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rest_n	bullet_n	great_a	powder_n	3,710	5	11.9725	5	true

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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08351	Of the art of great artillery, viz. The explanation of the most excellent and necessary definitions, and questions, pronounced and propounded, by that rare souldier and mathematician, Thomas Digges Esquire and by him published, in his Stratiaticos, and Pantometria, concerning great ordinance, and his theorems thereupon. Together, vvith certaine expositions, and answers thereunto adioyned: written by Robert Norton gunner. And by him dedicated, to the worshipfull Iohn Reinolds Esquire, master gunner of England.	Norton, Robert, d. 1635.	1624 (1624)	STC 18676; ESTC S119503	26,924	57

the Bore or ⅓ of the waight of her Shott in Corne powder for Cannons Or ⅔ of the Diametres or ⅘ of the waight of the Iron Shot of Corned Artillery powder for the Culuerings And foure Dyametres or the whole waight of the Shott of such powder for Sakers Falcons and lesser Ordinance is vsually accompted as their due proportionall Charges which charge if it could bee readily found would be iust so much powder as being all fired within the Cylinder will at that instant haue carryed the shotte iust to the mouth of the Peece 2. M. D. Whether one and the selfe-same Peece twice charged with one and the selfesame quantity of Powder and Bullet discharged also at the same Randon shall make the same Ranges M. N. No for at the Second time it will shoote further then at the first As well because the Ayre that before was still quiet and vnbroken will be then moued that way the shotte goeth and by the course of the shotte become broken And also for that the charged Cylinder will then be dryer and warmer then at the first and cause the Powder to fire quicker and better together which will adde more force thereunto 3. M. D. If a Peece be discharged with the waight of his Bullet in Serpentine powder and afterwards discharged with halfe the waight of his Bullet in such Corne powder as shall cause the Peece to cast the same ground No. I demand if the same Peece be againe Charged with halfe the quantity of either sort whether these Ranges shall also bee equall The forme of Charging being vniforme and temper of the Peece alike M. N. No for the last halfes will one of them be then more farther off from due proportionall Charge of the said Peece then the other was from his Mate at the first And therefore it is certaine that the last halfe of the Corne Powder will shoote much further then the halfe of the Sorpentine Powder can doe because there is more Petre in the quantity of the last halfe then in so much of the first halfe of the Corne Powder and lesse in the other 4. M. D. If two Peeces of the same Length and Bullet be charged with one kinde of Powder but seuerall waights I demand whether the Ranges shall be proportionall to the said waights No. Or to the Square Cube or Squared square rootes of the said waights Or whether the Proportion of the Ranges be not to be found without any further respect either to the length of the Peece or Ponderositie of the Bullet Considering by Hypothesis all those are equall M.N. Their Ranges will not bee proportionall to those Roots besides whether they should be alike or differently mounted being not here expressed Neither the different waights of the Powder therefore without them those nor any other proportion certaine can hold yet they may he found in a Compounded proportion hauing respect vnto the proportions betweene the force of the Powder waight of the Shott and length of the Peece 5. M. D. Whether the Proportion found in one kinde of Powder No. hold not in all other kindes of what mixture soeuer it be the Peeces and Bullets being as is before supposed equall M.N. No for the proportions of all different kindes of Powder equall in waight or Measure doe differ in Force accordingly more or lesse as there is more or lesse Petre and working therein Neuerthelesse the equality of the rest for that a lesser waight or measure of stronger Powder will equall the proportionall Force of a greater waight or measure of weaker Powder and these are for Action in Geometricall proportion augmented but for Resistance they are augmented in Arithmeticall proportion as an excellent Philosopher elsewhere doth largely Demonstrate 6. M. D. Whether the proportion of such Ranges He referreth this to a Booke neuer yet extant be not a Meane proportionall resulting of the Commixion of the equality of the Peeces lengths and Bullets and the inequality of the Powders Quantity The Quallity being supposed alike M.N. I say it cōmeth so neere to such a mean proportionallity as that in practise it might be accepted for the same indeed But it not being exactly so and also not being easily found by reason it lurketh vnder so many compounded varieties and contrarieties we must content our selues with such a necessary Neerenesse as in my Exposition of M. Digges his Definitions are exemplified or to be shewed elsewhere more largely Of the length of the Peece and Powder 7. Mr. Digges Whether two Peeces being in all respects equall sauing only in length being charged with one Bullet Yes and one quantity of Powder shall not make equall Grazes M.N. No for both by Master Digges his answer and mine to the first Question there is a Charge certaine which is that two Peeces of seuerall lengths and otherwise equall cannot with one Quantity of like Powder haue both of them such a Charge as can possibly be equally or proportionally neerest to their Charge certaine And therefore their seuerall Grazes must needs be also different 8. M. D. Not alwaies Whether the longer Cannon shall make the greater Range whatsoeuer Quantity or kinde of Powder they be discharged withall the Quantity of Powder being equall M. N. I imagine that Master Digges meant the Quality or Kinde of Powder which may cause proportionall difference according to their seuerall Forces Otherwise I may answer yes vnlesse the longer Peeces charge be as much ouer as the shorter is vnder the Charges duely certaine 9. M.D. Yes but not without respect of the Powder Whether there be not a certaine conuenient Length of the Peece in respect of his Bore or Bullet to make the vtmost Range in such sort that making the Cannon longer shall rather hinder then further M. N. Surely Master Digges meant herein as in the last the length of the Cylinder or Chace by name of making the Cannon longer then the question is by him truly answered yes If the proportional Force and Quantity of the Powder be therein also considered and excepted as I haue vnder his former Definitions exemplified 10. M.D. Whether this Length and proportion being found in one Peece No. hold in all other the proportion I meane for the Length must of necessity alter M. N. One proportion cannot hold for Cannons and Minions of not aboue 24. Dyametres and also for Culverings and Sakers not lesse then 30. Dyametres of their Bores in Length and the greater waight of the greater Shott resisting the powders Force so much the more by how much the more the Peece is mounted and doth likewise in his Course more by the greater grauity thereof affect to descend out of the straite Line of her Course then the lighter doth though both beginning with equall swiftnesse each of these and all or some of them together doe hinder generall proportions besides the lesse proportion of fortefying of the Cannon which Mettall then of the Culvering

Curve or Circular The 14. Theoreme When any Peece is mounted directly to the Zenith Then doth his Motion violent being in that scituation directly opposite to the naturall carry the Bullet in a perfect right line directly vpward till the force of the violence be spent and the Naturall motion haue gotten the victorie And then doth the Naturall returne the Bullet downward againe by the very same Perpendicular line And so is the whole motion of the Bullet in this case a very direct Perpendicular to the Horizon The 15. Theoreme But if any Peece be discharged vpon any Angle of Randon albeit the violent motion contend to carry the Bullet directly by the line Diagonall Yet the Perpendicular motion being not directly opposite doth though vnsensibly euen from the beginning by little and little drawe it from that direct and Diagonall course And as the violent doth decay so doth the naturall encrease and of these two right lined motions is made that mixt Curve Helicall Circuit of the Bullet The 16. Theoreme Any Peece therefore discharged at any Mount or Randon first throweth forth her Bullet directly a certaine distance called of Gunners their Point-Blanke Range and then it maketh a Curve declining Arke and after finisheth either in a direct line or nigh enclining towards it The 17. Theoreme The further that any Peece shooteth in her direct line commonly called Point-Blanke the deeper also she pierceth in her Battery if the Bullet bee not of substance brickle or frangeable The 18. Theoreme The more ponderous a Bullet is the more it shaketh in Battery albeit it pierce not alwayes so deepe as the lighter or letter shotte conueniently charged The 19. Theoreme Any two Peeces of Battery Ordinance charged with one kinde of Bullet and shott into one Rampire of massie vniforme kinde of Substance shall euer make their Profundities of pearcing Proportionall to their leuell Ranges Horizontall if they bee discharged either leuel or at one grade of Randon and at like distance The 20. Theoreme Any two Peeces of Batterie discharged into any Rampire of vniforme massie substance shall euer make their Pearcing depths proportionall to their lines Diagonall albeit these Peeces bee discharged from different Randons so as they batter at like distance The 21. Theoreme As Archimides line Helicall or Spirall is made by the direct motion of a point carried in a right line while that right line is Circularly turned as Semidiameter vpon his Circles Center So is this Artillery Helicall line of the Bullets Circuit created onely by two right lined motions becomming more or lesse Curve according to the difference of their Angles occasioned by the seuerall Angles of Randon Whereupon by demonstration Geometricall a Theoricke may be framed that shall deliuer a true and perfect description of those Helicall lines at all Angles made betweene the Horizon and the Peeces lines Diagonall The 22. Theoreme These direct or Diagonall lines are alwayes longest when the Peeces Axis is directed to the Zenith And alwayes as the Peeces Axis declineth more and more to the Horizon So doe the Diagonall lines grow shorter and at the leuell Horizontall shortest of all The 23. Theoreme These direct lines Diagonall albeit they encrease in length at euery grade of Randon from the Horizon to the Zenith yet is not their encrease vniforme or proportionall either to their degrees of Randon or Horizontall Ranges nor yet to their Circuits or Altitudes and yet such as may be reduced to a Theorike certaine The 24. Theoreme The middle Curve Arkes of the Bullets Circuits compound of the violent and naturall motions of the Bullet albeit they be indeed meere Helicall yet haue they a very great resemblance of the Arks Conicall And in Randons aboue 45. they do much resemble the Hyperbole and in all vnder the Ellepsis But exactly they neuer accord being indeed Spirall mixt and Helicall The 25. Theoreme Any Peece discharged at any one Randon with like Bullets and seuerall charges of Powder shall make both their lines Diagonall and Curve Circuits of different longitude but the Curve Arkes shall alwaies be as Paralels and their Longitudes Proportionall to their lines Diagonall The 26. Theoreme The last declining line of the Bullets Circuit albeit it seemes to approach somewhat to the nature of a direct line againe yet is it indeed still Helicall and mixt so long as there remaineth any part of the motion violent But after that is cleane spent the rest of his course to the Horizon is direct and Perpendicular and a perfect right line indeed which is best discerned in those Grades of Randon which are betweene the Zenith and the Mount or Randon Aequorizontall The 27. Theoreme This declining line doth alwayes make a greater and greater Angle with the Horizon as you raise the Peece to a greater Mount till you come to the Mount Equorizantall about which Point the same declining line becommeth Perpendicular before the Bullet fall to the Horizon The 28. Theoreme The Horizontall Ranges in all Peeces mounted from the Horizon toward the Zenith doth not still encrease but at euery grade of Randon are longer till you come to the Point or mount Tropicall commonly called the vtmost Randon which hath bin generally thought to be the grade 45. but is not so And from that Tropicall grade vpward the Ranges decrease againe till you come to the grade Aequorizontall so called because the Bullet then falleth a like distance to the leuell Ranges The 29. Theoreme This Aequorizontall Grade is as far distant from the Zenith as that Grade is from the Horizon which shall cause the Peece to shoot in the Horizontall plaine a distance equall to his highest Altitude or longest line Diagonall The 30. Theoreme The Mounting of any Peece aboue his Aequorizontall grade doth still decrease her Horizontall Ranges euen till it come to the Zenith But in a Proportion different from any of the former her Bullet ending euery of those Circuits in a direct line Perpendicular The 31. Theoreme The Gradual encrease and decrease of these Ranges Horizontall albeit they are equall in the Quadrant yet are they neither equall nor proportionall in the Horizon neither the Ranges nor their Interualls Neither compared between themselues nor yet conferred with the Chords or Sines of their Arks. And yet is there such a kinde of Proportionall encrease and decrease of the proportion of their Interualls as may be reduced to a Theorike certaine The 32. Theoreme The Tropicall grade commonly called the vtmost Randon is not as hath beene generally supposed the Medium or Middle betweene the Horizon and the Zenith Viz. 45. but rather betweene the Horizon and the grade Aequorizontall which will fall out much nigher 50. from the Zenith and 40. from the Horizon The 33. Theoreme The highest Altitude of any Bullets Circuit is farthest distant from the Peece when she is discharged at her vtmost Randon or point Tropicall and at all other Randons either aboue or beneath that Tropicall Point That highest Altitude

seuerally in a Saker three shotts one of Lead another of Iron and the third of Stone with 12. pound of powder as the Leaden shott would weigh then will the Shotte of Lead outrange the other two and that of Iron will out-range that of Stone But seuerally shooting those three with 8. pound of powder as the Iron shotte weigheth it will outrange the Lead shott and the Lead the Stone shott But shooting them againe seuerally with 4. pound of powder then will the Stone shott outrange the Iron and the Iron the Lead Besides the more a Peece is mounted the more doth the heauier waight of the shotte resist the Mouer which if it be too much or too little for the Force it then impaireth the Motion Therefore will the conuenient meane waight be proportionall 18. M. D. Yes Whether this conuenient waight of the Bullet alter not according to the Quantity or Validity of the Powder M. N. Yes for the Leaden shott will require the whole waight of ordinary powder or ⅘ of the Corne-powder And the Iron shott ⅘ of ordinary or ⅔ of the best And the stone ⅔ of the ordinary or ½ of the best powder As hath beene ordinarily obserued to doe generally his best execution But this holds not alwaies for the force of powder and other proportions and accidents are continually variable 19. M. D. Whether to finde the said conuenient Ponderositie of the Bullet it be sufficient to consider the Powder Both. or that the Longitude of the Peece also cause therein a diuersitie M. N. Yes the longer Peece will require the more powder to be fired within her before the shott can ariue to the iust mouth of the Peece to be then discharged out then the shorter will For if all the powder be fired before the shott ariue at the mouth the after-running thereof within the rest of the Cylinder will hinder the swiftnesse thereof by the Cylinders being too long And likewise if the shott be discharged out of the Peeces mouth before all the powder be fired and that it haue receiued all the force of the Powder for want of sufficient length in the Cylinder of the Peece it will be also hindered Therefore there is a conuenient length for the conuenient waight to accompany with it continually proportionall 20. M. D. If two Peeces be twice charged first with an Iron then with a Lead shott The Quantityes of Powder Vnanswered at both times equall Whether the differences of the Ranges be not deriued only from the proportions of the Waights of these Bullets All other circumstances by proportion differing not And what relation to the Ponderosity of the Bullets these Ranges haue M. N. To this I haue already sufficiently Answered especially in the three last precedent Answers For as much as herein the proper waight of the Shot due length of the Peece proportionall to the Force of the Powder and Heigth of the Bore doe all domineere in altering their Shotts Ranges And besides we seldome vse Leade shott but often Stone shott in great Ordinance wherefore the Questions and Answers may bee better applied to lion and stone then to Iron and Lead 21. M. D. Vnanswered Two Peeces being in all respects equall and charged with one kinde of Powder but different Bullets the one Iron the other Lead And either hauing the waight of his Bullet I demaund whether the ranges be equall M. N. No but proportionall according as the length of the Peece is neerest proportion as aforesaid 22. M. D. No. If one Peece bee charged three seuerall times first with a Stone Bullet then with Iron and finally with Lead And the Iron of such temper that it bee an exact meane proportionall in waight betweene the other two being all discharged with one quantity of Powder I demaund whether the Ranges shall bee in continuall proportion M. N. No for the length of the Peece Height of the Bore and force of the Powder will be neerer the conuenient meane for one of the said shotts then for any of the other two Therefore the continued proportion will not hold herein 23. M. D. No. Whether a Peece being twice charged first with Iron then with Lead hauing one quantity of Powder and the Range noted I demaund whether being charged with any other quantity of Powder the Ranges of the same Bullets shall not alway retaine the same proportion M. N. I also deny that the Ranges shall retaine the same Proportion for that the waight of one shott will neerer approach then the other towards the conuenient length of the Peece and force of the other quantity of Powder And therefore that aduantage will alter the proportion therein 24. M. D. If in a Falcon for example Vnanswered by experience I finde two such quantities of Powder as discharging the Falcon with the first Quantity of Powder with an Iron shott and againe discharging her with the second quantity and a Lead shott they Range both duely one ground I demaund whether in a Saker of the same Length with the Falcon Charging her first with an Iron Bullet then with a Lead Bullet vsing the same quantities of Powder whether their Ranges shall be proportionals And whether doubling either quantity of Powder it shall alter the proportion of the Ranges M. N I say vnto the first part of this double Question that the Saker shall not make proportionall Ranges of ground First for that the Saker is of a higher Bore And secondly for that the conuenient proportions of Powder cannot agree with those quantities But I neuer heard of a Saker so short as a Falcon by a foot at the least And to the second part I say if at the first they had beene proportionalls yet they would alter their Ranges by doubling conuenient proportions of either quantity of Powder 25 M. D. If two Peeces of one Length be of such different Quantity of Bullet No. that the one being discharged with a Lead Bullet the other with an Iron Bullet either hauing Powder the waight of their Bullet and so make equall Ranges I demaund whether either of them discharged with halfe the waight of their Bullets in Powder shall Range alike also M. N. No certainely for the halfes will bee further of then the whole waights were from the Conuenient meane Therefore their Ranges will not be alike for then the Iron shott will outrange the Leaden 26. M. D. Not alwayes If two Peeces be of one Length but of seuerall quantity of Bullet and yet of one kinde of Mettall or substance and discharged with the waight of the Bullet in one kinde of Powder I demaund whether they shall not Range one ground being equally Mounted M. N. Not at any time if the Peece of the lower Bore haue her due length For then shee will ouer-Range the other of the greater Bore 27. M. D. Vnanswered If there be once found by experience in some one Peece such a perfection of

a Falcon of three Inches Bullet waigh 700. pound I demaund how much a Cannon of eight inches will waigh that is able to receiue his proportionall Charge to that Cannon M.N. This cannot bee answered by the simple Rule of proportion because waight is not appertaining to Lines nor to Superficies but vnto Solid Bodies And also you may note that although M. Digges here compareth the Falcon which is at least 30. of the Dyametres of her Bore in Length and Fortefied with Mettall to endure the waight of her shott in powder with the Cannon that is but 18. or 24. Dyametres of her Bore in length and no better fortefied then to endure ⅔ of her shotts waight in Powder But comparing the Falcon with a Demi-Culvering that is of the same kinde and Fortification whose shott waigheth 10. pound the Question is Answered thus for Example The Cube of three the inches of the height of the Falcons Bore is 27. the Cube of 4½ the inches of the Demi-Culuerings Bore is 91. fere Now say by the Rule of three Vnanswered if 27. giue 91. what shall 700. giue And so hauing accordingly Multiplyed the third number by the second and diuided the product by the first you shall haue in the Quotient 2359. pound 7 27. for the waight of the said Demi-Culvering sought 44. M. D. If a Falcon of 3. inches Bullet require 3. pound of Powder for his charge I demand how much Powder will charge a Cannon of 8. inches Bullet M. N. Because this Question is of seuerall kindes of Ordinance as is said in the last precedent Answer I haue also applyed this Answer and the Example to the said Demi-Culuering thus for Example Multiply 91. the Cube of 4 1 ● by 3. l. the charge of the Falcon and the product will be 273. which I deuide by 27. the Cube of 3. the Diametre of the Falcon And the Quotient I finde to be 10. pound and ● ● for the Powder of the due charge for the said Demi Culuering sought 45. M. D. Not answered If the Falcon that carryeth Point Blank 150. paces and at the vtmost Randon 1300. paces I demaund how farre a Culvering at his vtmost Randon will reach that at Poynt-blanke or Leuell rangeth 250. paces M. N. Say by the Rule of 3 if 150. giue 1300. what shall 250. giue answer 2166. paces and ⅔ for the vtmost range of the Culvering sought M. D. And thus by obseruations vsed in one Peece by this Art of Proportion a man may discouer the Force of all Peeces M. N. The Gunner may know by her leuell right Range how farre his Peece will conuey her shotte at any Eleuation mounted If he multiply the number of Paces shee carrieth in a straite line shee lying leuell by 11. and diuide the product by 50. the Quotient will be the greatest digression which it maketh at the first degree more then at the Leuell But all other degrees proceed alwaies deminishing vnto the vtmost Randon and to know how they deminish take the number of degrees from one to 41. the best of the Randon and that will be 40. by which diuiding the said number of the former Quotient This Quotient will be the number of Paces which shall decrease from degree to degree from the first vnto the vtmost Random As for Example For the Culvering that shott 250. paces leuell in a straite Line I doe multiply that by 11. and it produceth 2750. which I diuide by 50. and the Quotient will bee 50. paces which it shooteth at the first degree more then at the leuell which 50. paces diuided againe by 40. the degrees betweene the first degree and the vtmost Randon this Quotient will be 1. pace and ¼ which I take from 350. namely from the 250. the 50. increased at the first and also the 50. to be increased for the second digression it leaueth 348. paces ¾ for the Range of the second degree vnto which adde 48. paces ¾ abating the one pace ¼ and there will bee 195. ¼ for the paces of the Range of the third degree and so proceed Certaine Erronious Positions and Grounds published by professors of this Art of Great Artillery noted by Mr. Digges 1. THat in all Peeces of Ordinance mounted aboue the vtmost Randon the Bullet is violently carried in a right Line to his vtmost distance from the Earth and then falleth perpendicularly downe to the Horizon 2. That all Peeces of one Bullet being charged with one quantity of the same Powder and discharged at one Randon shall make their Ranges proportionall to the Length of their Peeces 3. That if you Charge any one Peece with seuerall quantities of one kinde of Powder the Peece being discharged two seuerall times at one Randon and with the same Bullet shall make different Ranges proportionall to the waight or quantity of the powder 4. The fourth and chiefe of all the rest is the Grade of vtmost Randon For most Writers that euer I read agree in this that the mount of 45. grades aboue the Horizontall plane should make there the vtmost Range 5. That euery degree of Random doth equally encrease the Range in any one Peece from the Zenith to 45. their Tropike grade and so in decreasing likewise and that proportionally in all peeces more or lesse according to their Force 6. That in all sorts of Peeces the difference of their vtmost Ranges should be in proportion answerable to the waight of their Bullets and Charges of Powder Other Erronious Positions published concerning Ordinance Noted by Robert Norton 1. THat when a Peece is to shoot at a marke aboue the Leuell being within distance of the right Range then it by the vertue of the Fire that ascendeth ouer-shooteth the Mark. And that therefore to remedy it the Peece must bee so much imbased Sior Collado fol. 61. vntill a Plum line at the Cornice let fall will not enter but touch the lower side of the mouth of the Peece The same Author there affirmeth Folio 60. that if any Peece be to shoote from aboue downwards to a marke vnder the Leuell and the Peeces Mettall directed to the marke that then the Peece must be so much Eleuated more as may equall the Angle that the Peeces flatt of her mouth maketh with a Plum line applied thereunto to equall the Naturall defect caused by the ponderous descending of the shott in her mixt motion or crooked Range Mr. Smith hath published in his Art of Gunnery page 35. that if a Saker will conuey her Bullet at Point blanke 200. paces and at the best of the Randon 900. paces that then that Cannon will shoote 1620. paces at the best Randon that carryeth at Point-blanke 360. paces which is very erronious for that at the best of the Randon the shott rangeth rather 10. times as much as at the Leuell Range And also page 39. he affirmeth that if a Culvering be shotte off with 2 ● of the waight thereof and then with the whole waight of her shott in Powder that then the second shott shall bee neere ⅓ further then the first And page 46. that a Cannon that shooteth 1440. paces at 45. degrees will for euery degree of lesse Mount abate 32. paces in her Range And page 47. he saith that a Cannon that shooteth at her best Randon 1440. paces will shoot at 30. degrees but 960. paces whereas in that case shee will conuey her shott being like loden and mounted about 1269. paces And page 49. he saith that if you abate the Leuel Range of a Peece from the vtmost Range thereof and diuide the remainder by 45. degrees then the Quotient will show you how farre the shott is carryed at euery degree Or by deuiding the same number by so many degrees as you would eleuate your Peece at The Quotient hee saith doth shew how farre the Bullet doth range beyood Poynt-blanke and that thereby you may make a Table of Randons But he either forgetting or I thinke rather not knowing that the best Randon is but little aboue 40. degrees Eleuation or that the Peece shooteth thereat about 10. times as much as the Leuell Range Or that the Ranges deminish from 1. to the best Range and increase from the best to 90. degrees Eleuation It hath made him publish these and many other Erronious positions FINIS