is 10 inches ½ and take ½ of the circumference which is 33 inches reduce them into fractions according to the rule you haue 21 2 for the diameter and 33 1 for the circumferēce then multiplying the one by the other the product is 1386 4 which deuided by the denominator 2 yeeldeth in the quotient 346 ½ as before In this order you may find out the content of the plaine of any circle To find out the circumference of any bullet or globe diuerse and sundrie waies Question How many inches is about the circumference of that bullet or globe whose diameter is supposed to be 21 inches high Resolution After you haue with your callaper compasses found out the height of the diameter multiply the same by 22 so there will arise 462 the which deuided by 7 the quotiēt wil be 66 inches the true measure of the circūferēce Another way Triple your diameter and thereto adde the 1 7 part of the same your product is the circumference Example The triple of 21 is 63 and the 1 7 part of 21 is 3 which added to 63 is 66 inches as before Another way to worke the same Looke how many times you can haue 7 in the diameter so many times must you haue 22 in the circumference Example The diameter being 21 inches deuided by 7 yeelds in the quotient 3 by which if you multiply 22 your product will be 66 inches for the circumference as before In this order you may find out the circumference of any bullet or sphericall body c. To find out the superficies of any round body as bullet globe c. diuerse and sundry waies Question I haue a demy Cannon bullet of 7 inches diameter I demaund how many inches the superficiall content therof is Resolution To answer this and all such like I must in the order before shewed find out the circūference of the bullet and I find that a bullet of 7 inches diameter shall cōtaine 22 inches in circūference which circumference being multiplied in the diameter ariseth 154 inches the true number of inches contained vpon the superficies of a bullet of 7 inches diameter Another way Multiply the square of the diameter of any bullet or globe by 22 7 the product is your desire Example The bullet whose diameter was 7 inches being squared the square thereof is 49 which multiplied by 22 yeelds 1078 which sum deuided by 7 the quotient is 154 inches as before Another way Deuide the square of the circumference of any bullet by 22 7 your quotient nūbers will shew you the superficiall measure of the same Example The circumference of the bullet aforenamed of 7 inches diameter containeth 22 inches the square thereof is 484 inches that number deuided by 22 7 as you do in fractions in setting an vnite vnder the square number thus 484 1 and multiplying the said square number by the denominator of the other fraction being 7 ariseth 3388 which deuided by the numerator 22 the quotient is 154 inches the superficiall content thereof as before How you may find out the solid content or crassitude of any round bullet or globe c. diuerse wayes Question In the question before propounded of the bullet whose diameter was 21 inches I would know how many inches is in all the solid or massiue content thereof Resolution I multiply the diameter cubickly and after multiplieth that cubicke number by 11 so ariseth 101871 the which deuided by 21 my quotient is 4851 shewing there is so many inches iu the solid content of a bullet or globe of 21 inches diameter Another vvay Multiply the cube of ½ the circumference by 49 and deuide the product arising thereof by 363 your quotient will shew your desire Example The circumference of a bullet whose diameter is 21 inches containeth 66 inches the ½ thereof is 33 inches the cube whereof is 35937 that summe multiplied by 49 is 1760913 which deuided by 363 the quotient is 4851 inches as before Hovv you may by knovving the diameter and vveight of any bullet or other round bodie find out the diameter of any bullet or globe that vveigheth tvvise the vveight of the former Question There is a demy Culuering bullet of 4 inches diameter weighing 9 pound I demaund the true height of that bullet which weigheth 18 pound weight Resolution To worke this and all such like demaunds this rule is generall in multiplying the height of the lesser bullet whose weight is knowne cubically then doubling that summe and extracting the cubicke roote thereof the quotient will answer your question Example The bullet afore named of 4 inches diameter being multiplied cubically is 64 that summe doubled is 128 the cubicke roote thereof is 5 inches and a fraction remaining scarse the 1 30 part of an inch shewing the true height of a bullet that weigheth 18 pound In this order if you haue a bullet that is 3 times as heauie as another of like mettall whose weight is knowne and that you desire to know the diameter of the greater bullet in tripling the cubicke number of the lesser bullet whose diameter is knowne extracting the cubicke roote thereof you shall find out the true height of the greater bullet Or if you would find out the height of any bullet of like mettal that weigheth 4 times as much as an other bullet whose weight is knowne quatriple the cubicke number of the diameter of the lesser bullet and extract the cubicke root thereof your quotient will satisfie you Or if 5 or 6 times c. in working as I haue shewed you may find your request How you may Geometrically find out the diameter of any bullet that weigheth twise as much as another knowne bullet Take the true height or diameter of the lesser bullet whose weight you know and square the same as you see in the figure following Then draw a line that may deuide the said square in 2 equall partes in the 2 opposite angles and that line shall be the diameter of a bullet twise the weight of the other then deuide that diametrall line in 2 equall parts setting one foote of your compasse in the center or mids thereof and with the other foote draw a circle and that circumference wil represent the proportion of a bullet twise as much in weight as the lesser How you may Arithmetically prooue this conclusion The dyameter of the lesser bullet is 5 inches the square of it is 25. that some dubble is 50. the square roote of 50 is 7. 1 7 and so much is the diameter of the greater bullet as in the figure here drawne you may see Another way Geometrically to find the diameter of any vnknowne bullet that is double the weight of a knowne bullet Draw a straight line of what length you thinke good as you see the line A. B. then draw another crosse line perpendicular to the ground line as you see the line C. D. note the meeting or crossing of the lines as is the pointe E. This done
onely to shake and beate the wall and the Ordinance on the two other side mounts or platformes shooting something slanting are to coyne or cut out that which the Ordinance from the middle platforme doth shake or loose The Baskets ramd full of earth being placed betweene each peece of Ordinance are to defend the Gunners and Laborers from hurt of them that are besieged as afore I haue said And further it is to be noted that to batter the coyne or cullion point of any wall two places is sufficient to plant your Ordinance in Also you may batter and beate downe the wall of a Towne or Castell as well by night as day so as the enemie shall haue no time to builde vp in the night that which was dung downe in the daie as thus Lay your peece or peeces to the marke in the day light and note well what degree of the quadrant she lieth at which is soone done in putting the rule of your quadrant into the peece mouth so laid against the marke letting a line and plummet fall to the ground from the said point of your quadrant and at the lighting of the plummet on the ground there driue in a stake or wooden pin and letting a plumbe line fall likewise from the midle part of the taile or breech of your peece to the ground driue therein another stake into the ground then stretch a line from the said 2 pinnes so as the ends of the said line may reach 2 or 3 yards further then the pinnes at each end And there make them fast in driuing a pin of wood or yron into the ground at each end then bringing your peece or peeces to lie streight aboue the said line or lines so drawne which is easily done hauing a lanterne with a close couer you may both charge and recharge and shoote aswell by night as day according to your desire How you may know the true weight of any number of shot for seuerall peeces of Ordinance how many soeuer they be and how many Tun weight they do all weigh Question Suppose a Ship is loaden with Bullets to be caried to the siege of a Towne c. in which ship is 500 shot for whole Cannons 800 demy Cannon shot 900 Culuering shot 1000 demy Culuering short 1100 Saker shot 1200 Minion shot and 1400 Fawcon shot the question is to know the true weight of all the shot and how many Tun they do all weigh Resolution In the beginning of this treatise I shewed how to find out the weight of any vnknowne bullet by the weight of a knowne bullet of the like mettall so that multiplying the number of euery seuerall sort by the weight that one of them weigheth and adding all the products into one summe and then deuiding that totall by 2240 pound which is the pounds in a Tun the quotient will shew you how many Tun all those bullets weigheth Example Admit the Cannon shot weigh 60 pound a peece by which I multiply 500 the number of that kind of bullet so ariseth 30000 pound weight and then there is 800 demie Cannon shot of 32 pound weight a peece which multiplied as before makes 25600 poūd weight And then there is 900 Culuering shot of 16 pound weight a peece which makes 14400 pound weight And then 1000 demie Culuering shot of 10 pound weight a peece which makes 10000 pound weight And then 1100 Saker shot of 5 pound weight a peece which makes 5500 pound weight And then 1200 Minnion shot of 3 pound weight a peece which makes 3600 pound And lastly 1400 Fawcon shot of 2 pound weight a peece which makes 2800 pound weight All these summes added together makes 91900 pound weight which deuided by 2240 yeelds in the quotient 41 Tun and 60 pound weight remaining In this order you may know how many Tun weight any number of shot weigheth so that knowing how many Tun any ship is of burthen you may easily know how many shot will loade the said ship How any Gunner or gunfounder may by Arethmiticke skill know whether the trunions of the peece be placed rightly on the peece or not Measure the length of the bore of the peece from the mouth to the breech deuide that measure by 7 and multiply the summe that commeth in the quotient by 3 the product will shew you how many inches or other measure the trunions ought to stand from the end of the lowest part of the concauity of the sayd peece at the breech And note that the trunions ought so to be placed as ⅔ parts of the circumference of the peece may be seene in that place whereas the trunions are set Example Admit the cilinder or concaue of a Cannon or other peece of Ordinance be 10 foote ½ long I demaund where the trunions of the sayd peece ought to stand Answere Reduce the length of the concaue of the peece into inches you haue 126 inches the which deuided by 7 the quotient is 18 that multiplied by 3 makes 54 inches or 4 foote ½ so farre ought the trunions to be placed from the breech or lowest part of the hollow concauity of the sayd peece Another way Or multiplying the length of the concaue of the peece by three and deuiding the product by 7 the quotient will shew the true place how farre the trunions ought to stand from the lowest part of the bore or concauity of the peece Example 126 inches the length of the concaue of the peece multiplied by 3 makes 378 inches which number deuided by 7 the quotient is 54 inches as before And note that the trunions of euery peece were inuented to hold the peece vp in her cariage to moue her vp and downe to make a perfect shot and to hold her fast in her cariage after she is discharged for if the trunions be placed too neare the mouth the peece will be too heauy towards the breech so as the Gunner appointed to serue with her shall haue much adoe to raise her to coyne her vp or downe or being placed too neare the breech the contrary will happen How you may know what empty caske is to be prouided to boy or carry ouer any peece of Ordinance ouer any riuer if botes or other prouision cannot be gotten It is thought sufficient that 5 Tun of empty caske will swimme and carry ouer a Cannon of 8 or 9000 pound weight 4 Tun will carry ouer a demy Cannon 3 Tun a Culuering and 2 Tun a Saker accounting all prouisions to be made fast thereto as plankes ropes c. so that knowing what number of Ordinance is to be ferried or caried ouer any riuer adding all their weights into one summe by framing the Golden rule you may presently know what empty caske is to be prouided to ferry ouer all the sayd Ordinance at one instant Example If a Cannon of 8000 weight require 5 Tun of empty caske how much emptie caske is to be prouided to carry ouer so many Ordinance as is
open your compasse the iust length of the diameter of the lesser bullet whose weight you would double setting one foote of the compasse in E. and the other in D. and measure towards B. twise that diameter as is done in the points F. G. Then deuide the line E. F. in 2. equall parts in the point H. and after deuide the line E. H. in 2 equall halfes as in the point I. And lastly deuide the line I. H. in 2 equall partes in the point K. Which done open your compas placing one foote in K. and the other in G. draw ½ a circle as you see I do the semi circle L. C. G. After deuide the line C. D. in 2 equall partes in the point M. and opening your compasse the iust widenes of one of those parts set one foote in M. and with the other foote draw the line C. N. L. Which done the bullet whose diameter is the line L. E. wil weigh twise as much as the bullet whose diameter is the line E. D. as Ewclid in his 6. booke of Geometricall Elements doth demonstrate and proue The greater circle O. doth shew the proportion of a bullet that weigheth twise as much as the lesser circle N. both the said bullets being cast of one like mettall Another demonstration to proue the former conclusion by numbers In a conclusion before set downe where the bullet of a demy Culuering of 4 inches diameter weighed 9 pound I proued that a bullet whose weight was 18 pound should be more then 5 inches diameter Euen so I haue hereunder deuided the line E. D. of the former conclusion being supposed to be the diameter of a bullet whose weight is knowne into 4 equall parts or inches And likewise deuiding the Diameter F. E. into the like diuisions it containeth 5 of those parts and almost the 1 30 part of an inch more shewing the true height of a bullet that is twise as much in weight as the lesser bullet of 4 inches diameter as this figure sheweth As the vpper face or side of any square being doubled the square arising of that doubled side shall be in proportion iust 4 times as much as the first square was whereas a great many would thinke it wold be but twise as much Euen so the diameter of any circle being doubled the Area or superficiall content of the flat of the same circle so doubled shall be foure times as much as the other Also any cube globe or bullet whose diameter is in double proportion to another the solide content of that bullet whose diameter is so doubled shall be in weight 8 times as much as the lesser as these two examples in the conclusions following figuratiuely drawne sheweth How by knowing the superficiall content of the plaine of any circle to finde out the superficiall content of another that is twise the diameter of the first Question There is two circles drawne the one 7 inches diameter the other 14 inches how much is the content of the greater circle more then the lesser Resolution To answer this or the like by the theoreme afore meÌ„tioned I square the diameter of the lesser circle being seuen inches so ariseth 49 inches that square multiplied by 11 yeelds 539 the which deuided by 14 the quotient is 38 inches ½ shewing the superficiall content of the circle of 7 inches diameter Also working in the same order I find the content of the greater circle of 14 inches diameter to containe 154 inches which deuided by 38. ½ the quotient is 4 shewing that the superficiall content of the greater circle is iust 4 times as much as the lesser By knowing the weight and height of any one bullet to find out the weight of another of twise the height of the former Question If a bullet of 4 inches diameter weye 9 pound how much shall a bullet of 8 inches height weye Resolution To know this or the like multiply the diameter of ech bullet cubically and I find the cube of 4 is 64 the cube of 8 is 512 which knowne I frame the rule of proportion saying if 64 yeeld 9 pound what will 512 and in multiplying and deuiding according to the rule my quotient is 72 pound the weight of the greater bullet that is iust 8 times the weight of the lesser bullet For further proofe behold these 2 figures in cubick forme where you may see that the greater figure whose side is in double proportion to the lesser doth containe 8 times the quantitie of the lesser An easie rule to find out the diameter of any bullet and how to know how much one bullet is higher then another by Arithmeticke skill without any callaper compasses If you want a paire of callaper compasses take a line or a garter c. and gird the bullet or bullets whose height you desire iust in the mids laying that measure to an inch rule noting how many inches or other measure the same containeth then multiplying the said measures by 7 and deuiding by 22 the quotient will shew you your request And then abating the lesser diameter from the greater the remaine will shew you how much the one is higher then the other Example Suppose the circumference of the one bullet be 16 inches and the circumference of the other 26 inches in working as aboue is taught I find the diameter of the lesser bullet is 5 inches 1 11 and the diameter of the greater bullet 8 inches 4 11 so abating the lesser from the greater the remaine is 3 inches and 3 11 partes of an inch shewing the greater bullet is so much in height more then the lesser The like is to be obserued with any other By this rule you may know how much the circumference or any part of your peece is higher then another A table shewing the weight of all yron bullets from the Fawconet to the Cannon in Habberdepoiz weight Height of the shot in inches and parts of inches Weight of the shot in pounds and partes of poundes Height Weight 2. 1. 2 7 2. ¼ 1. ¾ 2. ½ 2. â…“ 2. ¾ 3. 3 7 3. 4. ½ 3. ¼ 5. 3. ½ 6. 2 9 3. ¾ 7. 6 7 4. 9. 4. ¼ 10. ¾ 4. ½ 12. â…” 4. ¾ 14. 5 8 5. 16. ¼ 5. ¼ 19. â…” 5. ½ 22. 1 7 5. ¾ 25. â…š 6. 29. ½ 6. ¼ 32. â…› 6. ½ 36. â… 6. ¾ 40. ¾ 7. 46. 7. ¼ 52. 6 7 7. ½ 56. â… 7. ¾ 64. ½ 8. 70. 8. ½ 76. â…” How you may Arithmetically know the true breadth of the plate of the ladle that is due for any peece of Ordinance by knowing the height of the bullet fit for the said peece Take a line and compasse the bullet in the mids laying the same measure to an inch rule deuide the same measure into 5 equall parts 3 of those parts is the iust bredth you ought to make your plate of which being orderly placed on the staffe and bent circularly serues to hold the powder in the
instrument Geometricall or by some line of measure truely deuided measure the distance from the peece to the place where the shot first fell or grazed noting how many pearches paces yardes or other measure that distance is which knowne deuide that distance by the degrees in the best of the randon being 45 your quotient will tell you how many paces yardes feete or other measure your peece will shoote further or shorter in mounting or dismounting a degree the which knowne as I haue said by one truely measured you may before you shoote know very neare how far or short your peece will shoote at the raising or dismounting of any degree allowing one and the selfe like proportions in charging both with powder bullet and wad How by Arithmeticke skill you may know how with one and the selfe same like charge in powder and shot how much far or short any peece of Ordinance will shoote in mounting or dismounting of any degree whereby you may know how far your peece will shoote at any degree of the randon by knowing the distance she shoots at the utmost grade Question If a Cannon at her vtmost randon that is at 45 degrees carry the bullet 1440 paces from the peece how far shall the same peece shoote being dismounted but one degree Resolution To answere this or all such like I set downe the numbers according to the rule of proportion and multiplying and deuiding accordingly I find she shall shoot short in dismounting a degree 32 paces or 53 yeards or 160 foote which substracted from 1440 rests 1408 paces so far shall the Cannon shoote in dismounting her one degree of her furthest range Or you may do the like in framing the golden rule saying If 45 degrees range 1440 paces what will one and you shall haue 32 paces in your quotient as before How by knowing the distance to the marke by the conclusion or rule before you may know whether your peece will shoote short or ouer the marke or you may know how far it is from your platforme to any marke within the reach of your peece onely by knowing the vtmost range of your peece and the degrees she is eleuated at Question Admit the same Cannon in the former conclusion which ranged at the best of the randon 1440 paces hauing the like charge in powder shot and wad is laid to shoot at a marke being mounted at 30 degrees I demaund how far it is from the peece to the said marke or how far the said peece doth carry so mounted Resolution To answere this I multiply the paces my peece reacheth at the best of the randon by those degrees in the proposition to wit 30 degrees and there ariseth 43200 which deuided by 45 my quotient is 960 paces that is 40 paces lesse then a mile so far will that peece shoot being mounted at 30 degrees And if you would know how much this is short of the vtmost range abate the same from the said range the remaine is your desire As 960 paces abated from 1440 rests 480 paces so much doth she shoote short of her best randon In this order by 2 shoots knowne you may know what any peece of Ordinance will do being mounted aboue 10 degrees to the best of the randon but vnder 10 degrees you should erre something in this practise because the range of the bullet flieth a great part of the way in an insensible streight line and the peece mouth eleuated aboue 10 degrees shootes or driues the bullet in a more circular proportion The range or flight of the bullet by the draught in the next leafe may be vnderstood And note that in seruice there is no peece of Ordinance lightlie mounted aboue 15 or 20 degrees except morter peeces and such like The direct straight range at 90 degrees This draught here drawne doth shew you the range or motion of the bullet through the ayre shot out of any peece of Ordinance at any degree of the randon How to make a table of randons or go very neare to know the true range of the bullet out of all sorts of peeces being mounted from degree to degree Many Authors haue taught how to make a table of randons whereas some of them neuer shot in any peece of Ordinance in their liues And for asmuch as I find their writing and reasons differing I thinke it will be a very hard matter to make a perfect table of randons except the same be tried and experimented with some peece of Ordinance in some conuenient ground I neuer heard nor reade of any that hath as yet fully put the same in practise the which would be much auailable to euery Gunner to know what euery peece would do at the mount of euery degree or point in the quadrant the motion or range of the bullet being something variable at the mount of euery degree You shall very neare find out the true range or randon of the bullet shot out of any peece of Ordinance the peece mounted at any degree of randon as thus Charge your peece with her due loading in powder shot and wad laying the peece at point blanke which you may easily try by putting the rule of the quadrāt into the peece mouth coyning the peece at the breech so as the plūmet may cut the quadrant in the line of leuell as you see in the first figure hereafter drawne that peece lyeth point blanke which done giue fire marke where the bullet first grazeth after bring your peece to the same platforme so as the wheeles and cariage stand neither higher nor lower then they did the first shoote and being charged with one the selfe like quantity in powder bullet wad as before the peece being of like tēper raise her mouth one degree as the second figure showeth discharge her and marke where the pellet falleth or grazeth first then measure how farre the first graze of the second bullet is beyond the graze of the first bullet so much will the peece conuey the bullet further at the mount of euery degree or very neare thereto But being mounted aboue 20 degrees she will shoote shorter shorter a litle at the mount of euery degree to the best of the randon according to the height circular motiō of the bullet If the peece be mounted to the best of the randon the plummet will cut the 45 degree of the quadrant as the 3 figure sheweth Or you may make a table of randons like the other as thus Measure the distance the peece cōueyeth the bullet at the best of the randō frō which abate the distāce the peece cōueyeth her bullet at point planke deuide the remaine by 45 the quotient will shew you how far the shoote is caried at the mount of euery degree or deuiding the sayd remaine by so many degrees as you would eleuate your peece at the quotiēt wil likewise shew you how far the bullet doth range beyond point blanke Example If a Cannon at point blanke
will a peece of 3000 weight and in working according to the rule the quotient is 10 shewing that 10 horses must be prouided to draw a Culuering of 3000 weight Also deuiding 3000 the weight of the said peece by 10 being the number of horses there will stand in the quotient 300 shewing the draught of each horse To know how many Oxen is to be prouided to draw any peece of Artillerie It is to be noted that 3 yoake of oxen is thought to draw as much as three horses and that 3 yoake of oxen is sufficient to draw a Saker of 1400 weight Question How many oxen must be prouided for a Cannon of 8000 weight Resolution In working as before I find that 34 oxen or 17 yoake of oxen will serue to draw a Cannon of 8000 pound weight And note that whereas there doth remaine 2 7 parts of a whole number neither men horses nor other cattell can in any such millitare questions be brought into a fraction but yet the rule it sheweth that 17 yoake of oxen is sufficient for the draught of a Cannō of 8000 pound weight when 3 yoake of oxen serue for to draw a Saker of 1400 pound weight If you deuide the weight of the whole Cannon being 8000 pound weight by 34 the oxen appointed to draw the same the quotient is 235 pound 5 17 so much did euery oxe draw How you may wanting both oxen and horses to draw any peece of Ordinance know presently how many men is able sufficiently to draw the same either on plaine or marrish ground Question I shewed in a conclusion before that 3 yoake of oxen would draw a peece of 1400 pound weight and that 90 men would draw a Cannon of 9000 pound weight now if there want both horses and oxen or that you are occasioned to draw the said peece through some marrish ground whereas horses and oxen cannot passe I demaund how many men is sufficient to hale a Saker of 1400 pound weight through the said marish ground Resolution If a Cannon of 9000 weight require 90 men to draw the same I find that a Saker weighing 1400 pound weight must haue 14 men to draw the same and euery one shall draw 100 weight for his part In drawing Artillery through any soft marrish ground it is requisite to haue in readinesse in the Maister of the Ordinance his carts which carrieth the prouisions for the Ordinance certaine hurdels of boords or rather flat bottomed boates in which any peece of Ordinance may be placed carriage and all and by force or strength of men may be drawne as easily as to draw the said peece on the firme land for that the said boate is apt to slide or swimme on the soft owish the ropes being made fast to the forestearne or sides of the sayd boates which boates do serue also for cariage of the Ordinance and all things thereto belonging ouer any riuer or soft owish ground c. How you may by the rule afore know how many oxen will draw any peece of Ordinance if you want men and horses I shewed that 90 men is able to draw a Cannon of 9000 pound weight and that three yoake of oxen will serue to draw a Cannon of 1400 pound weight now wanting men and horses I say if a Saker of 1400 pound weight require 6 oxen what will a Cannon of 9000 and in multiplying the weight of the Cannon by 6 the number of oxen appointed to draw the Saker and deuiding that product by the weight of the lesser peece the quotient is 38 oxen or 19 yoake so many must be prouided to draw a Cannon of 9000 pound weight which weight deuided by the 38 oxen appointed to draw the same the quotient sheweth that euery oxe drew 236 pound weight How you may wanting men and oxen to draw any peece of Ordinance know how many horses is requisite to draw the same Also I noted before that 3 horses would serue to draw a Fawcon of 900 pound weight I demand how many horses will serue to draw a Cannon of 9000 pound weight In working as before the quotient is 30 so mamy horses is requisite for that purpose which peece her weight deuided by the number of horses appointed to draw the same the quotient sheweth that euery horse drew 300 pound weight In this order you may know what number of men horses or oxen is able to draw any peece of Ordinance and what euery one seuerally doth draw How to know how many 100 of Haberdepoize weight any peece of Ordinance or other grosse weight containeth In the conclusions afore set downe thou must note gentle reader that euery 100 weight of most things is accounted after fiue score to the hundreth but if thou be desirous to know how many hundreth of Haber depoize weight any peece of Ordinance or other grosse weight cōtaineth thou mayst by Arithmetike soone be resolued for euery 100 of Haberdepoize weight containeth 112 pound the halfe hundreth 56 pound the quarter 28 pound and the pound 16 ounces so that deuiding the weight of any great peece by 112 thou mayst easily know how many hundreth of Haberdepoize weight the same containeth I would know how many hundreth of Haberdepoize weight is in a Cannon of 9000 pound weight I deuide the same by 112 as aforesayd and the quotient being 80 40 112 sheweth that a Cannon of 9000 pound weight containes 80 hundreth of Haberdepoize weight one quarter and 12 pound A Tun containeth 2000 of Haberdepoize weight How you may proportionally prooue all sorts of peeces of Artillerie for seruice whether they will hold or no. All peeces that shoote a bullet vnder 10 pound weight and duely fortified with mettall being shot 3 times first with the whole weight of the yron bullet Secondly with 5 4 partes thereof and lastly with 3 2 partes of the same will hold for any seruice being charged with her ordinarie charge albeit the said peece were discharged 100 times in one day How you may find out the proportionall charge afore named as thus Suppose a peece shoote a bullet of 6 pound weight and that you desire to know what 5 4 partes in powder of the weight of the bullet is multiply the weight of the said bullet by the numerator 5 and deuide by the denominator 4 the quotient is your desire Example 6 multiplied by 5 is 30 the same deuided by 4 the quotient is 7 ½ The like order you must vse in giuing her 3 2 parts in powder to the weight of the shot and your quotient is 9 pound How to prooue any peece that shooteth a bullet vnder 50 pound weight and aboue 10 pound weight Any peece that shooteth a bullet aboue 10 pound in weight and vnder 50 pound would for the first shot be charged with ⅔ parts in powder of the pellets weight for the second shot with ⅚ partes and lastly with the whole weight of the bullet Example Admit a peece shoote a bullet of 40 pound weight the