285 6 828 7 302 7 934 8 320 8 1044 9 337 9 1129 10 354 10 1214 20 454 20 1917 30 693 30 2185 40 855 40 2289 50 1000 50 2283 60 1140 60 1792 70 1220 70 1214 80 1300 80 1000 90 1350 90  than real and doth best agree with greater Ordnance but by help of it working by the Rule of proportion you may know the Random of any Piece of Ordnance by first as we have said before making one Shot and measuring from your Platform that distance You may make a Table for your Piece thus Suppose a Saker being mounted to 5 degrees shoot the Bullet 416 paces how far will it shoot being mounted 10 degrees As 722 the Tabular distance for 5 degrees of Mounture is to 416 paces the distance found So is the Tabular distance for 10 degrees of Mounture 1214. to the distance required which will be found to be 699 5 paces Now if you desire to know how much of the Horizontal line is contained directly under the right line of any Shot called the right Range made out of any Piece at any elevation First know that in plain Triangles the violent motion or right line of a Shot is supposed to be the Hypothenusal the Angle of Mounture to be the Angle at Base these are given and the Horizontal line is the Base which is to be found there the proportion will run thus As the Radius 90 deg is to the number of paces in a right Range So is the Sine Complement of the Angle of Mounture to the Horizontal Base or the right line which lyes parallel to the Horizon under the way of the Shot CHAP. XXI Of the violent crooked and natural motion or way of a Shot from the time he is discharged until it is descended BY the third and fourth propositions of the second Book of Tartagilia his Nova Scientia he sheweth that every body equally heavy as a Shot in the end of the violent motion thereof being discharged out of a Piece of Ordnance so it be not right up or right down the curved Range shall joyn with the right Range and to the natural course and motion betwixt them both which distinct motions you may see in the last foregoing figure In the 17 proposition of the same Book he proveth that every Shot equally heavy great or little equally elevated above the Horizon or equally oblique or level directed are among themselves like and proportional in their distance as the figure following sheweth as A E F is like and proportional in right and crooked Ranges unto H I and in their distances or dead Ranges A F unto A I. And in his 4th and 6th propositions of the same Book he proveth that every Shot made upon the level hath the mixt or crooked Range thereof equal to the Arch of a Quadrant 90 degrees and if it be made upon an elevation above the level that then it will make the crooked Range to be more than a Quadrant And if that be made imbased under the level that then the crooked Range thereof will be a Quadrant And in his 9th proposition of the same Book he shews that if one Piece be Shot off twice the one level and the other at the best of her Random at 42 ½ deg Mounture that the right Range of the length is but the ½ of the dead range of the best Random He that desires a further Demonstration of these Propositions may peruse his said second Book de Nova Scientia CHAP. XXII The making of a Gunners Rule which will serve for the elevation of a Piece which is sometimes better than a Quadrant and the dividing it into degrees by help of a Table fitting it for any Piece from 5 foot to 14 foot long BEcause the Quadrant cannot be conveniently used at all times especially when the wind blows hard and being near the Enemies Guns the Plumb-line is too long before it stands still to remedy this the Gunners Rule was invented the figure hereof is as followeth it must be 12 or 14 inches long according as the Gun will require it must have a long slit down the middle thereof like the Eye-Vane of a Quadrant or back Staff the head thereof make circular or a little hollow as you see in the figure the Instrument is described standing at 't is to be placed upon the Britch of a Piece of Ordnance in the middle of the small narrow slit you must place a Lute string or a well twisted Silk with a Bead running upon the same to be set to any number of inches and parts or to such a degree of the Quadrant as you must mount your Gun unto and on the one side of the slit you must place a division of inches and let every inch be divided into 10 parts and then it will serve for all sorts of Guns but if it be for a particular Gun then on the other side you may place the degrees and parts when you shall find by the length of your Piece how many inches and parts of an inch goes to a degree but to use it with all sorts of Ordnance let it only be divided into inches and parts To fit this Rule for one Gun only here is the Rule for the decimation of the degrees note this Table hath 11 Columns the first shews the length of the Piece in feet and half feet the other 10 Columns in the head are 10 degrees and under is inches and the 100 parts of an inch from 1 degree to 10 degrees and so you may take them out of the Table and put them on your Ruler The len of the Piece 1 Degree 2 Degrees 3 Degrees 4 Degrees 5 Degrees 6 Degrees 7 Degrees 8 Degrees 9 Degrees 10 Degr. Feet and ½ Feet Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 Inch. 100 4 Foot long 1 3 2 6 3 8 4 11 5 14 6 16 7 19 8 82 9 25 10 28 5 Foot and half 1 14 2 28 3 42 4 56 5 70 6 84 7 98 9 12 10 26 11 40 6 Foot long 1 22 2 44 3 66 4 88 6 10 7 38 8 58 9 78 11 8 12 29 6 Foot and half 1 36 2 72 4 8 5 44 6 80 8 17 9 53 10 89 12 25 13 63 7 Foot long 1 47 2 94 4 41 5 88 7 35 8 82 10 30 11 77 13 24 14 73 7 Foot and half 1 58 3 14 4 71 6 28 7 85 9 42 10 99 12 55 14 14 15 71 8 Foot long 1 68 3 36 5 4 6 72 8 40 10 8 11 76 13 44 15 12 16 82 8 Foot and half 1 79 3 58 5 37 7 16 8 95 10 74 12 53 14 32 16 12 17 92 9 Foot long 1 89 3 79 5 68 7 58 9 47 11 37 13 27 15 18 17 8 18 98 9 Foot and half 2 00 4 0 6 0 8 0 10 0 12 10 14 2 16 3 18 4 20 4 10
example 700 Geometrical paces or at any other distance But the truth is the observations are so fallible and the Gunners so few that have made them and made them exactly that the use of Artillery taking from it the Range of Point Blank must needs have very little of certainty in it If one would collect some certain Science touching th' ordinary Quadrant it would be necessary to make the Experiments not only with all sorts of Balls and with all the varieties of Powder but in all kind of Pieces as also in all those that being the same in specie are of different grandeur and lastly at all possible degrees of Elevation A Multiplication that almost runs up into infinity And we observe that these Experiments ought to be all made one by one for it is not true that by way of proportion one may from three or four Ranges of a Canon made at several elevations argue to any others no not of the same Canon laden with the same Powder and Ball. That this is so may be demonstrated by help of the Tables made by Signiore Galilaeo and by us For example That Canon which being elevated at the sixth Point curryeth its shot 4000 paces elevated at one Point ought to curry the sixth part at two points the third and at three points the half of that Range But the thing falls out far otherwise For being elevated to one point it curryeth 1032 instead of 666 which is the sixth part of that same greatest Range 4000 at the second point and note that with this Mounture Pieces carry alwayes the half of the greatest Range in our case will curry 2000 in stead of 1333 which is the third part At the third point it will curry 2824 instead of 2000 which is the half of the greatest Range at the fourth point it will curry 3464 instead of 2666 At the fifth point it will curry 3860 in stead of 2333 which are 5 sixths of that greatest Range See therefore how that increasing equally the Mountures of the Piece that is shooting first at one point only then at two three four c. unto the sixth the increases of the lengths of the Ranges do not increase equally that is with the same proportion wherewith the Or Mountures Randons increase But the first point currying 1032 the second increaseth above it 968 the third increaseth 824 the fourth 640 the fifth 396 the sixth 140. Therefore to derive some rule from the Experiments it were necessary to make them exactly at all the Grades of Randons in all sorts of Pieces with all varieties of Powders and different matters of Balls and happily one might say it were necessary also that every Gunner made them by himself Things almost impossible to reduce unto Rules from which any certainty might be gathered if the Theorick and Geometry had not given us a manifest Science thereof by means of that one sole Proposition of Galileo in which first of all men he hath advertised and taught us That Pro ects do all move in a Parabolical Line Upon this supposition we will ground the Instrument promised and though by the impediment of the medium the Parabola's become too deformed or by many other accidents the Ranges prove very inconstant yet it sufficeth us to have given indubitable satisfaction to the School of Mathematicians if not to that of Gunners Before we set down the making of our square which consisteth only in describing one single Semi-circle we will divide the ordinary Quadrant into unequal points so as they may not measure the Randons of the Piece but the lengths of the Ranges which is that that serves to our purpose Thus we shall be assured that the Gun if it shall be elevated to one point of the said Quadrant shall carry to such a distance whatever it be and elevated to two points shall precisely double that Range and if to three it shall carry three of those spaces if to four and a half it shall carry four and a half if to five and a quarter it shall carry five and a quarter and thus until you come to the sixth point shall the points of the Quadrant in the Instrument and the spaces of the Ranges in the Field alwayes increase in the same manner and with the same proportion and from the sixth to the twelfth point they shall go in the same manner decreasing The construction and demonstration is Geometrically taken from the proposition which we have made the First of this our Book of Projects which by the Amplitude given teacheth us to find the Elevation And it serveth in common for whatsoever sort of Artillery and Mortar Pieces and for any sort of Ball or Powder Now it is manifest by our I. Proposition that if the line of the Of Mounture direction or of the elevation of the Piece shall be AO or AP the Amplitude or length of the Range shall be as the Quadruple of the SO and if the direction shall be AM or AN the Range shall be as the Quadruple of RM and if the elevation were according to the line AFD the Range shall be as the Quadruple of QF but the lines SO RM and QF by our construction do equally exceed And therefore likewise their Quadruples or the Ranges aforesaid shall equally exceed one the other The use of the aforementioned Division made in the ordinary Quadrant LEt there be propounded any Piece of Artillery or Mortar-Piece and with it let there be one single Experiment made that is let it be elevated to any point as for example to the fifth Let it off and measure the length of the Range and let it be found verbi gratia to be 2000 parts this done we may know how far the same Piece will carry being charged in the same manner and elevated to any what-ever other Point or Minute which shall be easie by the Rule of three the points in this Instrument as well as the length of the Ranges being proportional The Praxis is this I desire to know how far the sixth point carrieth I thus say If five points give 2000 paces how much shall six points give and I find 2400 paces I say then that the shot of that Piece at the sixth point that is at the greatest Range will curry 2400 of those parts at which of the fifth point it curried 2000. And take notice by the way that instead of performing this operation with the points 7 8 9 10 11 and 12 It may be done with their Complements which are 5 4 3 2 1 and 0. But if it were required which importeth much more that we should elevate the aforesaid Piece in such sort that the length of the Range ought to be for example 1300 paces we are to work thus If 2000 paces were made by 5 points or to say better by 60 Minutes of the Quadrant by how many points shall 1300 paces be made the working will be 2000. 60. 1300. 39 and we shall find that for
for A C K and A C G make two right Angles Eucl. 13. 1. 8. To find the Angle G E A substract P E F half the Angle of the Figure found in the second Rule from 180 degrees For P E F G E A are equal to two Right Angles 13. 1. How to find the Lines 1. The Lines AK C K. Fig 6. In the Right angled Triangle A C K the Flanque A C is given and the Angles C K are found by the fifth and fourth Rules Therefore the Sides AK C K will be found by Trigonometrie 2. The Flanque in the Courtine and the flanquing Line of defence The Face which is given being added to C K found out last gives the flanquing Line of defence G K and A K one of the Lines last found being deducted from the Courtine that is given leaves the Flanque in the Courtine B K. 3. The Lines G Q Q C. In the right angled Triangle G Q C the Face G C is given and the Angles are already found in the fourth Rule For Q G C is equal to G K A therefore G Q Q C will be found 4. The outward side of the Polygon G H. To G Q doubled add the Courtine which is given 5. The Line A Q. To the Flanque which is given add the Line Q C found out in the third Rule 6. The Capitals G E G Z. In the right angled Triangle G Z E the Angle E G Z is found for it is equal to P E F half the angle of the Figure and the side Z E or Q A is found by the fifth Rule therefore G E G Z are found 7. The Gorge Line A E. Substract G Z found in the sixth Rule from G Q found in the third Rule and there remains Z Q or E A. 8. The side of the inward Polygon E F. Add the Courtine which is given to the Gorge line doubled found out in the foregoing Rule 9. The Radius P E Y P. In the right angled Triangle E Y P the side E Y is found for 't is half the side of the Figure found out in the last Rule and the Angle P E Y found in the second Rule of Angles therefore the sides E P Y P will be found 10. The bigger Radius G P. Add the Capital to the lesser Radius 11. The Fichant line of defence B G. Out of the sum of the Squares of G R B R extract the Root and that shall give G B. The demonstration is from the 47. 1. of Euclid R B is found out in the fifth Rule G R is had if to Z R or E B the sum of the Courtine and Gorge line you add G Z found in the sixth Rule And so you have the compleat constitution of Fortification Nor will it now be difficult for one that is not altogether unskilful in Trigonometrie which I have have taught in the third Chapter of my first Book of Practical Geometrie to find all the Lines and Angles by the like method out of what Data soever CHAP. VI. The delineation of Regular Fortifications either on Paper or in the Field SInce that in the foregoing Chapter the quantities of the Lines and Angles of Fortifications are determined to delineate the same either on Paper or in the Field there is nothing more required than what I have taught in my Practical Geometrie Therefore in the tenth Chapter of my Practical Geometrie you 'l find what you desire digested into ten Problems CHAP. VII An Explanation of the Orthographical Terms HItherto I have deliver'd the delineation of Regular Fortification That is I have describ'd the out-circuit of the Rampar only But now I pass to the Orthography in which all the parts of the Fortification as to their height and thickness are contain'd The beginning as it uses to be is drawn from the Explication of Terms The Horizontal Line is A E S V Z. The Orthography of a Fortification Fig. 8. is a Section of a Fortification made by a place per pendicular to the Horizon showing the height thickness and position of each part in the Fortification It is shown in the eighth Figure The Rampar A L I K E is a body of Earth surrounding the whole Fortification it includes also the Bulworks The breadth or thickness of the base of the Rampar A E. The thickness of the top of the Rampar L 3. The outward sloaping or rectination of the Rampar 3 E called in French penchant du Rempar Exterieur The outward Talu or Line forming the sloap of the Rampar E F called in French le Talu Exterieur du Rempar The inward sloaping or rectination of the Rampar A L Penchant du Rempar Interieur The height of the Rampar B L Haulteur du Rempar The brestwork of the Rampar in French called Parapett 4 G I K 3. It is a bulk of earth surrounding the whole Fortification rais'd upon the Rampar to a mans height The thickness of the base of the Brestwork D 3. The thickness of the top of the Brestwork O K You must take no notice of the little line intercepted betwixt I T I D. The sloap or inclination of the top of the Brestwork I K. The outward sloaping or rectination of the Brestwork K 3 't is in a direct or strait line with the outward sloap of the Rampar E 3. The outward Talu or Line forming the slope of the Brestwork 32 Talu Exterieur du Parapett The inward Sloap or rectination of the Brestwork T D penchant interieur du parapett The inward Talu or Line forming the inward Sloap of the Brestwork D T Talu Interieur du parapett The Step of the Brestwork D G called in French Banquet The plain or Walk upon the Rampar L 4 in french Terreplein The Fauss Bray or Parapett des Rondes 5 N P Q R it is a Brestwork rais'd round the Fort at the foot of the Rampar principally used for the defence of Moats or wet Ditches and in all things like to the upper Brestwork The plain or walk of the Fauss Bray E. 5. or Chemin des Rondes The Bank-side of the Ditch R S Lisier The Ditch S 87 V Le Fosse The inward sloaping descent of the Ditch S 8 Escarpe The inward Talu or Line forming the inward sloap of the Ditch S H Talu interieur du Fosse The outward sloaping descent of the Ditch V 7 Contrescarpe The outward Talu of Line forming the outward Sloap of the Ditch V 5 Talu exterieur du Fosse The lower width of the Ditch 87. The upper width of the Ditch S V. The depth of the Ditch 8 H 75. profundeur du Fosse The Couvertway N 6 Chemin Couvert Corridor The Brestwork of the Couvert way 6 X Y Z parapett du chemin Couvert It s Base O Z peid ou base du parapett de chemin couvert It s outward sloaping Y Z. Note that this Orthographical Section is not drawn by the Courtine but by the Face of the Bulwork and so the
c. Fourth way Take Salt-Peter six pounds Sulphur eight pounds and a half powder of the Second Bark of Elder Tree half a pound common decripitated Salt two pounds make Corn Powder of these according to the precedent order or accustomed method To these known things I shall add here a thing whereof you may make experience if you please it being only taken from the Books of Authors without any tryal made by me which you may also find written in the natural Magick of John Baptista Porta which is in our English Tongue where he saith that if you add burnt Paper in the Composition of Gun-Powder or the double quantity of Hay seed well beaten these will take away a great part of the strength and will hinder it from making so great flame and noise Some do say that the Gall of a Pike doth the same effect if it be mixed and mingled with the same but we shall leave the belief of these things to the faith of such Authors as have experimented the same There are some wise and knowing men in this Art attribute the cause of this noise or as some do express it this horrible noise produced by a Cannon after the firing not to the Powder but to the beating and contusion of the Air which is inraged or in a passion by being so furiously endeavoured to be stifled or choaked by a strange and extraordinary movement of which we have spoken more at large in the former Chapter where we treated of Salt-Peter Yet in favour of the Sons of Art we shall nevertheless give you the opinion of Scaliger taken out of his his fifteenth Book in his Exer. Exoter against Cardan of Subtil Exer. 25. Longe pejus illud cum sonitus causam a bellicis machinis editi attribuis Sal Petrae nam tenuissimum in pulverem comminutum cavernulas amisit CHAP. XX. The Proof or Tryal of Gun-powder IT is accustomary for men skilled in these Arts to try Powder three several wayes that is by sight by touch and by fire And first for the tryal by sight it is thus If the Powder be too black it is a manifest sign of too much humidity or too much coal now if it contain too much as you suppose rub it upon white Paper if it black the Paper more than other good Powder use to do it is a sign there is more coal in it than ought for such Gun-Powder as is of a fair azure colour or a little obscure somthing bordering upon red is the best sign and the most assured testimony of good Powder Secondly Gun-Powder its goodness is known by the touch in this manner crush some Corns under your fingers ends and if they easily break and return to Meal without resisting the touch or without feeling hard you may assure your self from thence that your Powder hath in it too much Coal If by pressing it a little hard under your fingers upon a smooth hard board or upon a stone you feel amongst it small grains harder or more sollid than the rest which do in a manner prick the ends of the fingers and do not yield to the finger but very difficultly or hardly you may infer from hence that the Sulphur is not well incorporated with the Salt-Peter and by consequence the Powder is not well and duely prepared You may draw infallible proofs or conjectures of the goodness of Powder by its burning if after you have made little heaps of Powder upon a clean and even Table distant one from another about a hands breadth you then put fire to one of them only and if it take fire alone and burn all away without lighting the others and make a small thundring noise or make a white clear smoak and that it rise with a quickness suddainly almost imperceptible and if it rise in the Air like a circle of smoak or like a small Crown this is an infallible sign the Powder is good and perfectly well prepared If after the burning of the Powder there remain some black marks upon the Table this then signifies that the Powder contains too much Coal which has not been enough burnt If the board looks greasie then the Sulphur and Salt-Peter is not enough cleansed and by consequence it retains much of their terrestrial matter and oyly natures which were naturally conjoyned to their matters If you find small grains white and Citrine it is a testimony that the Salt-Peter is not enough cleansed and by consequence it retains much of its terrestrial matter and of common Salt and besides the Sulphur hath not been well powdered nor sufficiently incorporated with the two other matters of its Composition If two or three Corns of Gun-Powder be laid upon a Paper distant about a fingers bredth one from the other and you put fire to them if the fire be good and strong they will fire at once and there will remain no grossness of Brimstone or of Salt-Peter nor any thing but a white smoaky colour in the place where they were burnt nor will the Paper be touched If small black knots which will burn downward in the place where proof is made remain after firing they do shew that the Gun-powder hath not enough of Peter and that it is of little force or strength Good Gun-Powder will not burn your hand if it be set on fire there Gun-Powder that is very sharp or eager in tast is not well purified and will turn moist Amongst many sorts of Powder to know the best make a little heap of every sort at a distance one from another observing well when you fire each heap which of them doth soonest take fire for that which soonest takes fire smoaks least and clearest and riseth quickly up close and round and leaves little or no sign behind it is the best Powder There are Instruments likewise invented for the tryal or proof of Powder which the most part of Fire-Masters and Gunners are accustomed to use which are described at large by other Authors therefore we shall not here repeat the same considering likewise that we have found by experience a great fallacy in the same for that one and the same Powder in the same measure and quantities hath raised the cover to different degrees of height CHAP. XXI To fortifie weak Powder and amend that which is spoiled and bring it to its full strength again and to preserve good Powder from decaying WE call such Gun-Powder weak which hath much degenerated from its first strength and the force which it did acquire in its first preparation as such as hath taken wind wet or air for these do diminish the quantity of Salt-Peter and actually separate the Sulphur and Coal There are two different wayes that these accidents do happen that is by being many years made or lying in a moist place long for in time the Salt-Peter alters and separates it self being naturally subject to alter and return into its first matter for Salt-Peter in its beginning or original being engendered of water