THE Complete Cannoniere: OR, The Gunner's Guide. Wherein are set forth exactly the Chief grounds and principals of the whole Art, in a very brief and Compendious form, never by any set forth in the like nature before. With diverse excellent Conclusions, both Arithmetical and Geometrical belonging thereunto: As also sundry serviceable Fireworks, both for Sea and Land service. A Study delightful and very useful for men of the best Quality, and embraced by the greatest Princes.  
UIRTUS GLORIAM PARET.  
Written by JOHN ROBERTS of Weston near bath, Gentleman, Practitioner and Professor in the Art thereof.  
LONDON: Printed by J. Okes, and are to be sold by George Hurlock at his shop in Thames-street near S. Magnus' Church. 1639.   

To the High and Mighty Monarch CHARLES By the Grace of God, of Great Britain, France, and Ireland, King, etc.  
SIR,  
BEing filled with an admiration of your Royal parts, and a declaratory Fame of the Virtues and heroic Actions of your Fame worthy Progenitors; and those transmitted unto You, by a successive Lineal and Hereditary right, so that that rare Conjunction of Castor and Pollux, I mean Majestas & ortu & Arte, are both happily conjoined in your most Sacred Personage. The curious survey of the multitude of your Princely parts breed in me a number of desires so that I have adventured to break the barren soil of my poor portion; that prosperous success should rather want to my endeavours, then diligent endeavours to my loyal determination. My submissive allegiance to Your Royal and Heroic Virtues, have been an encouraging cause to desire Your Majesty's gracious Patronage of this little Treatise of Gunner's Art; but how my unworthiness may hope of your Goodness, I cannot find but in the Notes of Your transcendent and gracious Disposition. Thus in the lowest humility of allegiance, I offer both myself, and the employment of my undeserving Service freely to your Highness' acceptance, and do desire both to be and appear to be  
Your Majesty's humblest and most devoted servant, john Roberts.   

To the right Honourable MOUNTIOY Earl of Newport, Lord Mountioy, Master of his Majesty's Ordnance.  
Right honourable:  
THe favourable countenance and furthering Respect which my Predecessors received of that renowned General, and ever memorable and remarkable Martialist the Right Honourable the Earl of Devonshire, of never dying Memory, your Lordships late deceased Honoured Father, together with the Duty and Oblegiance, all those of my Quality own unto your Honour; by reason of the Place and Dignity most deservedly You are in, and called to; makes me of Socrates' Opinion, in acknowledging all my utmost not able to reach the half height of your Lordship's Favour: Wherefore labouring like the Bee, sucking from the choicest Flowers the best Honey I can gather, the night of rest being come, I bring it to the Hive of your kind acceptance, and there leave it, as much labour bestowed about little, till diligent employment may more amply increase it. Right Honourable, I am loath to be troublesome, especially where affable Gentleness out paceth any merit in myself: Therefore presenting your Lordship with this Treatise of Gunner's Art, and my attendant Service, when it shall please your Honour to employ me; and praying devoutly for the endless prosperity of You, and yours, I humbly conclude  
Your Honours, in all duty to be commanded. John Roberts.   

The complete Cannoniere.  
And first of principals of Philosophy fit to be known.  
ALl motions or things movable endeth in their rest or repose.  
So all motions are made upon some quantity continually.  
Every simple bodies is either bright and light, or else gross, dark, and ponderous: and according to the variety and differences, it is always naturally carried towards some one or other part.  
The World hath height as upwards, or depth as downwards; and the depth dependeth upon the influence of the height.  
All pure and rare Bodies ascend as the fire, more than the air; but the thick and gross bodies descend, as the Earth more than the Water.  
Nothing worketh naturally in that which is wholly like, or wholly dislike, but in that which is contrary to it, and more feeble.  
The form working is aided by the qualities as the matter suffering, which suffereth by the quantity.  
Nature is extremely curious as well of her perfection, as of her conservation? and then when all things conspire.  
Aswell the action that cometh from the Agent, as the passion from the patiented hath proportion.  
Accident taketh his unity from the subject, and goetlis not from one thing to another.  
Every Corporal thing reposeth in its natural place, motion may be made any where within the Moon's Orb, nature admitteth no Empress.  
A body rarifying its self, the place thereof increaseth as the body increaseth.  
The resistance of the moved, proportioned to the mover furthereth the motion.  
The longer the chase of a piece, the louder the report.  
Also the force of the stroke dependeth on the swiftness of the course.  
A Table of the Square. A Table of Cubes. 1 1 1 1 2 4 2 8 3 9 3 27 4 16 4 64 5 25 5 125 6 36 6 216 7 49 7 343 8 64 8 512 9 81 9 729  

How to extract the square root.  
SEt down any number as comes into your mind, as thus, 2̇ 1 6̇ 0 9˙. Then begin at your right hand, and put a prick over the first figure, and then over the third, as you see above done; & ask what is the square root of 2. which is as many figures as you have under your first prick, & you shall find but 1. then put that figure in the quotient, and subtract that 1. out of 2. so remaineth 1. then double your quotient, & set that double under your second figure, dividing the number over by that double. But take heed you leave enough to take the square of that figure last set in the quotient out of the remainder. Lastly, double all your quotient, and divide as afore; then square your third figure in the quotient again, and subtract it out of the remainder, so have you done this sum. Look how often you have pricks, so often must you double and multiply squarely, and subtract also, so many figures also will there be in the quotient, as there are pricks. And consequently of any number whatsoever.   

To know the nearest root of a number not square.  
IF any fraction remain, by diligent observation of this, you may come as near you would desire in any practice, to guess within less than ordinary is known. Set next your right hand after your sum, either two, four, or six cyphers, the more, the lesser your error; and the nearer by much shall you come unto the root, observing the same manner in working as you did before.  
And now I will show you by particular questions in the art Military, how necessary it is for any one intending to be a complete martial man, to have good judgement in the extraction of the square and cubic roots, and also in the depth of Arithmetic, and what excellency of knowledge is attained unto thereby, and how fare they are from being Soldiers, as are ignorant thereof.   

The first Question.  
A General having 3 great Armies, would cast them into three square battles, but he knows not how many men he shall set in the front of each battle.  
The number of the 3 Armies are these, in the first there are 5625. in the second 9216. and in the third 15129.  
To do this, you must extract the root of every Army severally, so have you your desire.  
In the first you have 75. men square, in the second 96. men, and in the third 123.  
If you were commanded to make a square battle of all three Armies, add them first together, then extract the square root; and if any remainder be, you may employ them where you please.   

The second Question.  
A King hath a great Army in a valley that in marching, the front can be but 18. men, & the flank 44352 which he is desirous to cast into a square battle.  
Multiply the flank by the front, so have you the full number of the men: then extract the square root thereof, so have you what can be desired.   

The third question.  
A General hath 3 Armies in the Field, to the number of 28289. men, and none of these three apt to make a square battle; the Sergeant Major is commanded by his General to set them in three square battles.  
These are the 3 numbers of the three several Armies: In the first there are 10296. men: in the second 9493, and in the thire 8500 men.  
Mark this seriously for it is not ordinary; you shall find more exquisite work than you imagine, because the question is more difficult.  
First, extract the several roots of the 3 Armies.  
Then take the greatest squares of all 3 numbers, as 10201. and his excess 95. together with his root, which is 101.  
In the second the greatest square is 9409, and 〈◊〉 ●…cesse 84, and his root 97.  
In the third, the greatest square is 8464, his excess 36, and his root 92. And thus have I found the 3 excesses.  
Now for to end the 3 defaults or wants, I add one to each root, and multiply them squarely, and so of 1●…2. I find the square to be 10404, and if I subtract the first number, which is 10296, out of it there will remain 108 for the first want, and thus do by the other two, so your excesses and wants will be as are here set down in particular.  
 A B C Excesses 95 84 36 Wants 108 111 149  
Here I compare the excesses with the wants, to see if any two excesses will make up the others want, and I see by a light proof it will not justly serve.  
As for the wants, I do not compare them to the excesses, for every want is greater than the excess: therefore two wants fare too great for one excess.  
Wherefore when this rule faileth, take the two wants of any two numbers, and add them first together, then abate them from the third number, and if the remainder be a square number, you have gotten your desire.  
As for example, take the wants of the first and second, which makes 219, and that do I abate from the third number 8500, and there remains 8281, which I see may be a square number, and 91 the root thereof.  
Wherefore I say, that these three numbers following shall be the roots of the square battles, as here I have set them.  

The first battle 10404, and his Front 102.  
The second battle 9604, and his Front 98.  
The third battle 8281, and his Front 91.   
The sum total of all the 3 battles 28289 men.   

The fourth Question.  
A General having 3. Armies in three several battles, in the first 4900. men in the second 2401, and in the third 2500. so that the greatest is as much as both the other, except one man, and he is enforced to join all three battles into one: but is in doubt whether he may have good and convenient ground to encamp them in for●… of battle. Wherefore considering that all three battles together are but double to the greatest of the three alone: The Sergeant Major desiring a mere ground for his Army, so joined in one square battle, is in doubt what square of ground will serve his purpose; but sure he is, that it must be double to the ground, that the greatest Army of the three did use, and that was every way 21●…. foot: wherefore his demand is how many foot square shall the side of that ground be, that is, double to the former square, whose root was 210. foot.  
First multiply 210. by itself, and so have I the just 
〈…〉.  plat of ground of 44100 foot; that must I double, and it will be 88200. and out of this number shall I seek (as before is taught,) the nighest square root. For just square I see it is not, by reason that after the even cyphers, there followeth the figure 2. which is one of those figures that cannot begin any square number, therefore (as I said above) you must seek the nearest square root, which for brevity's sake, and because I have sufficiently already treated of, do leave it to your best leisure to practise. Infinite more questions tending to this purpose, could I set down, but that time will not permit, or my intended little volume contain, therefore I will proceed to show you the extraction of the Cubic root, which will be much to the purpose and subject I am now to treat of.   

How to extract the Cubic root.  
FIrst, begin at your right hand, and set a prick over the first figure, than another over the fourth, so leave two figures unprickt, and prick the third still until you have done thus, 79864345 As many pricks as are over the number, just so many figures will there be in the quotient.  
1 Then ask what is the Cubick root of the first prick, and set down that in the quotient: and if it be so that root doth not take all away of the number from the first prick, subtract as much as the root containeth, and set the remander over head the figures which stood there before, being canceled.  
2 Then triple your quotient, and that triple you shall set under the next number towards your right hand, before that prick which you did last end.  
3. Next, multiply that triple by the same quotient, and set it down under the first triple, and that number shall be your Devisor.  
4. Now must you look out a quotient that may declare how often the devisor is in the number over it.  
5. This being done, you must multiply the last figure in the quotient by your devisor, and set it under your devisor, with a line between.  
6. Then multiply the last figure in the quotient by itself, and then in the triple, and set that product below the former one figure more towards your right hand.  
7. Lastly, multiply the last figure cubically, & set that sum also one figure nearer the right hand: then add all these three multiplications together, and subtract it out of the first & second pricks; I mean out of all those figures unto the second prick: this done, triple all your quotient, and divide as before, and as you did by the first and second pricks after your division, so do by the rest, and you have obtained your desire. Look upon this following example.   

To find the nearest Cubic root not cubical.  
You must do it by addition of cyphers (as is spoken of before in the square root) in such sort that they must be always ternaries, as 3 or 6, or 9 or 12, and then proceed forward with the like order of work, as before.   

A question of doubling a Cube.  
IF the side of a Cube be 3 foot, how many foot shall the side of that Cube be, which must be double unto it?  
First find the quantity of that Cube that is propounded, and then double that quantity; lastly, extract the cubick root of that double number.  
As for example, the cube is 3, and therefore the whole Cube is 27, whose double is 54, and the Cubick root is 3 foot, and ●…/100 and 1/7 of 1/100.  
Cube of 2.  
Cube of 5.   

A question of two Cubes.  
A Cube of brass of four inches square, doth weigh 7. pound weight, what shall a cube of brass of nine inches weigh?  
The proportion of their sides are as 9/4, which I must set down twice, and multiply them together as fractions should be, and so will it be thus 999/444 that maketh ●…/●….  
Wherefore I multiply the weight of the lesser Cube, being 7. by 729. and it maketh 5103. and that do I divide by 64. and so find I 79. ●…/●…, whereby I may know, that the weight of the greater cube is 79. pound, and near ¼ of a pound.   

A question of a Gun.  
A Gun of six inches diameter, doth shoot a bullet of twenty pound weight, what weight shall that bullet be, that serves for a Gun of 14. inches in diameter.  
All Globes bear triple that proportion, that their diameter does. So in this example, the proportion of their diameters 
〈◊〉  being as 14. to 6. or as 7. to 3. I shall triple it, and 
Some●…ake more, as now is sound.  then have I the proportion of their globes.  
Wherefore I set the 3. fractions thus, ●…/●… and they make ●…/●…, that is 12. ●…/●… when you have divided the Numerator by the Denominator. And so is the proportion of the globes as well in weight as in bigness. Therefore I multiply 20. that is the weight of the lesser by the numerator of the proportion, & divide it by the denominator. And so shall I have 254. ●…/●… for the weight of the greater bullet.   

Another question of a bullet.  
A Bullet of Iron of seven inches diameter, weighed 27 pound, what shall be the diameter of that bullet, that shall weigh 125. pound?  
I set down ●…/●… and I see the cubic root of 125. is 5, and the like root of 27 is 3; which numbers I set in the room of the other thus ⅓ which declare the proportion between the diamiters of the two bullets. The diameter of the lesser is known to be 7. Therefore I multiply that 7 by 5, whereof cometh 35: that divided by 3, yields in the quotient 11.   

The proof hereof.  
Multiply both roots cubically, if their roots be in proportion as their weights, then is your work true, else not. As for example, 7 multiplied cubically, make 343, and 11 ⅓ multiplied also cubically, makes 428 ●…/●….  
To multiply a fraction cubically, as 11 ⅔ first reduce it, and make it 35: that 35. multiply cubically, you have your desire.   

How to turn a whole number into a fraction of the like denomination.  
SVppose 7 is the number you desire to turn into the like denomination, that is ●…/●… (as above) is of, Multiply 7. by 3. the denominater of the other fraction, and it maketh 21. that 21 multiply cubically, and it will be ●…/●…: These few rules diligently observed, will much enable an Artest to perform many things belonging to this subject, also much benefit, experience, and delight, shall any man reap, that hath judgement to try and practise the secrets thereof.   

A question of whole numbers and fractions.  
A Falcon of 2. inches in the diameter shoots a bullet of 3. pound, what shall the Culverin shot weigh, whose diameter is 5. inches ¼.  
To answer this and all such questions that must be cubically multiplied, you must reduce each bullet into his proper fraction. As for example, 2 ¼ maketh ●…/●… and also 5 ¼ maketh ●…/●… than I multiply each numerator cubically, and I find the Cube of the lesser to be ●…/●… and the Cube of the greater to be ●…/●…. Then I set down 3, the Diameter of the lesser fraction like as before thus ●…/●… which being wrought punctually by the rule of three in fractions, you shall have for the weight of the bigger bullet 20. pound, and almost ¼.   

How you Geometrically find out the Diameter of any bullet that weigheth twice so much as a known bullet.  
TAke the true weight or diameter of the lesser bullet, whose weight you know, and square the same as in the figure following: Then draw a line that may divide the said square into two equal parts, in the 2. opposite angles, and that line shall be the diameter of a bullet, twice the weight of the other; then divide that diametriall line in 2. equal parts, setting on foot of your compass in the Centre, and with the other foot draw a circle. and that circumference will represent a bullet twice as much in weight as the lesser.  
  

To prove it Arithmetically.  
THe diameter of the lesser bullet is 5. inches, the square 25. that sum double is 50. the square root of 50. is 7. and somewhat more, and so much is the diameter of the greater bullet.   

By one bullet to know the weight of another, the Diameter given.  
A Canon of 7. inches, shoots a bullet of 32. pound: I demand what weight that bullet shall be of, that is 9 inches in the Diameter.  
Multiply the Diameter of each Bullet cubically, as 7. times 7. is 49. and seven times 49. is 343, than 9 times 9 is 81. and 9 times 81. is 729. then by the rule of 3. say, if 343. give 32. pound, what shall 729. give? Multiply and divide, and your quotient will be 68 ●…/●….   

How by the weight of one Piece, to know the weight of the other.  
IF a Minion of three inches Bullet, weigh 500 pound, I demand how much a Cannon of 8. inches bullet will weigh, that is able to receive his proportional charge to the Minion. The Cube of 3. is 27. the Cube of 8. is 512: now by the rule of proportion say, if 27. give 512, what shall 500 give? multiply 512. by 500 and divide that product by 27, and you will have in the quotient 9481. ●…/●… the true answer to the question.  
The Cannon therefore that shall be able to carry a proportional charge to the Minion, must have 9481 ●…/●… pounds of mettle: but because commonly those greater sorts of Ordnance are not so massy of mettle as indeed they ought to be. The Gunners observe this for a general rule, that in all pieces of above 6. inches in boar, they abate ●…/●… of their ordinary charge.   

To know how many shots of Powder will be in a grand Barrel of Powder, for any Piece.  
SVppose a Culverin shoot 10. pound at one shoot, how many times will a grand Barrel of Powder serve the Barrel holding three hundred weight?   

Example.  
Divide 300. by 10. the quotient is 30. your desire.   

The proof.  
Multiply 30. by 30. or 30. by 10. gives 300. so may you know for all other sorts of Ordnance whatsoever.   

By knowing what powder a Piece must have, to know how much a piece of another boar will require; but, Cave.  
IF a Minion of 3. inches the Bullet, requires 3. pound of powder for his charge, what powder will a Cannon of 8. inches bullet require?  
Multiply 512. the Cube of 8. by 3. the charge of the Minion, and it maketh 1536. which divide by 27. the Cube of 3. the Diameter of the said Minions Bullet, so have you in the quotient 59 ●…/●…, so many pound of powder is the due charge of your Cannon, but by the rule aforesaid you find the Cannon hath not his proportional mettle, therefore you ought to abate ¼ of the powder, so will there remain 44. pounds, or near for your Cannon's charge.   

To find the superficies of a Bullet.  
FIrst, by a pair of Callibres find out the Diameter, which suppose it be 7. than must the circumference be near 22. but for speedy work, and to avoid a tedious discourse thereof, being that no great error ensueth thereby, take 22. now multiply that number by 7. it produceth the superficial content of that Globe, ball, bowl, or bullet.  

A Table showing the weight of all Iron Bullets, in Haberdepoize weight.  Height of the Shot, in inches and parts. Weight of the Shot in pound & parts. Height of Shot incircles &. parts Weight of Shot in pounds and parts. Height. Weight. Height. Weight. 2 1●…/●… 5½ 19●…/●… 2¼ 1½ 5●…/●… 22●…/●… 2½ 2⅓ 5¼ 25⅙ 2¼ 3●…/●… 6 29½ 3 4½ 6¼ 32⅛ 3¼ 5 6¼ 40¼ 3½ 6●…/●… 7 46 3¼ 7●…/●… 7¼ 52●…/●… 4 9 7½ 56⅝ 4●…/●… 10¼ 7¼ 64½ 4●…/●… 12⅔ 8 70 4¼ 14⅛ 8¼ 76⅔ 5 16¼     

To find out how many square inches are contained in a solid content of a bullet, and consequently, how many pound weight.  
THere is a bullet whose diameter is nine inches, how many square inches are there in the solid content? Multiply the diameter 9 cubically, ariseth 729. which multiply again by 11. maketh 8919: that divide by 21. yields 381 inches and ●…/●…: so many inches are in a bullet of 9 inches diameter. Now to know how many pound weight is contained in that globall body, multiply that quotient 381 ●…/●… by 4. and divide by 16. it will show how many pounds of Iron that bullet weigheth: for an inch square of cast Iron, weigheth four ounces ferè.   

To find the true content of a circle.  
TAke the one half of his diameter, and multiply it in one half of the circumference, and it produceth the Area, or square the diameter, and multiply the product by 11. and divide the result by 14. and it also showeth the content.   

Arithmetically to find out the mean proportion between two numbers.  
MUltiply both numbers one in another, and then extract the square root, so have you the mean proportional.  
Suppose the line given is 12. and the perpendicular 9 now you must multiply 12. in itself, and it maketh 144. then multiply 9 in itself, and it maketh in product ●…. then add both the multiplications together, and it maketh 225. Lastly extract the square root, and it leaveth 15. the justlength of the hypothenusal sought.   

Geometrically to find the mean proportiou between two lines.  
EXtend one of the lines to the number of inches he is in length, upon the end whereof erect a perpendicular to the just length of your other supposed line: then that line which is the hypothenusal to them both, is the mean proportional.   

The hypothenusal and one side given, find the other.  
MUltiply each number in itself: then subtract the lesser out of the greater: the square root of the remainder is the true length of the third side.   

Arithmetically to know how much of every sort of metal is in a piece of Ordnance.  
FOr every hundred pound weight of Copper, to p●… in ten pound of Latin, and eight pound of Tin. I d●…mand the quantity of each sort of metal is in a Culverin of 5600. pound weight?  
Note that I join all the several mixtures together, and they make 118. pound, which is my Devisor: then I multiply the weight of the piece by each mixture severally, and there ariseth of 100 of Copper 560000: the which sum is to be divided by the Devisor 118. and the quotient is 4745. and ●…/●… parts, so much Copper is there in that Ordnance, and thus must you do to know how much you have of the other two sorts of mettle.  
To prove this, add all three quotients together, if they make the sum before mentioned, it is right.  
The Latin doth incorporate, and causeth the piece to be of a good colour, and the Tin doth strengthen and bind the other mixtures together.   

To find the superficial content of the hollow concavity of a piece of Ordnance.  
SUppose the diameter be 7. inches, and the cilinder 12. foot, what is the content superficial?  
Reduce the Cilinder 12. foot into inches, maketh 144. which multiplied by 22. the circumference of the muzell ariseth 3168. the superficial content of the metal compassing the hollow cilinder.   

To find the crassitude, or solid content of the Cilinder of any piece.  
FIrst multiply one half of the diameter, in one half the circumference, or else square the diameter, and multiply that product by 11. and divide the result by 14, the quotient will show you the content: the which multiply in the length of the Cilinder, the product is your desire.  
If you desire how many foot in square measure it contains, divide the number of inches in the solid content, by the number of inches in a foot square, which are 1728. your question is resolved.   

To measure any sort of Timber.  
SUppose your timber be 8. inches one way, and 6. inches another way, and you are desirous to know how many inches in length will make a foot square.  
Multiply 8. by 6. and it maketh 48. which number divide 1728. (because there are so many inches in a foot square) and you shall have 36. inches in the quotient, so many inches long will make a foot square of Timber. Thus of all other cubically.   

A Table how to weigh a great deal with few weights.  
You may weigh any number of pounds from 

One to 40. with these 4. weights. 

1  
3  
9  
27    
One to 121. with these 5. weights. 

1  
3  
9  
27  
81    
One to 364. with these 6. weights. 

1  
3  
9  
27  
81  
243      
The pounds to be weighed, are weighed with as many namelike weights, to be done either double or threefold: sometimes by adding one weight to another, and sometimes by taking away and adding to the contrary balance.   

To measure any sort of board, glass, pavement, etc.  
FIrst multiply the breadth by the length, as a board is 17. inches one way, and 139. inches another way, multiply 139. by 17. and it maketh 2363, which divided by 144. leaveth in the quotient 16. foot and ●…/●… parts of a foot. Note that in flat measure there is but 144. inches in a foot, but in square measure 1728.   

To measure Land.  
MUltiply the breadth by the length (if square or long square) and divide the product by 160. because there is 160. square perches in an acre, so shall you come to the Area, but if your ground be irregular, you must cast it into triangles; & if it be a right angled triangle, multiply half the perpendicular by the whole base, and divide it by 160: but if it be an obtuse triangle, let fall a perpendicular from the obtruse angle to the base, and multiply half the length of that perpendicular by the whole base, and divide by 160. as before, you have the content.  
Also if you have a piece of Land to set out, as to know if it be 12. Perches in breadth, how many perches it should be in length, say by the back ward rule of 3. if 4. gives 40. what shall 12. give? multiply, 4. by 40. makes 160. which divided by 12. and it giveth 13, perches, and ⅓ so of all such like.   

To measure any irregular substance whatsoever, as a crown, Horsehead, or any Image, or concaved piece.  
TAke a vessel that is very staunch, and 4. square, and put water into it, & when the water is setted, mark with your knife how high it riseth in the Vessel, and then put in your irregular form whatsoever it be, & mark with a knife again how high the water than bears, or riseth; then take out the irregular form again, and measure exactly the space between the marks, and multiply the breadth by the thickness, and observe the length, and you have your desire.   

●…ow by knowing the weight of one Fathom of Rope, to know the weight of another.  
A Cable of 10. inches compass weighing 16. pound every Fathom, how much will a Fathom of that Rope weigh that is 15. inches in the Diameter, and made of the same stuff▪  
Multiply 15. the greater in itself maketh 225, and that multiplied by 16. the weight of a Fathom of the lesser Rope, maketh 3600. which divided by 100 being the square of the lesser rope, leaveth in the quotient 36. pound, the true content.   

By the compass of any small rope, to find the Diameter and weight of one, four, five, or six times as big.  
SUppose the small rope is 3. inches compass, and that it is required to know the height of another 5. times that compass, multiply the number 3. squarely ariseth 9 which multiply again by 5. maketh 45. then extract the square root thereof, and you shall have 6. ½ so much in Diameter is the greater, that done, you may as before find his weight and circumference.   

How to know what empty Cask will carry any sort of Ordnance over a river.  
IT is thought sufficient, 5. Tun of Cask will sw●… a Cannon of 8. or. 9000. weight, 4. Tun a 〈◊〉, 3. Tun a Culverin, and two Tun a Saker, accounting all provisions to be made fast the reunto, as planks & ropes.   

How, by knowing what powder a few pieces spend, being seldom discharged, to know how much many of the same will spend being often discharged:  
IF 4 Cannons be twice discharged, and shoot 24●… pound of powder, how much powder will serve 5. Cannons, to shoot every one 6. shoot, work by the double rule of 3. and say, if four Cannons shoot 240. pound, what shall 5. do? and you shall find 300. then say again, if 2. give 300. what shall 6. give? multiply and divide, and you shall have in the quotient 9●….   

To know how much powder each Cannon spent in the former conclusion at a shot.  
MUltiply 4. the number of Guns first propounded, by 2. the number of times they were discharged, ariseth 8. by which divide 240. the quotient will be 30 which they spent at a time.   

The proportions between Bullets of Iron, Stone, and Led.  
A Bullet of Iron to the like bullet of Marble, is in proportion as 15. is to 34.  
A Bullet of Lead to the like of Iron, is in proportion as 28. to 19  
A Bullet of Lead to the like of Marble, is in proportion as 4. to 1.   

By knowing the Diameter and weight of an Iron Bullet, to find the weight of a Bullet of Marble.  
ADmit an Iron Bullet weigh 9 pound, of 4. inches high, what shall a Bullet of Marble weigh of like Diameter?  
He shall have such proportion as 34. to 15; therefore multiply 9 by 15. the proportion of the Stone bullet beareth, and there ariseth 135. which divided by 34. the quotient is 3. pound, and ●…/●… parts of a pound.   

How to know Arithmetically where to place the Trunnions of any piece of Ordnance.  
MEasure the length of the bore of the piece from the muzzle to the breech; divide that measure by 7. and multiply that sum that cometh of the quotient by ●…. the product will show you how many inches the trunnions must stand from the lowest part of the concavity of the piece.  
And farther note, that the trunions ought to be placed as ●…/●… of the circumference of the piece may be seen in that place where the trunnions are set.   

How much rope will make breechings and tackle for any piece.  
IT is a rule, though not observed by the vulgar, yet by the most experienced Sea Gunners, that look how many foot your piece is in length, so many fathom of rope must there be in one tackle for ordinary or extraordinary pieces, and their breechings to be four times the length of the ●…eece, with some overplus for fastening at both ends. I have against stormy foul weather caused diverse quoyners to be bored twice through with an angor, and nailed down upon the deck, the thickest ends close as could be to the fore trucks, of purpose to hinder (what might be) the stretching or straining of the breechings & tackle, that the piece should not any way swerve. But if your piece accidentally break her tackle and breechings, you have no better way for the present to prevent danger, but with expedition to dismount her.  
Also I could wish the rammers and sponges made of small haser, should (for lasting and for better service also) be armed close and hard with strong twisted yarn from the rammers end quite to the sponge, which would much stiffen, and make it more useful and lasting to ram both wad and bullet close to the powder, especially being done in time.  
I do advise all his Majesty's Gunners of the Navy, to take an especial heed, and diligent care in the election and choosing of the Yeoman of the powder-roome, by reason he is upon all occasions to be amongst the ammunition: for by his negligence or dishonesty, infinite loss and danger may accrue; therefore it is fit such a man should be first known to be a loyal subject, and one that would perform the office with both care and diligence before he be admitted the charge thereof.   

The names of the principal members of a piece of Ordnance.  
FIrst, the uppermost part round about the piece, may be called the Superficies of her metal; the substance or whole mass of mettle, the Body; the hollowness thereof, the Concave, Cillinder, or Soul: the whole length, the Chase: So much of her Boar as containeth her powder and shot, is the Chamber, or charged Cillinder; the remainder her vacant Cillinder; the Spindals' or Ears are called her Trunnions; and the space between them, the gravity of her Centre; the pumell at her coil, the Casacabell, or her Deck: the little hole, the Touchhole; all the metal behind the touchhole, her breech, or coile, the greatest Ring at her touchhole, her Base Ring; the next Ring, or Circle, is the reinforst Ring; the next to that, the Trunnion ring; and the circle foremost, her Muzzle Ring. Lastly, the Ring between the Trunons and Muzzle ring, is called the Cornish ring; and all the Rings, Circles, and emenencies at her Muzzle, are called the Frieze, as you may see in the figure just against this matter.   

What instruments are most fit for a Gunner.  
THe Callabre Compasses, height board, inch sight-rule, Gunner's scale, Gunners quadrant divided into 90. degrees, and into 12. points, & their minutes, with a Geometrical square to take mountures, levels, heights, breadths, and distancies: a pair of straight pointed Compasses, with a little brass level, scales and weights, Priming Irons, moulds to make cross-bar shot for Muskets, a fair Book for your accounts, and an Iron with a Spring and a Transome to dispart a Piece of Ordnance; let the Transome be to go up and down, ●…ccording to the diameter and thickness of any piece; let the Transome be long enough to reach the Basering from the Touchhole. This Instrument is very necessary, though not commonly known.   

How to load and fire a Piece of Ordnance like an Artist.  
HAving all things fitted, and in readiness prepared for ●…vice, first, mark the wind, and be sure to lay ●…ur budge-barrell, and the rest of your powder to wea●…r your Piece, then place your Lindstocke to leawards, having cleared the Touchhole, sponge her well, standing by the right side of the Gun, and when he draws out the sponge, strike two or three blows upon the muzzle, to beat off the foulness of the sponge; then his assistant declining the Budge-barrell aside, he shall thrust ●…n the Ladle to fill it, striking off the heaped powdes, and giving a little shogge, the better to settle the rest in in the Ladle; so being filled and striked, stand by the right side of the Piece, (as clear as he can from the muzzle) and put in the Ladle to the bottom of the concave very steady quite home to the touchhole, and when it is arrived to the bottom of the boar, laying your right thumb upon the upper part of the Ladle-staffe, turn●… the staff, until your thumb be quite under it, and give a shake or two to free the powder from the Ladle, bearing him up, that non●… may come out again: Then put the powder home softly with the 〈◊〉 a●…ter which put in a good wadde, and thrus●…●…hom 〈◊〉 powder giving three or four hard str●…kes, which will gathe●… the scattered powder together, that it ma●… fire the better the ●…ssistant having a thumb upon the Touchhole all the while, then put in the shot, which with a Rammer h●… must put softly home, and afterwards another wadde and then give two or three good strokes with the Rammer more, to settle all close together, that there may be no vacuity between powder, first wad, bullet, or las●… wadde: This done, place your Budge-barrell again to wind-wards, and be sure to weather your Piece in the firing, to prevent all danger. Lastly, have special care in directing her to the mark, and in priming her, let the powder come from the Touchhole to the base ring, so may you fire there safely, without danger of the fire of the Touchhole to force your Lintstock out of your hand, provided you draw back your hand in the firing, your leg standing forwards, and so doing, the Piece will be loaden, and fired Gunner like. Some use to prime before the Touchhole forwards two or three inches, and fire there; for the bigger the Touchhole is, the more care must be taken in priming, and especially in firing.   

What powder is allowed for proof, and what for action of each Piece.  
FIrst, I will begin with the biggest Pieces, as with all sorts of Cannons, for proof ⅘ and for service ½, o●… the weight of her Iron shot. For the Culverings, the whole weight of their shot for proof, and foraction, ●…/●… and for the Saker and Falcon ●…/●…, and for lesser Pieces, the whole weight in action, until they grow hot; for than must abatement be made with discretion: But in proof the lesser Pieces should have once, and ●…/●… of the powder that the Bulletweigheth.   

If Weights, Scales, and Ladles be wanting, how many Diameters of a bullet will make a reasovable charge in powder for any piece named.  
FOR the Cannons 2. ½ for Culverings 3. and for the Saker 3. ½ for the lesser pieces, 4. Diameters of the Cillinder. For 3. Diameters makes ●…/●… and 3. ●…/●… makes ●…/●… and four diameters and a half makes the whole weight of a cast Iron shot, it being corn powder, which length will also serve for Cartredges for the like pieces.   

How Moulds, Forms, and Cartredges are to be made for any sort of Ordnance.  
CArtredges are made of Canvas, or paper Royal; which prepared, take the height of the bore of the piece, without the vent of the shot, and cut the cloth or paper of the breadth of three such heights, and for the Cannon in length three diameters, for the Culverin four diameters, for the Saker, Falcon, etc. ½ 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 somewhat larger for the sowing and glewing them together, having a due respect for the augmenting or diminishing of your powder, according to the goodness or badness of the powder, and to the extraordinary over-heating of your piece. Having resolved for what sort of Ordnance your Cartredges are to serve, you are accordingly to have a former of wood, turned to the height of the shot, and a convenient length longer than the Cartredge is to be: and before you passed your paper on the former, first tallow him, so will the paper slip off without staying or tearing. If you deal with taper-bored Guns, your formers must be made accordingly tapred. If you make your Cartredges of Canvas, half a diameter more is allowed for the seams; but if of paper ½ or ●…/●… of an inch overplus for the pasting, will serve, being leapt once about the former, having a bottom first fitted upon the end of the former, which must be hard and close pasted to the lower sides of the Cartredge; and then the bottom pasted also down hard round about: then dry them well before you fill them, and mark every one with ink or black lead, how high they ought to be filled, and let some want of their weight against times they are overhot, otherwise great danger may ensue.   

To make Ladles, Rammers, and Sponges of all sorts of Ordnance.  
IT is fit every Gunner should know how to trace, cut out, and also make up and finish all manner of Ladles, Sponges and Rammers, and to direct others how they should and ought to be severally fortified, made and distinguished, as followeth.  
For double fortified Cannons to charge them with two Ladle fulls, they are to be two diameters and a half of their shot in length from the head of the Ladle staff, which shall be one diameter more of plate, which must go about the said head. The brass plate must be in breadth two diameters unto the said head, where each side must have half a diameter more to enclose the head of the Ladle staff within the plate.  
The Button or head of the Ladle staff must be one diameter, and of such height or thickness, that it together with the brass plate, may be equal to the height of the shot (due vent abated.) For Sponges their bottoms or heads are to be made of soft fast wood, as Asp, Birch, Willow, or such like, and to be one diameter, and ●…/●… in l●…ngth, and not above ●…/●… of the shots height. The rest being covered with raw sheep's skins wool, and nailed on with copper nails, so that together they may fill the concave of the piece.  
The Button or head of the Rammer must be turned of hard wood, in length one diameter, and ⅓ of such height & thickness, that it may fitly enter into the piece, the shots vent allowed: it were the better for fashion and strength, if that ⅓ next the staff were handsomely turned with abatement, and a Ferrill or circle of brass fitted thereon to save the head from cleaving, when as with force we shall ram the shot home. All these heads and buttons must be pierced ●…/●… with a hole for the staff, an inch or more, whereinto the staff must be fastened, let the staff be one foot longer than the concave of the Gun.  
For the ordinary Cannons the Ladles must be of the same breadth, but must not surpass 2. diameters of the shot in length. And for the lessened Cannons, two diameters only to load at twice, all according to the fashion and breadth as before.  
The Ladles for Culverings and Demi-culverins, have four Diameters of their proper shot in length, and two in breadth.  
The Sakers, Falcons, and Faulconets, which may at one Ladle full be loaden, may have their Diameters of seven diameters and a half of their shot in length, besides that coverture of the head of the staff, and of breadth two; as all the rest have.  
For Periors, which usually have Chambers with Orloes ½ and ⅓ less in boar then their Chase containeth, to them three times the diameters of their Chambers may be allowed for the length of their Ladles.   

How to make a Ladle for a chambered bored piece.  
YOur Compasses opened to the just diameter of your chamber within ⅛ part of an inch thereof, divide that measure just in two equal parts, than set your compasses to one of them, and with the one foot fixed on a paper or smooth board, draw with the other foot a circle, the diameter whereof will be a just quarter of an inch shorter than the diameter of the Chamber bore, by the Circumference whereof you may find out the breadth of the plate of a Ladle that is fit for such a Chamber bored Cannon, by the rule afore set down how to find the true breadth of the plate of any Ladle for any other piece in taking the three fifts parts of the circumference thereof, the length ought to be twice the diameter, and ●…/●… parts to hold at two times the just quantity of corn powder.   

Example.  
The diameter of the circle drawn for any Cannon whose chamber bore is 7. inches, containeth 6. ●…/●… the Circumference whereof is near 21. inches ●…/●… and ⅕ parts thereof is 12. ●…/●… and so much aught that Ladle to be in breadth, and in length 18. in the ●…/●… parts. By this rule you may make a Ladle for any tapred piece.  
Take this for a general observation, that a Ladle 9 bales in length, and 2. bales in breadth, will near contain the just weight in powder that the Iron shot for any piece weigheth.   

How to find the height of the Chamber, and how to find the the thickness of Metal round about the Chamber of any tapred piece.  
TAke a straight piece of wire, and bow the end thereof in the bottom so as it may go through the touchhole, than put it to the bottom of the bore in at the touchhole, and with any thing mark the wire upon the upper part of the Metal, then measure by your rule how long the wire is from the stroke to the end; Then put in the same wire again, and put it up so as the bowed end may rest within the Cillinder, and make another mark on the said wire hard by the upper part of the metal, round about the Chamber, the which abated from the first stroke to the lowest end, the remainder is the Diameter of the Chamber bore in that place. This needeth no example.   

To know whether the carriage of your piece be truly board, and how to make them for any piece.  
MEasure the length of the Cillinder of your Gun, the planks of your carriage ought to be once and a half that length. Also measure the Diameter, and the planks at the fore end should be in depth 4. times the Diameter, and at the end next the ground two times ½ the Diameter, and in thickness once the Diameter.   

How you may find whether a piece have any flaws, cracks, or honeycombs.  
AFter you have cleared her, put a usual searcher made of two or three springs, with points, like great pin-heads bending outwards, which being bended together with your hand, until it will enter into the Piece, and put up to the touchhole, or bottom of the Cilinder, turning it round in putting it in, and pulling it out of the Chase, and if any honeycombs be therein, it will stick with the points therein. Also in a Sunshine day with a Looking-glass, the Sunbeams may be reflected into the Chase, as that the flaws, cracks, and honeycombs may be discerned. But if the Sun shine not, a wax-candle put upon a half pike will also show them: If no flaws be found, proceed to her proof, but if any be therein, the Piece is indeed very dangerous both in firing, and loading; and if it can possibly be prevented, not to be used at all, but with great care and good respect first had in her proof.   

The allowance for vent, comparing the height of the shot with the height of the bore of the Piece assigned.  
MAny Gunners hold, that a quarter of an inch space between the Boar and the Bullet is vent suitable for all Ordnance, and not too much, nor too little. But others maintain ●…/●… part of the Diameter of the Pieces Cilinder is more proper and correspondent for all sorts of Pieces whatsoever; take which you please.   

To dispart a Piece of Ordnance.  
TO dispart a Piece, is to bring the mettle at muzzle equal with the mettle at the base ring: In true founded Ordnance, the half of the Diameter of the Cilinder is her dispart: also you may put a priming Iron (such a one as I spoke of before, with a Spring and Transome) into the Touchhole, to the bottom of the concave there, and putting down the Transome hard upon the superficies of the mettle of the base ring, which resting there, apply the instrument to the muzzle, and place him upon the lower most edge of the concave perpendicular, and raise your dispart from the Muzle-ring as high as the Transome, so you have laid the mettle at the Muzzle in a horizontal line with the mettle at the base ring. But for niceness I would make another dispart upon the Trunnions, which may be thus done, Lay a piece of soft wax upon the Trunnions, and let one raise it in height, I mean, make it longer or shorter, until that the mettle at the top of the base ring, the wax between the Trunnions and the dispart on the muzzle ring, be all three of a precise height, and in an equal strait line direct.  
If I were to fire a Piece of Ordnance at a mark, to gain credit indeed thereby, I would have a twine silk thread that should touch both the tops of the Disparts, & come to the upper part of the base ring upon the midst thereof, by which thread I would direct my Ordnance to the mark many degrees better.  
I could wish that the Disparts should be skrewed into the muzzle ring of the Pieces, that it might be used to that purpose, and had always in readiness belonging to the same Gun, and upon any occasion taken out at pleasure.  
Also I could advise the Sea-gunners' upon some occasions to use disparts between the Trunnions of their Pieces, made of a just heights of purpose to serve there: 
〈…〉  let them be tied about the Piece with a twine, because else at every shot they will be to seek, when upon the sudden they should use them; which I can by good experience speak, they will much avail, and stand you in great stead. I could express diverse other ways to dispart a Piece, but these being sufficient, I hold it needless to spend time, and fill this little treatise with unnecessary Instructions.   

The Geometrical finding the Diameter for the weight of any shot assigned.  
SUppose your shot be one, two, or three pound weight of metal or stone assigned, if of one pound divide the Diameter into 4. parts, and five such parts will make the Diameter of a shot of the said metal or stone, that shall weigh just two pound.  
Divide the Diameter of a shot weigheth just 2. pound in 7. equal parts, and 8. such parts will make a Diameter of a shot of 3. pound. And divide the Diameter of a shot of 3. pound into 10. equal parts, and 11. such parts maketh a shot of 4. pound  
Divide the Diameter of a shot of 4. pound into 13. parts, 14. such parts will make a Diameter for a shot of 5. pound.  
And so dividing each next Diameter into 3. parts, equal more than the next lesser was divided into; and it will with one part added from a Diameter of a shot, that will weigh just one pound more: So you may proceed infinitely increasing, or decreasing by taking one part less than it is appointed to be divided into.   

To tertiate a Piece of Ordnance.  
THere are three differences in fortification of each sort of Ordnance, be they of Cannons, or Culverings; for they are either ordinary fortified, lessened, or double fortified, as legitimate Pieces, bastard Pieces, or extraordinary Pieces. For the Cannon double fortified, hath fully one diameter in thickness of metal at her Touch hole, and ●…/●… at her Trunnions, and ●…/●… at her muzzle. And the lessened Cannons have at their Touchhole but ●…/●… and at the Trunnions ●…/●… and at the muzzle ●…/●… whereas the ordinary fortified Cannons have ⅞ at the Touchhole, and ⅝ at the Trunnions, and ⅛ at the muzzle. Now all the double fortified Culverings, and all lesser Pieces of that kind, have one Diameter, and ⅛ at the Touchhole, and ●…/●… at the Trunnions, and ●…/●… at the muzzle. And the ordinary forified Culverings are fortified every way like the double fortified Cannons. And the lessened Culverings like the ordinary fortified Cannons in all points.   

The difference between the common legitimate Pieces, and the bastard pieces, and extraordinary.  
COmmon or legitimate Pieces are such Ordnance, as have a due length of their Chases, proportioned according to this height of their proper bores. Bastard pieces are such as have shorter Chases than the proportion of their boar doth require. And extraordinary pieces are such Ordnance, as have longer chaces than the proportion of the boar alloweth: And these are called Bastard Culverings, and extraordinary Culverings, so likewise of Saker and Falcon.   

To cool a Piece of Ordnance, when she is grown hot with overmuch firing.  
IF you cannot have time to rest her, because the Service is hot, as it was with us at Bargain, in that case she must be cooled with sponges wet in lee and water, or water and vinegar, or with the coolest fresh or salted water, bathing and washing her both within and without, until she come unto her due temper; but if time would permit, rest her one or two hours in twelve, and cool her as before every eighth or tenth shot.   

Reasons that cause a Shot, though well directed, to err in her charge, and to be either wide, short. or over at the mark.  
MAny accidents may make a shot to deviate from the expected course, though well directed. As if the soul of the piece lieth awry in the body of her metal And if the Trunnions also be not duly placed directly in a Diagonal line with the Axis of the piece. If the platform be unequal. Also if the Gunner shoot without a just dispart. If one wheel be higher than another. If the naves be one longer and wider than the other. When one wheel meets with a stone to stay it: or that one wheel reverseth in soft ground, and the other in hard. The Carriage or Trunnion ears are higher one than another. If the carriage be too wide, so that the piece lieth not fast therein, but starteth in her discharge. If the shot be not equally round, the wind, if vehement, may somewhat hurt. The slight ramming, leaving space between powder, wad, and bullet, may alter her course. These and many more, are true and infallible causes of the failing of a shot at an assigned mark, yet the piece well directed.   

The difference between shooting by the met all of the piece, and the dispart.  
THeir differences are uncertain, by reason there are seldom any constant proportion held in the founding especially concerning the eminencies of their muzzle and basering: for laying the piece directly to the mark, with her due dispart, and then take of that dispart, and lay her by the metal, observe the difference with a squadrant, and you shall sometimes find that the piece will be elevated more by the mettle than by the dispart, four, five, yea sometimes six or seven degrees. And so consequently will the randons of the metal be more than the randons of the dispart, (which by the table of Ranges) may for every elevation be made certainly known; but this take for an example, on the level the metal rangeth near double the distance of the dispart in most pieces.   

To know at how many degrees of mounture a Piece will convey her bullet far thest, called her best Random.  
THe approved best Artists of late times, maintain with good reason, that the utmost degree of Randon is at or about 24. degrees of the quadrant, nevertheless most ancient authors hold 45. being the middle or mean between the level and the perpendicular; namely, the half of 90. degrees. But because the piece rangeth a bullet but one tenth part of the utmost random as it doth also at 84. degrees of the elevation, therefore it stands with more reason, and experience also hath found, that the utmost random of any piece should be (being duly charged & discharged) at 42. degrees, the half of 84 the elevation.  

A necessary Table of Periors and Drakes proportioned.  Names of Pieces. Height of the bore in inches▪ Length in Diameter. Weight in ●…et. pound Weight of Powder. Length of the Ladle. Canon Pe●…ior. 9 10. 12. 8 3500 3, 3⅓ 4. 3 D. Canon Drake 6½ 16 3000 9 pound. 4½ Culverin Drake 5½ 16 2000 5 4½ D. Cul. Drake. 4 ●…/●… 16 1500 3½ 4½ Sa●…er Drake. 3½ 18 1200 2 4 ●…/●…  

A Table truly proportioned for our English Ordnance.  Boar. Height ●…f Shot. Weight of Shot. Ladles length. Ladles breadth. Length of the piece. Weight of the piece. Weight of Corn P●…wder. Inches. Inches. Lib. Inches. Inches. Foot. Lib. Li●…. 8 7¼ 63 24 14 12 8000 27 
〈…〉  7 6¼ 39 22 12¼ 11 7000 18 
〈…〉  6½ 6¼ 30 21 11½ 10 6000 14 5¼ 4¼ 15 19 9 12 4300 10 
〈…〉  5 5 15½ 20 10 4400 12 5½ 5¼ 20 21 11 4600 15 4¼ 4 9 17 7 11 2200 6 
〈…〉  4½ 4¼ 10½ 18 8 2400 7¼ 4¼ 4½ 12½ 19 9 2500 8 3¼ 3 5 30 9 9 2400 4 
〈◊〉▪  3¼ 3½ 5¼ 31 9 1500 4¼ 4 3¼ 5½ 32 10 1600 5½ 3 2½ 3 25 5½ 7½ 1200 3 
〈…〉  2¼ 2⅓ 2 22 5 7 700 2 
〈…〉  2¼ 2 1●…/●… 18 3●…/●… 6 500 1 
〈…〉  1½ 1¼ ¾ 11½ 2●…/●… 4 300 ⅓ 
〈…〉  ¼ 1 ●…/●… 9 2 3●…/●… 202 ½ 
〈…〉   

A Table of Randous for the six first poyntr of the Quadrant.   1 2 3 4 5 6 ●…once 375 637 795 885 892 900 ●…aulcon. 550 935 1166 1254 1309 1320 Minion. 450 765 954 1026 1071 1080 ●…ake 625 1062 1325 1425 1487 1500 D. Culverin. 725 1232 1537 1653 1725 1740 Culverin. 750 1275 159●… 1710 1785 1800 De●…-canon. 625 1062 1●…25 1425 1487 1500 Canon of 7. 675 1147. 1431 1489 1606 1020 Double Cau●…n. 750 1275 1660 1710 1785 1800   

The use of this Table.  
FIrst, by this Table, having resolved upon the point of mounture, look against the name of the Piece, and right under that point in the common angle, you shall find the number of paces of her Random sought.   

A Table of the proportion of right ranges and first what a Range is.  
A Right Range in any piece is indeed so fare as the Bullet is carried violently in a strait line, which by some Gunners of these our modern times, is by them properly called the Right Range. This kind of shooting is so fare as a mark is within the strait line of a Piece, which for some elevations and mountures is much more than for others: for that the more a piece is mounted, the farther she conveyeth her shot in a right Range.   


A Table of right Ranges.  0 192 1 209 2 226 3 243 4 260 5 277 6 294 7 311 8 328 9 345 10 362 20 532 30 702 40 872 50 1042 60 1212 70 1382 80 1552 90 1722   

The use of this Table, with a plain Example.  
HAving found by experience, that at 60 degrees of mounture the piece assigned shot 200 paces in a right line, and would know how far the same Piece would shoot in a strait line being mounted to 10 degrees, say by the Table, if 285, the number against 6 degrees, giveth 200 paces, what will 354, the number therein against 10 degrees give? Multiply 354 by 200, the product will be 70800, which divided by 285, produceth in the quotient 283 paces, and ●…/●… parts.   

Of 〈…〉 at a Mark beyond the right line of the 〈◊〉 〈◊〉, or right range of the sh●…t, and of the dead 〈◊〉 of any Piece at every degree.  
THe dead range consisteth of the addition of the right and crooked ranges together into one, and that called the dead Range, which is the whole distance from the platform unto the first graze of the Bullets, whereby for the first six points of the Gunners quadrant, you having the dead range of one shot made out of any Piece; whether it be of a Culverin, (which is between 30. and 4●…. Diameters of her boar in length) by the range of numbers set against the letter S. in the Table here underneath; or whether it be of the quality of a Cannon, (that is between 18. and 24. Diameters of her boar in length by the rank of Numbers set against the letter C. in the said Table) you may, having one shot, by that shot, and by the rule of proportion, know the dead range of any other point of mounting sought.   

Example.  
SUppose a Culverin that shooteth level 260. paces, I would know how fare she would convey her shot upon an horizontal plain, she being mounted to the third point of the quadrant. Say by the rule 3. if 192. (the number against S.) for the level range in the Table giveth 2032, the number under the third point, what will 260. give? Multiply 2032 by 60, and divide that product by 192, and you shall have in your quotient 2751 ●…/●… for the number of paces she will convey her shot, being so mounted.  

The Table of dead Ranges.   0 1 2 3 4 5 6 Points S 192 985 1623. 2032 2185 2281 2300 Paces. C 201 958 1600 1983 2135 2232 2250 Paces.   

To know how the range of his Piece increaseth, or decreaseth from degree to degree.  
FIrst, you must find by the table of right Ranges how much your level right Range of your Piece is, which number of paces divide by 25, and multiply the quotient by 11, and the product will be the first and greatest digression, which is between the first and second degrees, which divided by 40, the degrees contained between the first degree, and 42 the utmost Random, and the quotient showeth the number of paces that the shot shall lose at every digression, from degree to degree, to the last Random, and contrariwise for the increasing digression from 42 degrees, the utmost Randon down to the first degree.   

How to find the right Line, or right Range of any Bullet for every elevation by any one right or dead Range given for the Piece assigned.  
AS for example, you are to seek the right Range of 30 degrees for that piece, whose dead Range for 30 degrees is known to be 2200 paces, by it multiply the tabular number of right Ranges for 30 degrees, which are 695, and divide the product by 2150, the tabular number for 30 degrees in the Table of dead Ranges, and the quotient will be 711 paces for the right Range of that piece mounted and discharged at 30 degrees elevation.   

Another Example.  
SUppose the level right Range is given, and the right Range of 30 degrees sought, say, if 192 the first number in the Table of right Ranges, give 695, the tabular number thereof for 30 degrees, what shall 197 paces give, the level right Range given be, multiply and divide, and the quotient will be 713 paces, for the right Range sought.   

To find how much of the horizontal line is contained directly under the right range of any shot.  
TO find what partlyeth under the right Range at 30 degrees elevation, the right Range at 30 degrees by the precedent example being found to be 713 paces, and the right sign of sixty grades, the compliment of 30 being 866, which multiplied together, and the product divided by 1000, the whole sign leaveth in the quotient 621 ●…/●… for the number of paces lying directly under the ●…ight Range.   

To find how much of the horizontal line lieth under the crooked Range of a shot made out of any piece of Ordnance at any elevation assigned.  
THe crooked Range is so much of the course or way as the shot maketh as it goeth Helically between the right Range and the natural motion, or before it maketh the first graze; And may be thus found by deducting of the level distance contained directly under the right line, or right Range of any shot made (found by the precedent Chapter) out of the dead Range thereof, found by the Chapter before going. For the remainder will be the paces, or other measures lying directly under the crooked Range.   

To make a good shot in a piece not truly boared, and to know how much any piece will shoot amiss, the metal thicker of one side than another.  
SVppose a Cannon is said to be two inches thicker of one side in her mettle, than another, the distance to the mark suppose to be 500 paces. that is 2500 foot, the which divided by 9 foot, the just length of the Cillinder of the piece, yields in the quotient 277 foot ●…/●… that again being multiplied by ½ the superfluity of the mettle being 1 inch, makes still 277 ●…/●…, which is the true demand sought.   

To remedy a Piece not truly bored.  
SEarch the piece with an instrument to know which is the thicker side; then divide the over plus of the metal in two parts, as before, suppose 2 inches, setting the dispart of your piece on that part to wards the thickest side of the pieces muzzle, and bringing the middle part of the metal at the base ring to that dispart and the upper part of the mark all in one line, fire her, and without question you make a very good shot, care being taken in loading.  
If the thicker part of her metal be above, than you ought to make your dispart one inch more: if under, one inch less.   

To choose a Piece to shoot at single mark, the course also to be observed therein.  
BY my will I would choose a piece as I had formerly practised in, and well examined her qualities; and when I came to load her, I would not ram home her powder any thing hard, but very easy, least in taking fire, it should lie blowing first, and cause the piece to start from her position, but let her be duly directed by a true disparture, that the axes of her boar may precisely respect the mark. And lastly, endeavour heedfully to prevent all impedimentall accidents which otherwise may happen, and give fire.   

Having found the first Shot faulty to the right or left hand, over or under, to amend the next time, and make an effectual shot.  
IF it were wide towards the right or left hand, I would place my eye on the base ring at the next time, a little more to the same side accordingly more or less; if it were too high, direct the dispart under the mark as much: if two low, lay some small stone, or other thing, on the highest of the base ring, and by that bring the dispart and the mark into one with discretion.   

How to plant Ordnance in secret and double Batteries, so they may not easily be dismounted.  
THey must be planted upon a platform that descendeth behind, that in their reverse they may go under the vamure of the Tronier, the Tronier being vaulted, they must by tackles be brought up above the vamure, and opened, and fire given immediately at the opening, so in their reverse will they be again under the vamure, and be free from dismounting, so long as the furnemouth and vamure is able to keep from the ruin of Counter-batteries.  
Take this by the way for a note, that a Cannon at 120 Paces, will pierce a wall or rampart, meanly settled, only 10 or 12 foot, but in close sandy ground, 20, or 24 foot deep: And that a Cannon may being well fortified and discreetly managed, be discharged 100 times in one day.  
Note that a Cannon with one shot will ruin more than a 100 hods of earth can repair.  
Further note, that 1000 shot made out of 10 Cannons will ruin more than 1500 shot can do out of made out of 5 Cannons: And less can the enemy repair the first than the last; for a Cannon shot made every eighth part of an hour, at 100 paces distant, will make as much ruin as twelve men can keep in repair.   

To make a shot in the night at a mark shown you in the day, how to prepare for it.  
I Would first lay the Piece precisely to the mark in the the day, then with a chalk line, dipped in Gum-water, I would strike a right line on the upper part of the metal, from the breech to the muzzle, upon which I would apply a good Magnetical needle, or fly with a chart exactly divided, and note the intersection; then from the end of the line that was marked, or stricken upon the mettle, I let fall plumb lines upon the platform, and at the places where they touch, I knock in at each a small nail. Lastly, with a Quadrant I observe the elevation of the concave, or else with some staff take the perpendicular height of some mark made in the mettle as well at the breech, as at the muzzle above the said two nails: and so you may again lay the piece thereby, always to have the selfsame position, and so shoot as certain at the mark by night, as by day.   

To make a goodshot at an Enemy's light in a dark Night, not having any Candle, or other light by.  
I Would light two pieces of match, the one as much longer as the other, as the quantity of the dispart of the piece, and set the longer upon the upper part of the Muzle-ring, and the shorter upon the base ring, still traversing and quoining the piece, until I have brought the light of the Enemies, and the lights of the two matches all three into one line, and so give sire.   

To order a Piece, to make a goodshot at a movable Mark, as at a ship under sail, Boat rowing, or Horsman riding.  
TAke a piece that will reach the Mark in a straight line, then observe how the Mark moveth: Next, note the wind if it blows much, whether sideways, with, or against you, and accordingly take advantage: Then with the dispart considered, observe some cloud, or mark, or point of land that lieth in the course of his motion, and when according to the swiftness thereof he is come so near it, as I guess the shot and he may meet at the Mark, I give fire: wherein remember this secret of Nature, that any Piece will shoot farther from Sea to Land-ward, than from Land to Seaward.   

To shoot at a Squadron of men, and what Piece to choose.  
ACcording to the distance, I would choose a Piece that in a straight line can reach the mark, be it with Demi-culvering, Saker, or Falcon, and plant my piece if I could parallel to the Champion plain, that the shot may range to shoot at girdle-height, unless the ground be stony; for than would I place my shot short of them, that grazing amongst the stones, the stones may spoil them more than the shot of itself can do by much; but in no case would I shoot wide, or over them; for that were both loss, and foul shame for the Gunner.   

To shoot farther than ordinary in one and the selfsame Piece with like quantity of powder and shot.  
I Will gently put home the powder, and wad the same accordingly, than the shot being involved with paper, leather, okam, or such like, to fill close the concave of the boar, I would drive the shot close to the powder with a good wad, putting after it a Tampion of Cork, and with a sponge moistened with oil, I would anoint the vacant Cilinder, and so barricadoe the piece, that it should not reverse in the discharge.    

Of Powder, Peter, and Match.  

To refine Saltpetre wet.  
TAke what quantity of Saltpetre you please, and put the same into a clean Cauldron, and put thereon a little fair water, and boil them together until it raise the scum; which take off, and keep, and let it congeal and shoot in coolers, as at first it did, and what remains, boil again with more clear water until it congeal.   

To know if Salt-peter be well refined.  
TAke and lay it on a board, and put a coal unto it, if it raise an azure scum, it is yet greasy, if it leaves pearls it is yet earthly: but if it burn into the board, and leave nothing but a black colour, and rise with a long flamed ventosity and exhalation, it is well refined.   

Several ways to know whether powder be decayed or no, whether by moisture or age, in part or in whole.  
IT is the practice part of a Gunner really to know his powder, and whether it be decayed or not, by mutation or corruption. And there are especially three ready ways to find the same. The first, by the sight; the second by the feeling, and the third and surest by firing it. By sight, if it be not black and dark, but bright, and inclining to a bluish tawny colour. By feeling, grasping it in the fist, if it run through the fingers quickly, and avoideth the handling, and cling not together. By fire, if fired, it rise quick, and spread in a moment, smoke little, but riseth in a clear flash: unto which add further, if it leave no seezes, but carry all away, the powder is good, or else the contrary may be judged.   

To renew powder decayed in part.  
OF ten-times in Forts, but most common and usually at Sea, powder gathereth humid vapours, which will in short time destroy the strength and vigority thereof, and makes it of little, and sometimes of no use, without renewing it. And sometimes it may decay by age. Let therefore the Gunner first prove the powder by fire; and if it make a flame with a long tail, that is, if it sleep in its burning, more or less, then for every hundred pound of powder, add four pound, or six pound of refined Saltpetre, mixing them well together, and put them to be beaten and wrought for the space of three hours, and then moistening, corning, and drying the same, as aforesaid, proving it in meal dried, how it will rise by firing; and so doing, the powder may be made serviceable, if the coal be not corrupted.   

To renew powder totally decayed.  
IF it be wholly decayed, lay a reason frail, or mat in the bottom of a buckingtub, upon a faggot made of purpose, or lathe, set on edge, to keep the mat from the bottom, and put in s●…awlayd cross-ways: upon which power the decayed powder, and warm water, being put thereon, and let it stand and soaketen or twelve hours, that all the Saltpetre may be assuredly dissolved: then let out the liquor tap which congeal to Peter, and thereunto add a due proportion of Coals and Sulphur, and make it into powder, as is formerly taught for the Coals and Sulphur dissolving, will remain the straw, frail, or mat.   

To make powder that shall not waste with ●…ime.  
TAke what quantity of powder you will, and mix it with Aquavitae, and make it up in balls, and dry them well in the Sun, or in a warm place, and keep them in an earthen pot well glazed, until you have cause to use them. This powder will not decay, nor waste with age.   

To preserve powder that is good, and keep it from decaying.  
I Would advise every Gunner to choose the driest place he can possible, to keep his provision and store of powder in, and every fortnight or three weeks at the most, to turn his barrels upside down, so will the Peter be dispersed in every place, and be in every part alike, otherwise, if it be let stood long unremoved, the Peter will (as nature forceth it to its proper element) descend for the most part, to the bottom of the Barrel, and the upper part will want, and be much weakened, and in time quite decay, and lose its proper virtue: for one pound of powder in the bottom of any Cask, with long standing, will have more strength than three at the top.  
Also it were good discretion after you have put your powder in Cartredges, to barrel them up, and some times to turn them, as aforesaid. I would advise you likewise to place all those Cartredges that you keep and ma●… for your pieces, when they are hot, by themselves, that yo●… 〈◊〉 have them to hand, when need requires.   

To make extraordinary Match to fire Ordnance.  
TAke as many threads of gross Cotten yarn, as hath not taken Salt-water, and work them bobbing-wise of a complete bigness, and boil them in Saltpetre water, and squeeze them, and roll them on a table, whereon mealed Peter and Sulphur is spread: then draw them through the palm of your hand, and dry them well. You may do it also with cotton match.   

To make a match will resist fire and water.  
TAke Salt-peter refined one part, Sulphire ½ part, and put them into a pot with ⅓ part of Camphiere mealed with the Sulphur, and one part of fine mealed quick lime, with so much linseed oil and a little liquid varnish to temper them well together. Then take of Cotton bobbing match, as big as your little finger, and put it into the mixture to soak over a fire until it be well imbibed, and have soaked up the most part of the liquor, then take the feezes or remainder, and put them into the palm of your left hand, and with your right draw the match through it twice or thrice, clasping close your fist, that the match may receive the substance of it thereinto: then dry it upon a line, and keep it for special uses, for Vaults, Mines, and moist weather.   

To make a very violent match.  
TAke two ounces of powder, four ounces of Peter, two ounces of Aquavitae, dissolve them over a fire, and put in your cotten-match, and soak it up: if you imbibe the fesills for your ●…ockets therein, it will be very proper; you may roll and rub them in meal powder upon a table dry, and keep them in a dry place, and it will be for your purpose.    

Of Fireworks.  

To make certain Fireworks, very necessary both for Sea and Land-service.  
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, resin Roch three parts, Turpentine 1 part, Verdigrease ½ part, Bolearmonicke ⅓ part, bay salt ⅓ part, Colophania ⅙ part, Arsenic ⅛ part, mix them very suently 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 4 parts, Linseed Oil 1 part, Turpentine ⅓ part, Sulphur 1 part, Tar ⅓ part, Tallow one part; and as soon as this is cold, bore two holes in each of the same next the Iron an inch deep, with a sharp Iron Bodkin, filling the same with fine bruised powder, and putting in every hole a little stick of two inches long, which are to be taken out when you would fire the same, this composition will burn furiously.  
And remember you cut off the staff some three inches from the work, and put thereon a brass socket of five or six inches long, and then cut the end of your stasse 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 c●…position and work contain in weight about 7●… po●…, then will it do execution, and work a better effect, ●…n if it were of less weight, by much; by reason the composition else would be wasted, before it comes to effect its execution.  
To burn the sails of Ships a pretty distance, or to fire thatched houses, Corne-s●…acks, or any other cumbustible matter apt to burn, when you cannot come to the same; it is good to have certain strong Crossbows to bend with racks or gaffells, and so shoot Arrows armed at the heads with wild fire, made of the composition as above, & about three inches in length, & 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 diverse services may do great good.   

To charge Trunks.  
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 wild fire a little lower than the concave of the Trunk, ●…et the Ball be bored through cross-ways, and primed full of fine powder. Lastly, with slow receipt, then with powder, then with a Ball again as aforesaid, until you have filled the same within ¼ of an inch of the mouth, which would be filled up with fine powder and receipt mixed together. Some do use to have at the mouth two Iron stirts to stick them in the side of any thing, or to defend one's self from the enemy from taking it off with a thrust while they do execution.   

To make the Ball.  
THe Ball of wildfire must be thus made, Take untwisted match, tow, and hemp, the which would be moistened in Aqua vita, or boiled in Salt-peter water: then take of bruised powder six parts, of Saltpetre 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 okam abroad in thickness of the back of a knife, and as broad as great Oyster-shell, put into the same as much as you can grasp together in your sister, and tying the same hard with a packthread, coat it over with molten brimstone, and when you would use the same, bore it through with a B●…dkin, 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 part, of Rosen 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 Tar ¼ part, of Aqua vitae ½ part, of Linseed oil ½ part, of Verdigrease ¼ part, of Campheire 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 bored 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 ends 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.   

To make Powder-chests.  
THey are to be made first of three boards, two to be nayl●…d together like the ridging of a house, and one longer and broader to the bottom thereof: between which three boards put your Cartredge, then make it up like a Sea-chest, and fill it with stones, nails, and what such like you will: then nail the cover on, and the ends to the decks, in such a place that you may fire the powder underneath through a hole made to put a Pistol in.   

To make Roche-Sulphure.  
ROche-Sulphure is made, one pound of Sulphur melted on a slow fire, and one quarter of a pound of mealed powder put thereto by little and little, and in the cooling put three ounces of Cornepowder, mixing them well together; to which put one pound of molten suet, so have you made good Roche-Sulphure.   

A true receit of a Composition that will burn and feed upon the Water.  
TAke Mastic half a pound, white Frankin sense, Gum, Sandrake, Quicklime, Brimstone, Bitumen, Camphire, and of the best and driest Gunpowder, of each of these one pound and a half; Rozin one pound, Saltpetre four pounds and a half, mix them all together, and you have your desire.   

A Receipt of a Composition that will burn under water.  
TAke Brimstone one pound, Gunpowder ten Ounces, of the best Saltpetre you can get, one pound and a half, Camphire beaten with Sulphur and Quicksilver; mix them well together with oil of Peter, or for want of it, let it be Linseed oil boiled, unill it will scald a Feather: fill a Canvas ball with this Composition, arm it, and ballast it with Lead at the bottom; make a little vent at the top, fire it well, and cast it into the water, and you shall find the experience worth your labour.   

A Receipt of a Composition that will kindle with the water.  
TAke of Oil of Tyle one pound, linseed-oil three pounds, oil of yelke of Eggs one pound, new quicklime eight pounds, Brimstone two pounds, Camphire four ounces, Bitumen two Ounces; mingle all together very well, and you shall have your desire.   

How to know the just time or hour, that any quantity of a lighted Match shall do execution at the time desired.  
TAke our ordinary Match which is used for the Musket, rub, or beat it against a post to soften it, then either dip the same in the water of our ordinary Saltpetre; then dry it very well either by the fire, or in the Sun, according as your haste requires: or else beat a little Brimstone very small, and put a little fine Gunpowder amongst it, and rub the Match with them, being made liquid with a little Aqua vitae, and dried as before said: then try first how long one yard of this Match thus prepared, will burn, which imagine to be about a quarter of an hour; and if one yard will burn so long, than four yards will be just an hour: Take therefore as much of this Match as will burn so long as you will have it to be ere your work should fire, bind the one end unto your work, lay lose powder well dried, under, and about it lay the rest of the Match in hollow or turning, so that one part of it touch not another, and fire it.  

For Firepikes 4 pound a piece for one dozen.  
Powder 20 pound.  
Peter-roch 5 pound.  
Peter-meale 5 pound.  
Sulphur 3 pound.  
resin 2 pound ½.  
Turpentine 1 pound.  
Linseed oil 1 pound.  
Sum 38 pound, 8 ounces.  
For arming.  
Sulphur 6 pound.  
Turpentine ½ pound.  
Thread 4 pound.  
Summe 10 pound ½.  
For Arrows 2 dozen, each 1 pound.  
Powder 12 pound.  
Sulphur 3 quarters of a pound  
resin 3 quarters of a pound.  
Rochpeter half a pound.  
Peter-meale 3 qua. of a pound  
Sum 15 pound 3 quarters.  
For coating.  
Sulphur 5 pound.  
Peter-Roch 2 pound.  
Peter-meale 1 pound.  
1 yard of Canvas & marvel.  
Sum 9 pounds.  
For2dozen of balls wetworks of 4 pound a piece.  
Powder 48 pound.  
Peter-roch 16 pound.  
Pitch 2 pound.  
resin 2 pound.  
Turpentine 8 pound ½.  
Linseed oil 1 pound.  
train-oil 1 pound.  
Summe total 90 pound ½  
For Coating.  
Pitch 14 pound.  
resin 2 pound.  
Sulphur 8 pound.  
Canvas 4 yards.  
Small Marle 3 pound.  
Sum 31 pound, ½.  
For 1 dozen of pots, each one 1 pound, ¼.  
Corn-powder 1 pound ½.  
Serp. powder 9 pound.  
Sulphur 3 pound.  
Peter-roch 1 pound & ●…/●….  
Summe 15 pound.  
For Capping.  
Canvas 1 yard.  
Okam ¼ of a pound.  
Sulphur three fourth pound.  
Packthread 1 ounce.  
Sum 1 pound, 9 Ounces.     

A short View of the Chiefest Heads which are contained in this Book of GUNNERY, Viz.  

FIrst of the principles of Philosophy sit to be known. page. 1.  
A Table of the Square: A table of Cubes. pag. 2  
How to extract the square root. pag. 2.  
How to know the nearest root of a number not square. p. 3.  
●…oure several questions upon the same, and all fully answered. pag. 4, 5, 6.  
How to extract the Cubic root, with the manner how it is to be done. pag. 7.  
How to find the nearest Cubic root, and not cubical. p. 8.  
A question of two Cubes. pag. 9  
A question asked about a Gun. pag. 9  
A question of a Bullet. pag. 9  
How to turn a whole number into a fraction. pag. 10.  
A question of whole numbers and fractions. pag. 10.  
How you may Geometrically find the Diameter of any Bullet, that weigheth twice so much as a known Bullet. p. 11.  
Then to prove it Arithmetically. pag. 11.  
By one Bullet to know the weight of another, the Diameter given. pag. 12.  
How by the weight of one Piece, to know the weight of the other. pag. 13.  
To know how many shots of powder will be in a grand Barrel of powder, for any pee●…e. pag. 13.  
The example how to do it, and the proof. pag. 13.  
By knowing what powder a Piece must have, to know how much a piece of another boar will require. pag. 13  
To find the supersicies of a Bullet. pag. 13  
A Table showing the weight of all Iron Bullets, in Haberdepoize weight. pag. 14.  
To find out how many square inches are contained in a solid content of a Bullet, and consequently, how many pound weight. pag. 14.  
To find the true content of a circle. pag. 15.  
Arithmetically to find out the mean proportion between two numbers. pag. 15.  
To know Arithmetically, how much of every sort of mettle is in 〈◊〉 Piece of Ordnance. pag. 16.  
To fi●…●…he superficial content of the hollow concavity of a Piece of Ordnance. pag. 17.  
How to find the solid content of the Cillinder of any Piece. pag. 17.  
To measure any sort of Timber. pag. 17.  
Directions how to weigh a great deal with a few weights. pag. 18.  
How to measure any sort of Board, Glass, or Pavement. pag. 19  
To measure Land an easy way. pag. 19  
How to measure any irregular substance whatsoever. viz. as a Crown, Horsehead, or any Image, or concaved piece. p. 19  
How by knowing the weight of one fathom of rope, to know the weight of another. pag. 20.  
By the Compass of any small rope, to find the Diameter and weight of one, four, five, or six times as big. pag. 21.  
How to know what empty Cask will carry any sort of Ordnance over a River. pag. 21.  
How by knowing what powder a few Pieces spend, being seldom discharged, to know how much powder ●…ny of the same will spend being often discharged. pag. 21.  
To know how much powder each Cannon spent in the former conclusion at a shot. pag. 21.  
The proportigns between Bullets of Iron, Stone, or ●…ead. pag. 21.  
By knowing the Diameter and weight of an Iron Bullet, to find the weight of a Bullet of Marble. pag. 22.  
How to know Arithmetically where to place the Trunnions of any Piece of Ordnance. pag. 22.  
How much rope will serve to make breechings and tackle for any Piece. pag. 22.  
The names of all the principal members of a piece of Ordnance, and how they are placed. pag. 25.  
What instruments are most fit for a Gunner. pag. 25.  
How to load and fire a piece of Ordnance ●…ke an Artist. pag. 26.  
What Powder is allowed for proof, and what for action for each Piece. pag. 27.  
If Weights, Scales, and Ladders be wanting, how many Diameters of a Bullet will make a reasonable charge in powder for any piece named. pag. 28.  
How Moulds, Forms, and Cartredges are to be made for any sort of Ordnance. pag. 28.  
To make Ladles, Rammers, and Sponges for all sorts of Ordnance. pag. 28.  
How you may find whether a Piece have any flaws, cracks, or honeycombs. pag. 32.  
To dispart a piece of Ordnance. pag. 33.  
The Geometrical finding the Diameter for the weight of any piece assigned. pag. 35.  
How to tertiate a piece of Ordnance. pag. 35.  
To cool a piece of Ordnance, when she is grown hot, with overmuch firing. pag. 36.  
Reasons that cause a shot, though well directed to err in her charge. pag. 37.  
To know at how many degrees of mounture, a Piece will convey her Bullet called her best Random. pag. 38.  
A Table truly proportioned for our English Ordnance. p. 39  
A Table of Randons', for the six first points of the Quadrant. pag. 40.  
A Table of right Ranges, also the use of the Table, with a plain example. pag. 41.  
Of shooting at random at a mark beyond the right line of the Pieces reach, or right range of the shot; and also of the dead range of any Piece at every degree, with the example. pag. 42.  
To know how the range of his Piece increaseth, from degree to degree. pag. 43.  
Ho●… 〈◊〉 ●…nd the right line, or right range of any Bullet for every elevation, by any one right or dead range given for the Piece assigned. pag. 43.  
To make a good shot in a Piece not truly bored, and to know how much any Piece will shoot amiss, the met tall ●…icker of one side than another. pag. 44.  
●…o remedy a Piece not truly bored. pag. 45.  
To choose a Piece to shoot at a single mark, the course also to be observed therein. pag. 45.  
Having found the first shot faulty to the right or left hand, over or under, to amend the next time, and make an effectual shot. pag. 45.  
How to plant Ordnance in secret and double batteries, so they may not be easily dismounted. pag. 46.  
To make a shot in the night, at a mark shown you in the day, and how to prepare for it. pag. 46.  
To make a good shot at an Enemy's light in a dark Nighs, not having any Candle or other light by. pag. 47  
How to order a Piece, to make a good shot at a movable Mark, as at a ship under sail, Boat rowing, or Horseman riding. pag. 47.