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 composea 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 Pro●icient 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 ●●t 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 ●●●ture 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 〈◊〉 of the Diameter at Britch. The lesser Cannon at Britch to be 〈◊〉 ●o big as the greater Cannon 9/16 at Trunions, and 〈◊〉 at Muzzle, whereas ordinary fortified Cannons have at the Touchhole 7/8 at the Trunions 5/8 and at the Muzzle 〈◊〉, all lesser Pieces in that kind have 18/1● at the Touchhole 〈◊〉 at Trunions, and 〈◊〉 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 〈◊〉 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 100l. of Copper, add 8 l. of Tin, and 10 l. of Latin. Others to ever 100l. add 20l. of Bell-Metal, which is 25l. of Lead and Tin to every 100l. 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 8000l. in length about 12 foot, carries a Shot of 7● inch. Diameter, and its weight is 58l. of Iron, its bore is 8 inches, requireth for her charge in Powder, 32l. 8z.  
Demi-Cannon of the greater size, called by some Cannon of Seven, whose weight of Metal is 7000l. in length about 12 foot, carrying a Shot of 6● inch. Diameter, and its weight of Iron is 42l. 10z. the Diameter at bore is 7 inches, requireth for her charge in Powder 20l.  
Demi-Cannon great size, it's weight of Metal is 6000l. in length about 12 foot, carrying a Shot of 61/4 inch. Diameter, and its weight in Iron is 34l. the Diameter at bore is 6 〈◊〉 inch▪ requireth for her charge of Cannon Powder 18l.  
Demi-Cannon ordinary, its weight of Metal is 5600l. in length 11 foot, carrying a Shot of 6 〈◊〉 inch. Diameter, its weight in Iron is 32l. the Diameter at bore is 6 〈◊〉 inch. requireth for her charge in Powder 171/2 pounds.  
The lowest Demi-Cannon, whose weight of Metal is 5400l. being in length sometime 10 and sometimes 12 foot, it carries a Shot of 6 inches, the weight of that Shot in Iron is 30l. the Diameter of the bore is 61/4 inch. it requireth for charge in Powder 14l.  
Culverin of the largest size, weighs about 4800l. being in length 10 or 12▪ foot, it carries a Shot of 5 〈◊〉 inch. Diameter, the weight of that Shot in Iron is 20l. the Diameter of the bore is 6 〈◊〉 inch, it requireth for charge in Powder 12l. 8z.  
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 51/4 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 〈◊〉 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 〈◊〉 inch. Diameter, the weight of that Shot of Iron is 12 l. 11 z. Diameter of the bore 4 〈◊〉 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 41/4 inch. Diameter, weight of that Shot of Iron is 10 l. 12 z. Diameter of the bore 41/2 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 〈◊〉 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 33/4 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 〈◊〉 inch. Diameter, weight of that Shot 6 l. 0 z. Diameter at the bore 33/4 inches, charge of Powder 4 l.  
Saker of the lowest size, of 1400 l. weight, in length about 8 foot, carries a Shot of 31/4 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 ●alf, if of 1000 l. three pounds and a quarter.  
The ordinary Minion of 750 l. in length 7 foot, height of the Shot 3 〈◊〉 inch. weight of the Shot 3 l. 4 z. height of the bore 3 inches, charge of Powder 2 〈◊〉 pounds.  
Faucons of 750 l. length 7 foot, height of the Shot 21/2 inch. weight 21/2 pounds, height of the bore 23/4 inch. charge in Powder 21/2 pounds.  
Fauconet of 400 l. in length 6 foot, height of the Shot 2 〈◊〉 inch. weight 1 l. 5 z. height of the bore 21/4 inch. charge 1 l. 4 z. of Powder.  
Rabnet of 300 l. length 5 foot, height of the Shot 1 〈◊〉 inch. weight 8 ounces of Iron, height of the bore 11/2 inch. charge of Powder 12 ounces.  
Base of 200 l. length 4 foot, height of Shot 11/2 inch, weight 5 ounces, height of the bore 1 〈◊〉 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 Frizes.  
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; bu● 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 ●all down from the head of the Ghynne a Plummet with a Line▪ or for want of a Plummet any stone made fa●● to a Line, and so moving the Ghynne ●●til the said Plummet ●all ju 〈…〉 upon the Centre of Gravity, which is between the Ears of the Piece, that the met●● may fa●l near equal, or that an easy hand may poise i●; and this care must be the more, if the Ground whereon the Ghynne stands be sandy or lose Ground, or 〈◊〉 Earth be b●ggy soft, so that the feet may ●●il or sink in or give way▪ according 〈◊〉 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 Give, 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 fa●l 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 in to 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 Gee● 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 i● 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 wil● 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 Chance, 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 out 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 differing, 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 hardness 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 ●ettle 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 Hoofs 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 Did Walls, of Caves, Cellars, Uaults, 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, Uitriol, 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 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.  
Salt-Peter 100 l.  
Sulphur 25  
Coals 25   

The first.  
Salt-Peter 100 l.  
Sulphur 18  
Coals 20   

The first.  
Salt-Peter 100 l.  
Sulphur 12  
Coals 15   

The Second.  
Salt-Peter 100 l.  
Sulphur 20  
Coals 24   

The Second.  
Salt-Peter 100 l.  
Sulphur 15  
Coals 18   

The Second.  
Salt-Peter 100 l.  
Sulphur 10  
Coals 8    
You must first finely powder these compositions or mixtures, for Cannon or Musket Powder, and after moissen 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 Bowls, 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 Britchend.   

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 Baptist● 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 never theless give you the opinion of Scaliger, taken out of his his fifteenth Book, in his Exer. Exoter. against Cardan of Sub●il. Exer. 25.  Lo●ge p●jus illud cum sonitus causam a bellicis machinis editi, attribuis Sal Petrae; nan● t●nuissimu●n in pulverem comminu●um 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 no● 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 forti●● 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 fir●t strength, and the force which it did acquire in its first preparation; as such as hath dak●n wind, we●, 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 mo●st place long; for in time the Salt-Peter alter● 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 bu●●our, 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 abando●● 〈◊〉 two matters that adhered to it▪ the Sulphur and Coals losing nothing of their weight, seeing that no humidity that is attracted, can ●e able to dissolve them▪ b●● ra●her by the contrary, the Coal doth attract greedily, and becomes more ponderous.  
If for the reasons afore said 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 Aquavitae, 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 conseqnently, 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.  
Now to prepare ●ommon 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 o● 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 fin● 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 cyphe 〈…〉 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 over head.  
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 d●●● 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 2●09 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 18158●● 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 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944784 918330048 973 946729 991167317 974 948676 924010424 975 950625 926859375 976 952576 929714176 977 954529 932574833 978 956484 935441352 979 958441 938313739 980 960400 941192000 981 962361 944076141 982 964324 946966108 983 966289 949862087 984 968256 952763904 985 970225 955671625 986 972196 958585256 987 974169 961504803 988 976144 964430272 989 978121 967361669 990 980100 970299000 991 982081 973242271 992 984064 976191488 993 986049 979146657 994 988036 982107784 995 990025 985074875 996 992016 988047936 997 994009 991026973 998 996004 994011992 999 998001 997002999 1000 1000000 1000000000    

CHAP. 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.   woodcut of calipers measuring a piece of shot 
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.  
Cube each Diameter, then multiply the Cube of the Shot whose weight is required 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.  
Example.  
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 18, 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. iv  
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.   nested circles inscribed by angles   

QUEST. VI  
If a Shot of three Inches and a half weigh sir 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 〈◊〉 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 3½ 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?  
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 Inches. The Parts. The Feet. The Inches. The Pounds. The Inches. The Parts. The Inches. The Parts. The Pounds. The Ounces. The Inches. The Parts. The Pounds. The Ounces. The Paces. A Base. 1 2/8 4 6/8 200 2 0/8 4 0/8 0 8 1 1/8 0 5 60 A Rabanet. 1 4/8 5 6/8 300 2 4/8 4 1/8 0 12 1 3/8 0 8 70 Fauconets. 2 2/8 6 0/8 400 4 0/8 7 4/8 1 4 2 2/8 1 5 90 Faucons. 2 6/8 7 0/8 750 4 4/8 8 2/8 2 4 2 5/8 2 8 130 Ordinary Minion. 3 0/8 7 0/8 750 800 5 0/8 8 4/8 2 8 2 7/8 3 4 120 Minion of the largest size. 3 2/8 8 0/8 1000 5 0/8 9 0/8 3 4 3 0/8 3 12 125 Saker the lowest sort. 3 4/8 8 0/8 1400 6 4/8 9 6/8 3 6 3 2/8 4 12 150 Ordinary Sakers. 3 6/8 7 9 0/8 1500 6 6/8 10 4/8 4 0 3 4/8 6 0 160 Sakers of the oldest sort. 4 0/8 10 0/8 1800 7 2/8 11 0/8 5 0 3 6/8 7 5 163 Lowest Demiculvering. 4 2/8 10 0/8 2000 8 0/8 12 0/8 6 4 4 0/8 9 0 174 Ordinary Demiculvering. 4 4/8 10 11 0/8 2700 8 0/8 12 6/8 7 4 4 2/8 10 11 175 Elder sort of Demiculvering. 4 6/8 12 13 0/8 3000 8 4/8 13 4/8 8 8 4 4/8 12 11 178 Culverings of the best size. 5 0/8 10 11 0/8 4000 9 0/8 14 2/8 10 0 4 6/8 15 0 180 Ordinary Culverin. 5 2/8 12 13  4500 9 4/8 16 0/8 11 6 5 0/8 17 5 181 Culverin of the largest size. 5 4/8 12 1● 0/8 4800 10 0/8 16 0/8 11 8 5 2/8 20 0 183 Lowest Demicanon. 6 2/8 11 0/8 5400 11 4/8 20 0/8 14 0 6 0/8 30 0 156 Ordinary Demicanon. 6 4/8 12 0/8 5600 12 0/8 22 0/8 17 8 6 ●/●/8 32 0 162 Demicanon of great size. 6 6/8 12 0/8 6000 12 0/8 22 6/8 18 0 6 5/8 36 0 180 Canon Royal, or of 8 0/8 12  8000 14 6/8 24 0/8 32 8 7 4/8 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 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.  
Inches. Quart. Lead. Stone. Both together. Pound. Ou. Pound. Ou. Pound. Oun. 1  0 1 2/3 0 0 1/3 0 2 1 2 0 6 ¼ 0 1 ¾ 0 8 2  0 14 0 4 1 2 2 2 0 12 0 8 2 4 3  3 2 0 10 3 12 3 2 5 0 1 0 5 0 4  7 7 1 8 8 15 4 2 10 8 2 2 12 10 5  14 7 2 14 17 5 5 2 19 4 3 12 23 0 6  25 0 5 0 30 0 6 2 32 0 6 0 38 0 7  40 0 8 0 48 0 7 2 48 0 10 0 58 0 8  59 0 12 0 71 0  
Its 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.  
●aving 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 Ordinance.  
If a Saker of 4 inches Diameter weigh 1400l. 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 1400l. 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 Ordinance.  
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 4000 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 hand 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) hand 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 the sixth part.  
The Naves, the Cheeks called Limbres, and wheels, are usually made of Elm, but the Transoms, Axeltreces, 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 jog, 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 his 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 Paggots 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 or 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 it 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 E; 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.  
 plumb line, quadrant, and compass  

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 h m, being next the sights, be 〈◊〉 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.   woodcut of people using quadrants to measure the height of a tower 
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 of 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 height equal with our standing, adjoining with it the height of your eye downwards.  
 woodcut of people using a quadrant to measure the height of a tower   

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.  
 woodcut of people using quadrants to measure the height of a tower   

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.   woodcut of people using a quadrant to measure the height of a tower 
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 〈◊〉 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.   two lines forming a 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.   triangle with labeled angles and sidse, a castle wall at its apex 
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, 〈◊〉 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.   woodcut offering bird's-eye view of fortifications, overlaid by triangles with labeled angles 
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 the 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 by 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, nothing 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 just 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 whither 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.  
 trapezoids with labeled angles  

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 C, 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 C passeth to 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 subrended 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.  
 woodcut of person using quadrant to measure distance between cannons and city walls   

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, wh●ch 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, nothing 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.  
 woodcut of person using quadrant to measure distance between cannons and city walls   

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 multiplye● by 200 paces, the distance Stationary C D, there amounteth 160000, this divided by 1200, yieldeth in the Quotient 133 ⅔; 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.  
YOu must ascend some high Tower, Hill, Cliff, or other place, from whence you may commodiously behold on every part those places you intent a Plot of, there set up your Instrument upon its staff, and in such sort place it by help of your Needle, that the four Semidiameters stand due East, West, North, and South; then turn your Index to Town, Village, Haven, Road, or such like, espying through the Sights the middle or most notable mark in them, noting withal in a Table by itself the degrees cut by the Index in your Instrument, which we call the Angles of position, and so make a Table of the first Station. Then search out  square inscribed by a circle, its circumference divided into 360 degrees with your Eye, viewing round about, some other lofty place, from whence you may behold again all these places, for that shall be your second Station, and turning thereunto the Index of your Instrument, note what degree it toucheth; this done, remove your Instrument thither, and place it in all respects as 'twas before, and turning the Diameter or Index of your Instrument to every place, espying through the Sight all such marks as you saw before, noting again the degrees ●ut, or Angles of position, writing the names of every place, and its degree by it; so have you a Table also of your second Station; with these Tables you shall resort to some plain smooth superficies of Board, Parchment, Paper, or such like, and thereon describe a large Circle, divide it into 360 degrees, like to the Circle of your Instrument; then from the Centre thereof to every degree noted in your first Table, extend straight lines, writing upon every one of them the name of his place; and upon that line that represents your second Station fix one foot of your Compasses, opening the other at pleasure; and draw another Circle, and divide it also into 360 degrees, and from the Centre thereof extend right lines to every degree noted in your second Table, writing as before upon every one of them the name of their places or marks; finally, you shall note diligently the concourse or crossing of every two like lines, making thereon a star or such like mark, with the names of the place● thereunto belonging. Now if you desire to know how far every of these Towns, Villages, etc. are distant from each other, you shall do thus, measure the distance between your Stations by Instrument or otherwise, as you have been before taught, and divide the right line between the Centres of your Circles into so many equal parts or portions as there are Miles, Furlongs, or Scores, between your Stations; then opening your Compasses to one of those parts, you may measure from place to place, always affirming so many Miles, Furlongs, or Scores (according to the denomination of that one part whereunto you opened your Compasses) to be between place and place, as you find by measuring there are parts.   

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 ●eat, 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.   various labeled angles 
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.   tables for types of shot and types of cannon, two eight-inch rulers, and a quadrant 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 ⅗ 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 ●/● 4 3 D. Canon Drake. 6 ½ 16 3000 9 pound. 4 ½ 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 founde● 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.   two cannons firing at a tower, and a cannon in the tower firing at a church The way of Shoting Mira Comme; or by the mettle of the piece. 412. Paces. Shooting punctually, Levill by a dispart 206. Paces. 248 4/10 paces, right Range 
folio 72: 73.  
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.  The Degrees of Mounture. Paces diff. 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 Falconer. 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 usually 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.  
A TABLE OF Right Ranges, or Point Blanks. A TABLE OF Randoms, or the first Graze. The Degrees of the Pieces Mounture. The Right Range in Paces, 5 Foot to a Pace. The Degrees of Mounture. The Paces of the Random, 5 Foot to a Pace. 0 192 0 192 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   
This Table is rather proportional 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.   parabolas of cannonballs in flight, inscribed by labeled triangles  

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.   a 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  74 12 53 14 32 16 12 17 92 9 Foot long. 1 89 3 79 5 68 7 58 9 47 11 ●7 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 1● 71 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, ●lanks, 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 France, 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 Uffanogive 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 you 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 battery 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 advantae 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.  
 cannon firing on a wall from a variety of angles 
How one must Batter a Courtine   
 cannon firing on a bulwark from a variety of angles 
How one must Batter a Bulwark  
betwixt 86 and 87    

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.  
Two of these Mortars are represented unto you, in the Plate and Figures following number. Now for the shooting a way of your great Granades or Fireballs, you must ever remember, but to take ⅕ or 1/7 parts of fine Powder of the weight of your Granado or thing which you shoot; but if you are to shoot away a Bullet without any Fireworks in it, or some massy stone, or such like solid thing, than you must take but half the weight of it in fine Powder, which, having given fire to the Mortar, will send it going merrily.  
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  
A Mortar Shooting upon a Castle   a quadrant, mortar, and labeled parabolas describing the paths of various shots 
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 aboveall, have a very combustible quality, proper to the Compositions of artificial fires.   

To prepare Oil or Balsam of Sulphur.  
Fill a long body of Glassfull 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 putrification, 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 Aquavitae, 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 versable 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. IU.  
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 Low 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 chafe 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 soeveraign.  
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 Plaintain 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 ●/●● 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 2/9 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 1l. Salt-Peter 1l. Sulphur 1l.  
Powder 3l. Salt-Peter 2l. Sulphur 1l.  
Powder 4l. Salt-Peter 3l. Sulphur 2l.  
Powder 4l. Salt-Peter 3l. Sulphur 1l.   

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, 〈◊〉 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 ma●ter 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 ●he last Chapter, according as you shall find most convenient. And this is out 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 th●● it is always sufficient justice, so that the Wars where such things are practised, be ●ot 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 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 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 ●/3 part, Bay salt ●/● part, Colophonia ●/6 part, Arsenic 1/8 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 ⅔ part, Sulphur 1 part, Tarr ●/● 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 f●e 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 E●●cution.  
To burn the sails of Ships a pre●●y 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 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 perpendlcular 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 quanity 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 month 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 Brandywine.  
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 nor 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 accustomed 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 grossy 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.   a square inscribed by various lines and angles 
Again, I say, that this Parabola is described by the Impetus given; for A, OF, and EBB, or those three lines equal to DG the Altitude, GF the Semi-base, and GL are in continual proportion. Wherefore GL is the sublimity, by the V Proposition 
De metu Projectorum.  of Galiaeus, and its Corollary.  
Then thus: the Impetus of the Parabola AGNOSTUS in the point A, is as much as that of the Cadent naturally falling from L to D, (by X. of Galiaeus) 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.   various labeled lines and angles 
First, it is manifest that the point P cannot be in the line LD; because since the line AC toucheth each Parabola, that ID 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 EGLANTINE: for drawing the Diameter, suppose MN, through the ●●rtex, that MN should be cut into two equal parts by the line EGLANTINE, is absurd: for only ID, of all the lines parallel unto it in the angle GOD, can be cut into two equal parts.  
Now let the point P fall any where at pleasure, and draw the Horizontal line PR: for as much as PN and PM are equal, by the TWO of * this, NR and RAMIRES, PR and RS 
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.  shall be equal. And because the Parabola AP hath the Impetus BASILIUS; that is, AM, the Point O shall be its sublimity: and for that reason the lines OPEN, PR, and PM shall be in continual proportion; and the Rectangle OPM equal unto the square PR: and changing the lines with their equals, the Rectangle BSA shall be equal to the square SIR: therefore the R is in the point Periphery of the Semicircle: which is absurd; for the right line OF shall meet with the Periphery in two several points: wherefore, etc.  

COROLLARIES.   a parabola inscribed by various angles 
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 AB less elevated, than that which shall be projected along AD 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.   a parabola inscribed by various angles 
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.  
7. We will therefore make a Corollary of that which to Galilaeus was an arduous Theorem, to wit, that the Semi-right 
* Or Randon.  projection is the greatest of all those made by the same Impetus. For, if you suppose the Angle GOD to be Semi-right, CD shall be the Semi-Diameter; that is the greatest of all the Sins that can be given in the Semicircle.  
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 AB: for it hath been demonstrated to be Quadruple of the right line CD, that is double to AB.   a parabola inscribed by a right triangle   

PROP. II.  
The Impetus and Amplitude being given, to find 
I incite this Proposition, as being also cited in the ensuring Discourse.  the direction according to which the Parabola was made; as also to find the Altitude.  
LEt the given Impetus be AB, and let AD be the fourth part of the Amplitude given. About AB described the Semicircle ACB, and erect DCE, (which if it shall not fall in the Semicircle, the the problem is impossible) and let it cut the Semicircle in the points C and E. I say, that either the direction AC or A, if the given Impetus AB be retained, shall described a Parabola, whose Amplitude shall be Quadruple to the line AD, this is manifest from the things preceding. For projections made with the Impetus AB, according to the directions AC, or A, have an Amplitude Quadruple to GE, or FC or AD, which are equal to one another; and the Altitude may in the one be OF, as also in the other AGNOSTUS, as appeareth, etc.  
 labeled parabola and lines   

In this place I have thought sit to insert the Tables following: the first Classis of which containeth three Tables, the same with those of Galilaeus, which we placed Part. 1. 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 Dialouge. 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 Number of the Table are double to the right Sins of the arches of the elevation.  Degr. of Elevat. Ampl. 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 29 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. 1 3 2 12 3 27 4 49 5 76 6 109 7 149 8 194 9 245 10 302 11 364 12 432 13 506 14 585 15 670 16 760 17 855 18 955 19 1060 20 1170 21 1284 22 1403 23 1527 24 1654. 25 1786 26 1922 27 2061 28 2204 29 2350 30 2500 31 2653 32 2808 33 2966 34 3127 35 3290 36 3455 37 3622 38 3790 39 3960 40 4132 41 4304 42 4477 43 4651 44 4826 45 5000 46 5174 47 5349 48 5523 49 5696 50 5868 51 6040 52 6210 53 6378 54 6545 55 6710 56 6873 57 7034 58 7192 59 7347 60 7500 61 7650 62 7796 63 7939 64 8078 65 8214 66 8346 67 8470 68 8597 69 8716 70 8830 71 8940 72 9045 73 9145 74 9240 75 9330 76 9415 77 9494 78 9568 79 9636 80 9698 81 9755 82 9806 83 9851 84 9891 85 9924 86 9951 87 9973 88 9988 89 9997 90 10000  

TABLE III. The Altitudes and Sublimities of the Semiparabola's, whose Amplitudes are equal, Viz. always 10000 parts; the Altitudes are the halfs of the Tangents of the Angles of the Elevation; and the Sublimities are the halfs of the Tangents of the Compliments of the Elevation.  D. of Elev. Altitudes. Sublimities. 1 87 286450 2 175 143186 3 262 95406 4 350 71503 5 437 57150 6 525 47572 7 614 40722 8 703 35577 9 792 31569 10 882 28356 11 972 25723 12 1063 23523 13 1154 21657 14 1247 20054 15 1340 18660 16 1434 17437 17 1529 16354 18 1625 15388 19 1722 14521 20 1820 13737 21 1910 13025 22 2020 12375 23 2122 11779 24 2226 11230 25 2332 10723 26 2439 10252 27 2548 9813 28 2659 9404 29 2772 9020 30 2887 8668 31 3004 8321 32 3124 8002 33 3247 7699 34 3373 7413 35 3501 7141 36 3633 6882 37 3768 6635 38 3906 6400 39 4049 6175 40 4196 5959 41 4346 5752 42 4502 5553 43 4663 5362 44 4828 5718 45 5000 5000 46 5178 4828 47 5362 4663 48 5553 4502 49 5752 4346 50 5959 4196 51 6175 4049 52 6400 3906 53 6635 3768 54 6882 3633 55 7141 3501 56 7413 3373 57 7699 3247 58 8002 3124 59 8321 3004 60 8660 2887 61 9021 2772 62 9404 2659 63 9813 2548 64 10252 2439 65 10723 2332 66 11230 2226 67 11779 2122 68 12375 2020 69 13025 1919 70 13737 1820 71 14521 1722 72 15388 1625 73 16354 1529 74 17437 1434 75 18660 1340 76 20054 1247 77 21657 1154 78 23523 1063 79 25723 972 80 28356 882 81 31569 792 82 35577 703 83 40722 614 84 47572 525 85 57150 437 86 71503 350 87 95406 262 88 143186 175 89 286450 87 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. on Impet. 1 75 2 349 3 523 4 698 5 872 6 1045 7 1219 8 1392 9 1564 10 1736 11 1908 12 2079 13 2250 14 2419 15 2588 16 2756 17 2924 18 2090 19 3256 20 3420 21 3584 22 3746 23 3907 24 4067 25 4226 26 4384 27 4540 28 4695 29 4848 30 5000 31 5150 32 5299 33 5446 34 5592 35 5736 36 5878 37 6018 38 6157 39 6293 40 6428 41 6561 42 6691 43 6820 44 6947 45 7071 46 7193 47 7314 48 7431 49 7547 50 7660 51 7771 52 7880 53 7986 54 8090 55 8192 56 8290 57 8387 58 8480 59 8572 60 8660 61 8746 62 8892 63 8910 64 8988 65 9063 66 9135 67 9205 68 9272 69 9336 70 9397 71 9455 72 9510 73 9563 74 9613 75 9659 76 9703 77 9744 78 9781 79 9816 80 9848 81 9878 82 9903 83 9925 84 9945 85 9962 86 9976 87 9986 88 9994 89 9998 90 10000  

TABLE V The Degrees of Elevation to which the Piece is ● 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, on equal increases of the Projection. Spaces. Deg. of Elevat. Compliment. 10 00 17 89 43 20 00 34 89 26 30 00 52 89 08 40 1 09 88 51 50 1 26 88 34 60 1 4● 88 17 70 2 00 88 00 80 2 18 87 42 90 2 35 87 25 100 2 52 87 08 110 3 09 86 51 120 3 27 86 33 130 3 44 86 16 140 4 01 85 59 150 4 19 85 41 160 4 36 85 24 170 4 54 85 06 180 5 11 84 49 190 5 29 84 31 200 5 46 84 14 210 6 04 83 56 220 6 21 83 39 230 6 39 83 21 240 6 57 83 03 250 7 14 82 46 260 7 32 82 28 270 7 50 82 10 280 8 08 81 52 290 8 26 81 34 300 8 44 81 16 310 9 02 80 58 320 9 20 80 40 330 9 38 80 22 340 9 56 80 04 350 10 14 79 46 360 10 33 79 27 370 10 5● 79 09 380 11 10 78 50 390 10 29 78 31 400 11 47 78 13 410 12 06 77 54 420 12 25 77 35 430 12 44 77 16 440 13 03 76 57 450 13 22 76 38 460 13 42 76 18 470 14 01 75 59 480 14 21 75 39 490 14 40 75 20 500 15 00 72 00 510 15 20 74 40 520 15 40 74 20 530 16 00 74 00 540 16 21 73 39 550 16 41 73 19 560 17 02 72 58 570 17 23 72 37 580 17 44 72 16 590 18 05 71 55 600 18 26 71 34 610 18 48 71 12 620 19 10 70 50 630 19 22 70 26 640 19 54 69 06 650 20 16 69 44 660 20 39 69 21 670 21 02 68 58 680 21 25 68 35 690 21 49 6 21 700 21 13 67 47 710 22 37 67 23 720 23 02 66 56 730 23 27 66 33 740 23 52 66 08 750 24 18 65 42 760 24 44 65 16 770 25 11 64 49 780 25 38 64 22 790 26 06 63 54 800 26 34 63 26 810 27 03 62 57 820 27 33 62 27 830 28 03 61 57 840 28 34 61 26 850 29 06 60 54 860 29 36 60 21 870 30 14 59 46 880 30 50 59 10 890 31 27 58 33 900 32 05 57 55 910 32 45 57 15 920 33 28 56 32 930 34 13 55 47 940 35 02 54 58 950 35 54 54 06 960 36 52 53 08 970 37 58 52 02 980 39 16 50 44 990 40 57 49 03 1000 45 00 45 00  

The use of the Precedent TABLE.   a high, arcing parabola inscribed by a lower, flatter one 
I know that its very seldom, and perhaps never found, 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.   labeled parabolas, angles, and lines 
The Angle of Elevation C A B gr. 30, being given, the right Angled Triangle E A C shall be given in Specie: and because A B is given in paces, A E shall be given, which is the fourth part thereof, namely 600 paces. Let us therefore, to find the quantity of A D, work in this manner by Calculations and Sins.  
Say, if as the Right Sine 86602 of the Angle A C E, gr. 60. that is, of the Compliment of the Elevation, is to the side A E, which is 600: so is the whole Sine 100000 to a fourth number 693: and thus the Hypothenuse A C shall be 693 Paces. But because that the right angled Triangle A C D is given in Specie, begin again and say, as the right Sine 50000 of the angle A D C, which is equal to the angle given of the Elevation E A C, is to the right Line A C, which is found to be 693 paces, so is the whole line to a fourth number 1386. And thus the right line sought A D, shall be 1386 paces. But because A D, 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 C F, than F A and F D shall be the Taugents, one, of the angle of elevation, and the other of its Compliment. Say, therefore as the whole Sine is to C F, 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 the Semirect, or greatest * Random, as you well call it. 
Or the best of the Random.   

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 Proporsitions 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.   labeled parabolas, angles, and lines, identical to previous figure 
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's 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.   labeled parabolas, angles, and lines  labeled parabolas, angles, and lines 
But when from the point A it is required to shoot downwards by a descending Hill, as AB, we shall find the quantity of the Range AB, that is, the place where the Ball falleth, in this manner. Let the direction A, that is, let the angle of the Pieces Elevation be given; also let there be given the angle of the Hills inclination CAB. Let us imagine the Horizon to be AC, and let us draw BE and HDF perpendiculars to the same: and conjoin or draw a line from C to H, which line shall be parallel to A Now upon the Table of Amplitudes we shall find how many paces AD is, but we seek the quantity of AB. Therefore make the calculation thus; as FD the Tangent of the angle of the Pieces Elevation is to DH, the Tangent of the inclination of the plain; so is AD, known in paces, to a farther number. And this shall be the measure of DC in paces; and thus the whole line AC shall be known in paces. Then say again, as AC the whole Sine is to AC known in paces, so it AB the a fourth number: and this last number shall be the measure sought of the right line AB in paces; that is, the length of the Range upon the descending plain AB. It happeneth also many times, that we are to shoot at plains perpendicular to the Horizon, as at the Walls of Cities, or Towers, or other ways; therefore also in this case we will subjoin the Computation for finding the Altitude of that point in the said Wall where the Ball is to hit.   labeled parabolas, angles, and lines 
Let the Direction of the Piece be the Line AB, and the Horizon AC, and the Wall of the Tower DE perpendicular to the Horizon: and let the distance AD be known in paces. Let us suppose that the Ball passeth freely without hitting the Wall, and falleth upon the Horizon in C. The Table of the Amplitudes giveth the quantity of AC, but we seek the Altitudes DE. Draw CB perpendicular to the Horizon, and DF parallel to AB, and then draw a line from F to A, which shall pass thorough the common Section of the Parabola, and of the Wall, as may be collected from the things already demonstrated. Now say, as CA the length of the Horizontal line is to CD the difference betwixt the lines AC and AD already known, so is BC the Tangent of the angle of the Elevation of the Piece, to CF the Tangent of the angle FAC. Again say, as the Sine Total is to AD known in paces, so is the last found Tangent of the angle FAC to a fourth number: which shall be the desired measure of the right line DE in paces. And thus we have found the point E in which the said shot would stick. The same calculation may be also deduced. Although the Wall DE be not perpendicular, but scarved, as those of the modrens Fortresses; but fearing to procure you more trouble than benefit, I will refer the care of that to the Geometrician that hath a mind to undertake it.   labeled parabolas, angles, and lines 
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 Balls are to hit, and the Rangers to determine.   labeled parabola, angles, and lines 
Let the height of the Hill or other place be G F, and from the point F, let a line be drawn upon the plain of the Field G E: and let us suppose the Horizon to be F B: now having made the Range F C B E at an Elevation, the measure of G E is sought.  
By the Table of Amplitudes, we find the quantity of A B, and by the Table of Altitude, we find A C, the height of the Parabola. And for the working of the Computation, it may be performed sundry ways.  
Let the number of A B be squared, and divide that square by A C, and the Quotus shall be the right side of the Parabola F C B: Then multiply that Quotus by C D, and the square Root of the Product shall give D E.  
Or we may work thus:  
Draw the number D C into C A, and the square Root of the product shall be the mean proportional betwixt D C and C A. Then say, as C A is to the  Root, so is A B to another number. And this fourth number shall again be D E.  
Or lastly, in this manner:  
Say, as the number C A, the Altitude of the Parabola in the Table, is to the number C D, the Altitude of the Parabola and Range together, so is A B the Semi-Amplirude of the Parabola in the Table to another fourth number.  
Then take the number that is mean-proportional betwixt that last number and A B, for that mean-proportionall shall give you the said D E. And for as much as D G, equal to A B is known, the whole line G E shall be known.   labeled parabola and lines 
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.   quadrant measuring an angle 
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 sallible, 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 * Randons' increase. But the first point currying 1032, the second increaseth above it 
Or Mountures.  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.   quadrant measuring an angle 
Now it is manifest by our I. Proposition, that if the line of the * direction, or of 
Of Mounture.  the elevation of the Piece shall be A O, or A P, the Amplitude or length of the Range shall be as the Quadruple of the S O; and if the direction shall be A M, or A N, the Range shall be as the Quadruple of R M: and if the elevation were according to the line A F D, the Range shall be as the Quadruple of Q F: but the lines S O, R M, and Q F, 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  ot●er 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, ●he 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.   labeled rectangle inscribed by a labeled parabola 
Take the Rect-angled Plate A B C D, of Brass, or other solid Matter, having the side A E long, for the applying of it to the Piece. Upon the Diameter A B, draw a Semicircle A F B, which shall be the Semicircle of Proposit. I. De Projectis; and in B place the Thread and Plummet, and divide the Semicircle A F B into 90 equal parts, which shall be the 90 degrees of the Quadrant; or into 144 equal parts, which shall be the equal Points and Minutes of the ordinary Quadrant. Let us now demonstrate Geometrically, that this square is convenient to measure, with exceeding plainness, the lengths and the Altitudes of the Ranges, the times of their Durations, the sublimities of the Parabola's, and the Elevations of the Pieces. And then we will set down the Division of the Lines thereupon, without the need of any Table for the using of the same.   various labeled lines emerging from the mouth of a cannon 
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 A B I be prolonged indefinitely, as also the perpendicular T B L; then by imagination take B L of such a length, that it may be really equal to half the greatest Range of our present Piece. And about the Diameter B L, let there be imaginarily drawn the great Semicircle B I L; cutting the Circumference B I in any point I; and draw the Horizontal line I M. It is manifest, by the  Propos. I. of Projects, that the line M I shall be the real fourth part of the length of the Range; as also, that D M shall be the (not imiginary, but real Altitude of the said Range; and so the other measures in the Semicircle B I L, shall be all true and real. Now observe, that the Triangle H B F is like to the Triangle B I M, 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 A C, as is between all the true measures in the imaginary and great Semicircle B I L; that is, the lines, A B, B F, F H and H B, shall be to one another in the same proportion respectively as L B, B I, I M, 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 reduced to Manual practice, and that with facility. Every one seethe that for our obtaining knowledge of the quantity of the lines A B, B F, F H, and H B, 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 A B, and Semi-Diameter E D, 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 A B 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 A B 1500, is the half of the greatest Range 3000; as also, that the perpendicular Semi-diameter E D 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 A B in the precedent figure in 2000 equal parts: also let the Semi-Diameter E D 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.   various labeled lines emerging from the mouth of a cannon 
If you desire the Altitudes, and not the lengths of Ranges, then make the same working as before, but not with the lines I O and M L, which give the lengths, but with H O and H L, which give the Altitudes. And if we would have the sublimities, it would be necessary to work with G O and G L. Butler, 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 I O 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 M L. 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.  
The times or durations of the Ranges are given by the Lines H I and H M: and to find the Quantity of these it may be done two ways. First, by way of calculation: For the square of the time H I (in the precedent Figure) is always equal to the two squares of the Altitude H O, and of the fourth part of the length I O. Secondly, by making to all the Divisions of the Perifry B, C, D, (in the present Figure) from the Centre A the circular guides B E, C F, D H: for A H being thus divided into very small equal parts, it shall measure all the right lines, A B, A C, and A D, which are the times of the Ranges.   various labeled lines emerging from the mouth of a cannon 
Yet we confess as to Military use, the Amplitudes or lengths of Ranges, only seem to Import; and they are of great moment: the rest are all accessary curiosities, which serve much more to the pleasures of Geometry, than to the occasions of War; therefore he that would have the square made only for this respect of Longitudes, may take the Semicircle A B C of Brass (as in the present Figure) having its side A D, and with the Semicircle E B, divided into most minute and equal parts, beginning the numeration from the point E; and may give moreover to all the points of the Perifry F, G, H, I, their guides G H, and F I parallel to A C: And thus he hath divided and numbered upon E B all the lines F N, and G O, which serve for the Amplitudes or Longitudes of the Ranges.   labeled parabola and lines  

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 th●●● Panahola, 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 * Grazing. 
Di striscio.  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.  
1. WE will speak only of the Ranges of Great Guns; therefore, Let us suppose, that that portion of the Line which the Ball maketh a little before, and a little after its blow, be as it were a Right Line. I know that we treat of a Line really curved; but being (if it were entire) in length more than three thousand Geometrical paces, we may take a yard, or a foot, or an inch thereof, without any sensible error, to be a Right Line.   three lines of increasing size, labeled A, B, and C 
2. Let us suppose secondly, that the Forces or Impetus' of 
Galil. 2. de Motu equabili.  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, the Impetus' or Forces of the Movable in battering 
Galil. 3. de Mota equabili.  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.   three unlabeled lines of varying size 
4. Let us suppose, in the next place, that all the Ranges have, as to themselves, the same Impetus: which will happen if the Piece being fixed always in the same place with the same Charge, the same Mounture, and Distance, etc. the obliquity of the Wall be only varied.   a right triangle and a wall 
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 A C. 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 Impotus 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.   an arc, inscribed by triangles, atop a plane 
Let us suppose, now, that the force of th' Evidence A B be as A C. To know the force of any other Incidence D B, let D B be taken equal to B A, and having drawn D E perpendicular unto the Plane, the force of this Incidence shall be as that same Line D E. For if A B and D B are equal, and are the Ranges of the same Piece, they shall be passed in the same Time. Therefore A C and D E, are also past in the same Time: 
By Supposit. 2.  Therefore th' Impetus', as to the Wall, are as A C to A D. 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.  
IT is deduced from hence as a Corollary, that the Perpendicular Incidence A B, 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 D B 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.  
Let a Projection be made along the Line A C, and another along the Line A B. And let the P●ane of the Triangle A B C be perpendicular to the Wall. Because now the Space A C is passed by the Ball in the Time A C; and the Space A B, that is (the parallel Motion deducted) the same Space A C, is passed in the Time A B, the Forces shall be reciprocal to the Times: that is, the force along A C shall be as A B, ● and along A B, shall be as A C. 
By Supposit. 3.    a right angle and a wall 
3. Projects shall then have the same force in battering, when the Impetus' shall be as the Secants of the Compliment of the Incidencies.   a right angle atop a plane 
For if the Impetus' along A B and A C shall be as the Spaces A B and A C, the Movables shall, in the same Time, pass the two Lines A B and A C, that is, the same 
By Supposit. 2.  perpendicular Approximation A B. Therefore they shall have the same force against the Wall.   an arc, inscribed by a triangle, and a wall 
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 Reflexious, 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 12 4/5 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 fathon●s 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 extende● 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 Armoty, 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 opportunities 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 fathoms.  
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 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 fign 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 The first leap 392 790 The second leap 275 1065 The third leap 179 1244 The fourth leap 150 1394 The fifth leap 81 1475 The sixth leap 73 1548 The seventh leap 78 1626. The eighth leap 124 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 537 ½ 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 remmed 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, and the other be forced 
Of this there is a controversy between Borellius who published a Treatise de vi percussionis, the which was writ against by Honorato Fabri ●● his Dialogues of Motion.  horizontaly, 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 ●● least a thousand times lighter than water: and sccing 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 Peril 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 1/●, also horizontally shot off out of an other Gun 12 foot and ½ long, spent only 6 seconds in the air; another Gun shot off at the Elevation of 15 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 rock 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 f●ll, * 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 
Experiments of this kind the Reader will doubtless find, as also others about Pendulums in the Opuscula Posthuma of 1. Bap. Batiani.  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 D●kes 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, un till it touch it, as it had made before the bending of it.   various angles and parabolas 
But now let us suppose that horizontal shot O P, or T V, removed to the lower figure in which let A B be the horizontal plain, and let the the v horizontal shot be A I, Galeus contends that the middle range of 45 degrees, which is the longest of all, is eleven fold the length of the horizontal shot O P, or A I: And in those Guns which are half the weight of the foregoing greater Guns, to be in respect of A I, 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 A G E B; 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 Elevationof 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 A C 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 F E 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  1 8758 2 7813 3 7077 4 6482 5 5991 6 5581 7 5234 8 4932 9 4669 10 4440 11 4237 12 4055 13 3889 14 3741 15 3606 16 3483 17 3370 18 3266 19 3279 20 3080 21 2996 22 2978 23 2845 24 2776 25 2712 26 2651 27 2593 28 2538 29 2486 30 2437 31 2391 32 2344 33 2300 34 2260 35 2221 36 2183 37 2146 38 2111 39 2077 40 2044 41 2012 42 1981 43 1952 44 2007 45 2041 46 2076 47 2113 48 2150 49 2189 50 2230 51 2272 52 2317 53 2363 54 2412 55 2463 56 2516 57 2572 58 2633 59 2695 60 2762 61 2832 62 2908 63 2989 64 3075 65 3168 66 3268 67 3376 68 3493 69 3621 70 3762 71 3916 72 4086 73 4276 74 4489 75 4732 76 5006 77 5303 78 5690 79 6263 80 6641 81 7274 82 8059 83 9061 84 10430 85 12330 86 15140 87 19850 88 29250 89 37480 90 00000 Finis.  

The Second Table.  deg  1 1.142 2 1.280 3 1.413 4 1.543 5 1.669 6 1.792 7 1.911 8 2.028 9 2.142 10 2.253 11 2.361 12 2.467 13 2.572 14 2.674 15 2.774 16 2.872 17 2.968 18 3.063 19 3.156 20 3.248 21 3.339 22 3.428 23 3.516 24 3.603 25 3.689 26 3.774 27 3.858 28 3.941 29 4.024 30 4.105 31 4.186 32 4.267 33 4.347 34 4.426 35 4.505 36 4.584 37 4.662 38 4.740 39 4.818 40 4.895 41 4.972 42 5.050 43 5.127 44 4.985 45 4.902 46 4.819 47 4.736 48 4.653 49 4.570 50 4.487 51 4.403 52 4.318 53 4.234 54 4.148 55 3.062 56 3.976 57 3.889 58 3.800 59 3.712 60 3.622 61 3.532 62 3.440 63 3.347 64 3.253 65 3.158 66 3.061 67 2.963 68 2.864 69 2.762 70 2.659 71 2.554 72 2.448 73 2.339 74 2.228 75 2.114 76 1.998 77 1.880 78 1.758 79 1.634 80 1.506 81 1.375 82 1.241 83 1.102 84 0.960 85 0.812 86 0.661 87 0.504 88 0.342 89 0.174 90 0.000 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 a 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.  
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.    

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, a middle Range 
Former Figure.  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 sound 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 〈◊〉, or at least by reason of the resistance of the air breaking the water it ought to descord 30 foot.   
FINIS.