 2841 3169 3521 3849 4176 4516 0169 0496 0841 1169 1521 1849 2176 2500 2849 3184 3524 3856 4196 4521 0176 0516 0849 1184 1524 1856 2196 2516 2864 3201 3529 3876 4201 4529 0196 0521 0864 1201 1529 1876 2201 2521 2881 3204 3536 3881 4209 4544 0201 0529 0881 1204 1536 1881 2209 2529 2884 3209 3556 3889 4224 4561 0209 0544 0884 1209 1556 1889 2224 2544 2889 3216 3561 3904 4225 4564 0224 0561 0889 1216 1561 1904 2225 2561 2896 3225 3569 3921 4241 4569 0225 0564 0896 1225 1569 1921 2241 2564 2900 3236 3584 3924 4244 4576 0241 0569 0900 1236 1584. 1924 2244 2569 2916 3241 3600 3929 4249 4596 0244 0576 0916 1241 1600 1929 2249 2576 2921 3249 3601 3936 4256 4601 0249 0596 0921 1249 1601 1936 2256 2596 2929 3264 3604 3956 4276 4609 0256 0601 0929 1264 1604 1956 2276 2601 2944 3281 3609 3961 4281 4624 0276 0609 0944 1281 1609 1961 2281 2609 2961 3284 3616 3969 4289 4641 0281 0624 0961 1284 1616 1969 2289 2624 2964 3289 3636 3984 4304 4644 0289 0625 0964 1289 1636 1984 2304 2641 2969 3296 3641 4001 4321 4649 The 4 Last Notes of Square numbers. 4656 5044 5441 5809 6196 6569 6964 7344 7729 8116 8489 8889 9264 9649 4676 5049 5444 5824 6201 6576 6969 7361 7744 8121 8496 8896 9281 9664 4681 5056 5449 5841 6209 6596 6976 7364 7761 8129 8516 8900 9284 9681 4689 5076 5456 5844 6224 6601 6996 7369 7764 8144 8521 8916 9289 9684 4704 5081 5476 5849 6225 6609 7001 7376 7769 8161 8529 8921 9296 9689 4721 5089 5481 5856 6241 6624 7009 7396 7776 8164 8544 8929 9316 9696 4724 5104 5489 5876 6244 6641 7024 7401 7796 8169 8561 8944 9321 9716 4729 5121 5504 5881 6249 6644 7025 7409 7301 8176 8564 8961 9329 9721 4736 5124 5521 5889 6256 6649 7041 7424 7309 8196 8569 8964 9344 9729 4756 5129 5524 5904 6276 6656 7044 7441 7324 8201 8576 8969 9361 9744 4761 5136 5529 5921 6281 6676 7049 7444 7341 8209 8596 897● 9364 9761 4769 5156 5536 5924 6289 6681 7056 7449 7344 8224 8601 8996 9369 9764 4784 5161 5556 5929 6304 6689 7076 7456 7349 8225 8609 9001 9376 9769 4801 5169 5561 5936 6321 6704 7031 7476 7356 8241 8624 9009 9396 9776 4804 5184 5569 5956 6324 6721 7039 7481 7376 8244 8641 9024 9401 9796 4809 5201 5584 5961 6329 6724 7104 7489 7381 8249 8644 9025 9409 9801 4816 5204 5600 5969 6336 6729 7121 7504 7389 8256 8649 9041 9424 9809 4836 5209 5601 5984 6356 6736 7124 7521 7904 8276 8656 9044 9441 9824 4841 5216 5604 6001 6361 6756 7129 7524 7921 8281 8676 9049 9444 9841 4849 5225 5609 6004 6369 6761 7136 7529 7924 8289 8681 905● 9449 9844 4864 5236 5616 6009 6384 6769 7156 7536 7929 8304 8689 9076 9456 9849 4881 5241 5625 6016 6400 6784 7161 7556 7936 8321 8704 9081 9476 9856 4884 5249 5636 6025 6401 6801 7169 7561 7956 8324 8721 9089 9481 9876 4889 5264 5641 6036 6404 6804 7184 7569 7961 8329 8724 9104 9489 9881 4896 5281 5649 6041 6409 6809 7201 7584 7969 8336 8729 9121 9504 9889 4900 5284 5664 6049 6416 6816 7204 7600 7984 8356 8736 9124 9521 9904 4916 5289 5681 6064 6436 6836 7209 7601 8001 8361 8756 9129 9524 9921 4921 5296 5684 6081 6441 6841 7216 7604 8004 8369 8761 9136 9529 9924 4929 5316 5689 6084 6449 6849 7225 7609 8009 8384 8769 9156 9536 9929 4944 5321 5696 6089 6464 6864 7236 7616 8016 8400 8784 9161 9556 9936 4961 5329 5716 6096 6481 6881 7241 7636 8025 8401 8801 9169 9561 9956 4964 5344 5721 6100 6484 6884 7249 7641 8036 8404 8804 9184 9569 9961 4969 5361 5729 6116 6489 6889 7264 7649 8041 8409 8809 9201 9584 9969 4976 5364 5744 6121 6496 6896 7281 7664 8049 8416 8816 9204 9600 9984 4996 5369 5761 6129 6516 6900 7284 7681 8064 8436 8836 9209 9601 5001 5376 5764 6144 6521 6916 7289 7684 8081 8441 8841 9216 9604 5009 5396 5769 6161 6529 6921 7296 7639 8084 8449 8849 9225 9609 5024 5401 5776 6164 6544 6929 7316 7696 8089 8464 8864 9236 9616 5025 5409 5796 6169 6561 6944 7321 7716 8096 8481 8881 9241 9636 5041 5424 5801 6176 6564 6961 7329 7721 8100 8484 8884 9249 9641 How long soever a Number be, if its ending be not found in its proper place in Pag. 31 or 32, It is no Square. You have 4 numbers, of which you tell me nothing, but that one of them ends in 2, another in 35, another in 789, and the last ends in 6796. Pag. 31. 32. tell me, that no square number can end so. I therefore tell you, that none of your 4 numbers is a Square. But of these 896824656. 896835044. 896845441. 8969305809. 8969416196. 8969426569, I find the 4 last figures in the uppermost line of this page, and yet I must not say that any of them is a true Square; Page 29 makes me see they are not. Having the two, three or four last figures of any Square number, to exhibit as many of the last figures of its side, is a New Question: To which, the just Answers are manifold and not obvious. A particular account of them is ready for the Press, when it shall be desired.