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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A64804 Military and maritine [sic] discipline in three books. Venn, Thomas. Military observations. 1672 (1672) Wing V192; ESTC R25827 403,413 588

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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
to make the Range of 1300 paces it would be necessary to give the Piece the Mounture of 39 Minutes of the Quadrant or of three points and a quarter The manner how to Compose our Square BUt if we would frame an Instrument which shall not only measure the length of the Ranges made at several Randons but also the Altitude of the Parabola the duration or time of the flight or Range the sublimity and the other things demonstrated in the aforesaid Book of Projects all this shall be performed with the sole and simple Semi-circle of I. Proposition But let us proceed to the making of it That this is so shall thus be demonstrated having reference to the I. Proposition of Projects and its Corollaries Let the line of the direction ABI be prolonged indefinitely as also the perpendicular FBL then by imagination take BL of such a length that it may be really equal to half the greatest Range of our present Piece And about the Diameter BL let there be imaginarily drawn the great Semi-circle BIL cutting the Circumference BI in any point I and draw the Horizontal line IM It is manifest by the afore-cited Propos I. of Projects that the line MI shall be the real fourth part of the length of the Range as also that DM shall be the not imiginary but real Altitude of the said Range and so the other measures in the Semi-circle BIL shall be all true and real Now observe that the Triangle HBF is like to the Triangle BIM as being right-angled and having two angles at the Point B. Therefore the same Proposition shall be between all the small and imaginary measures of the square AC as is between all the true measures in the imaginary and great Semi-circle BIL that is the lines AB BF FH and HB shall be to one another in the same proportion respectively as LB BIIM and M B. Therefore as to arguing in the proportions we may without any error as well make use of those feigned proportions upon the square as of the true ones imagined in the Amplitude of the Air. It remains now that we shew how this Doctrine which hath hitherto been a meer Speculation may now be reduced to Manual practice and that with facility Every one seeth that for our obtaining knowledge of the quantity of the lines AB BF FH and HB and their proportions in the precedent Figure it would be necessary that all the aforesaid lines were divided into most Minute parts with some common measure To this purpose therefore we will divide the Diameter AB and Semi-Diameter ED into equal and very small parts as appeareth in the following Figure upon which let us describe the imaginary square and then let us give to each division of the circumference its guides parallel to those Diameters that so in them the number and quantity of the lines which shall be Indices of the length and Altitudes of the Ranges may be read or found And in the point of the angle of Semi-circle B place the Thread and Plummet As to the number of parts into which the Diameter AB is to be divided it shall be left to the choice of every one but yet it will be convenient to make choice of the number 2000 for that it will facilitate the Arithmetical operation It is to be noted that if any one will make a square as hath been said on purpose for one kind of Artillery onely he shall without the least trouble of Calculation have the measures of all its Ranges The Division of this square is to be made a posteriori in this manner Make an Experiment of the greatest Range of that same Piece to which you would have the square to be adapted and let it be found v. gr to be 3000. Then divide the Diameter of the square into 1500 parts and the perpendicular Semi-diameter into 750 equal parts that is imagine that the Diameter AB 1500 is the half of the greatest Range 3000 as also that the perpendicular Semi-diameter ED 750 is the fourth part of that greatest Range And thus every of the other Elevations being afterwards given as soon as we shall apply this Square to the Muzzle of the Piece we shall immediately see how many paces is the length and how many the Altitude of the Range c. And this square made v. gr for a Canon of 60 pound Ball would be also good for every other Canon of 60 pound Ball that should be the same in length and other proportions with that It 's true indeed that if we would make the square universal to serve indifferently for all Species and Magnitudes of Artillery we must then do thus Divide the Diameter AB in the precedent figure in 2000 equal parts also let the Semi-Diameter ED be divided into 1000 equal parts we by reason of the smallness of the figure have divided it only into 100 taking the parts by ten and ten This done let there be drawn by the Divisions of the Circumference cut into equal degrees as is usual the guides parallel unto the Diameters that so one may upon those Diameters read or find the quantity of the right lines as they shall happen to be If you desire the Altitudes and not the lengths of Ranges then make the same working as before but not with the lines IO and ML which give the lengths but with HO and HL which give the Altitudes And if we would have the sublimities it would be necessary to work with GO and GL But which more importeth if any one after the previous Experiment hath been made shall desire that the same Piece may make an assigned Range in length v. gr 2200 paces we are to find what elevation ought to be given to the Piece Work thus If the 1250 paces of the previous Experiment give IO numbred what shall the 2200 paces give and you shall find a number which suppose for example to be ascribed on the square unto the line ML the Peice Therefore is to be raised to such a Randon that the thread may pass thorow the point M and then the Range shall be 2200 paces A Table which sheweth how many Degrees and Minutes of the Ordinary Quadrant inserted Page 20. each Point of one Square the Points of which are unequal doth contain Points unequal of the Square Degrees of the ordinary Quadrant half 02 23 I 04 48 half 07 15 II 09 44 half 12 19 III 15 00 half 17 50 IV 20 54 half 24 18 V 28 13 half 33 14 VI 45 00 half 56 46 VII 61 47 half 65 42 VIII 69 26 half 72 10 IX 75 00 half 77 41 X 80 16 half 82 45 XI 85 12 half 87 37 XII 90 00 For Example It is demanded where the Division of the one seventh unequal point doth fall Look upon the present Table right against the number VII and you find that it falleth upon gr 61. and min. 47. of the ordinary Quadrant BUt since we are fallen upon the