Description and use of three general Quadrants accommodated for the ready finding the Hour and Azimuth universally in the equal Limbe The Compleat Modellist shewing how to raise the Model of any Ship or Vessel either in proportion or out of proportion and to find the length and bigoâ—ss of every Rope in all Vessels exactly with the weight of their Anchors and Cables There is a new Book called the Pilots Sea-Mirror which is a Compendium of the largest Wagoner or the lightning Sea-Collumbe Containing all Distances or thwart Courses of the Eastern Northern and Western Navigations with a general Tide Table for every day and the Change and Full of the Moon exactly for eight years also Courses and Distances throughout the Straights Printed for George Hurlock at Magnus Church Corner by London Bridge The Saints Anchor-hold in all stormes and Tempests Published for the support and comfort of Gods people in all times of Trial by John Davenport Pastor of the Church in New-Haven in New-Ingland There will shortly be made publick a Book Intituled The Mariners Compass Rectifled containing First a Table shewing the hour of the day the Sun being upon any point of the Compass Secondly Tables of the Suns rising and setting Thirdly Tables shewing the points of the Compass that the Sun and Stars rise and set with Fourthly Tables of Amplitudes all which Tables are Calculated from the Equinoctial to 60 degrees of Latitude with Tables of Latitudes and Longitudes after a new order with the description and use of all those Instruments that are in use in the Art of Navigation either for Operation or Observation THE COMPLEAT Ship-wright CHAP. 1. Of Geometricall Problemes BEfore we proceed to draw the Draught of any Ship or Vessel it will be necessary to be acquainted with some terms in Geometry as to know what a Point and a Line meaneth which every Book treating of Geometry plainly teacheth and therefore we shall passe that by supposing that none will endeavour to study the Art of a Ship-wright that is ignorant of these things and therefore leaving these Definitions I will proceed to some Geometrical Problemes necessary to this Art PROB. 1. How to draw a Parallel Line PArallel lines are such lines as are equidistant one from another in all parts and are thus drawn Draw a line of what length you please according to your occasion as the line A B then open the compasses to what distance you pleas or as your occasions require and set one foot of the compasses towards one end of the given line as at A with the other foot make a piece of an arch of a circle over or under the given line as the arch C keeping the compasses then at the same distance make such another arch towards the other end of the line setting one foot in B and with the other describe the arch D then laying a Ruler to the outside of these two arches so that it may exactly touch them draw the line C D which will be parallel to the given line A B or equidistant for so signifieth the word Parallel to be of equal distance PROBL. 2. How to erect a Perpendicular from a point in a right line given LEt there be a point given in the line A B as the point C whereon to raise a perpendicular Set one foot of the compasses in the given point C and open them to what distance you please as to the point E make a little mark at E and keeping the compasses at the same distance turn them about and make a mark at the point F in the line A B Then remove the compasses to one of those marks at E or F and seting one foot fast therein as at the point F open the other foot wider and therewith draw a small arch over the point C as the arch D then keeping the compasses at the same distance remove them to E and seting one foot in E with the other foot draw another little arch so as to crosse the former arch in the point D through the crossing of these two arches A D draw a line to the given point C as the line D C which shall be perpendicular to the line A B. Diverse other wayes there are to raise a perpendicular which I shall leave to the farther practice of such as desire diversity of wayes and proceed to the raising of a Perpendicular on the end of a line PROBL. 3. To raise a Perpendicular on the end of a line DRaw a line at pleasure or according to your worke as the line A B On the end thereof as at B set one foot of the Compasses and open them to what widenesse you please as to C and keeping fast one foot at B pitch one foot by adventure in C then keeping one foot of the compasses in C and at the same distance remove the foot that was in B to the point D in the line A B then keeping the compasses stil at the same distance lay a ruler to the points D and There are other wayes to effect this which I shall leave to farther practice of the learner this being the properest for our purpose PROB. 4. From a Point given to let fall a Perpendicular upon a Line given FRom the point C let it be required to let fall a perpendicular upon the line A B proceed thus Fix one foot of the compasses in the point C and open them to a greater distance then just to the line A B and make with the same extent the two marks E and F in the given line A B then divide the distance betweene the two points E and F into two equall parts in the point D then lay a Ruler to the given point C and to the point D and draw the line C D which will be perpendicular to the given line A B. CHAP. II. Of your SCALE BEing perfect in the raising and letting fall of perpendiculars and in the drawing of Parallel lines you may proceed to draught but first I will unfold unto you the use of a Diagonall Scale of Inches and Feet whose use is to represent a foot measure or a Rule so small that a Ship of 100 foot by the Keel may be demonstrated on a common sheet of paper really and truly to be so many foot long and so many foot broad of such a depth and of such a height between the Decks And therein the first thing to be considered is the length of the platform and of the Vessel you intend to demonstrate to the end you may make your Scale as large as you can because the larger the Scale is the larger will the draught be and so the measure of the demonstration will be the larger and more easie to unfold The Scale adjoyning consisteth as you see of 12 feet in all 11 thereof are marked with figures downwards beginning at 1 2 3 4 and so to 11 the first at the top is sub-divided into inches by diagonal lines as the distance between the first line of
the Scale and the first diagonal line is one inch the second is 2 and the third 3 inches and so to Six The way to demonstrate the Scale you see is very easie Draw Seven lines parallel to each other and of what length you please to retain what number of Feet you please then beginning at the top set off with the compasses the length of your Feet both allow and aloft then draw lines thwart the parallel lines to every foot of the Scale and set numbers to them beginning at the second foot 1 and to the third 2 to the fourth 3 and so forward leaving the first Foot to be divided into Inches by the Diagonall lines as you see in the foregoing Scale CHAP. III. Concerning the drawing your Draught upon Paper HAving fitted your Scale ready draw a line to represent the Keele of the Ship as you see in the draught following of 60 foot long by the Keele and 20 foot broad the streight line that representeth the Keele is marked with A B. Then draw a line underneath of equall length to signifie the bottome of the Keele Then next you may proceed to the Stern-post as the line A C will signifie the foreside or the inside thereof racking the one quarter of his length aft and for the length of the Stern-post it must be directed to the built of the Ship as whether she be to be a deep Ship or a shallow Ship so that the draught of the water ought to be respected first and then the lying of the Ports for the convenience of Ordnance for that the upper transome of the Buttock commonly is just under the Gun-Room ports to the upper edge of the said transome we understand the length of the Stern-post although if the Stern-post were continued to the height of the Tiller and another Transome fard there for the Tiller to run on it would steady the quarters of the Vessel very much and do good service The Stern-post being drawn we may proceed to draw the Stem which in the following Draught is not so much racked as was the old proportion of England which was the whole breadth of the Ship for then it should be 20 foot but it is no more then 15 foot just ¾ of the breadth for too much racke with the Stem doth a great deale of damage to any Ship if we consider that in this small Vessel had we given 5 foot more Racke all the weight of the Ships Head and Boltspreet Foremast Manger Halsps Brest-hooks aloft had been so much farther forward where there would have been want of Bodie to lift it so that it must of necessity be detriment to the Vessel when she saileth against a head sea and a great strain to her Now it will be very good to spend as much of this racke as we can under the water for it will help the Ship to keepe a good Winde by giving her something more Body in the water Next draw the Water-line in the following draught signified by the pricked line it is drawn to 9 foot height afore and to 10 foot height abaft from the upper edge of the Keele and higher abaft then afore for the most Ships saile by the Sterne and also for that the Guns should lie something higher abaft then afore from the water Then proceed to hanging of the Waals and here you see the lower Waalle drawne from the head of the Sterne-post to signifie that it should lie against the end of the Transome that the Transome Knees might be bolted to the Waals without board to one foot and an halfe under the water-Water-line a little before the middle of the Water line and at 9 foot high on the Stem and the next Waale parallel to the lower Waale one foot and an half asunder so that the upper Waale will lie just at the waters edge in the mid-ships the upper edge of the Gun-deck will lie one foot aboye the water line abaft and halfe a foot above water on the Stem so then letting the lower sell of the Ports be two foot from the Gun-decks the lower edge of the Ports wil be three foot from the water abaft and two foot and an halfe afore in the middle of the Gun-deck 2 foot 9 inches sufficient for so small a Vessel a greater Vessel would require to have the Guns something farther from the water then if another Waale be required first set off the Ports in their places that the Waale may ly above the Ports or else he would be cut with the ports in pieces the upper Deck with height respecting the bignesse of the Ship having respect to not over building small Ships to damage their bearing of Sail. Then for the Head the length of the Knee would be two thirds of the breadth so then the Knee of the Head in this Draught will be 12 foot 8 inches long and for his place as low as conveniently he can provided that the Rails of the Head fall not fowl of the haâ—shols because that in placing of the Knee low giveth room to round the Head and steeve it to content The place of the Knee will be at or very neer the upper Waal the upper edge of the Knee against the upper edge of the uper harping which will be very well for the lower Cheeks of the head to be faced against for by that means they wil be clear of any Seame to avoid Leakings and will very well bolt the end of the harping if a Brest-hook be fastned also within board against them will very well fasten all together Then for the steeving of him and rounding the Knee a regard must be had to the lying of the Boltspreet leaving room enough for the Lyon and Scrowl under the Boltsprit Then for the rounding of the Rails round them most at the after ends For the heights between Decks and Steeridge Cabine Fore-Castle those heights are commonly mentioned in contract by the Master or Owners building Place this Draught at Page 8 CHAP. IV. Shewing how to sweepe out the Bend of Moulds upon a Flat FIrst draw a line as the line AB then in the middle thereof as at the point C raise a perpendicular as is the line CM perpendicular to the line AB then set off the halfe breadth on either side at the Points AB and draw the two lines IA and KB parallels to CD signifying the breadth of the Vessell 20 foot then draw the two lines EF and HG signifying the breadth of the Floare thwart Ships 8 Foot more then one third part of the breadth which was formerly an old Proportion so that according to that it should have been but 6 Foot 8 Inches Herein any may do as they please give more or less my judgment is rather more then less for that it maketh a Vessell to carry more in Burden and I conceive it may if it be well ended forward it will not damage the Sayling I also think it doth stiffen a Vessell on this account Our English
Vessells have been used to have their breadth lying at the height of the Halfe Breadth then observing 1 3 breadth for the length of the Floare Thwart Ships it maketh the Vessells Body to be very neare a Circle as is a Cask which causeth such Vessells to be easie to slew in the Water yet I would not exceed neither or run into extreams herein but if I were to make a Vessell stiff I would that the Halfe Breadth be more then the draught of Water which causeth that the Body be stronger in the Water and will not Slew so easily Now to sweep out the Sides under Water I draw the Diagonall lines DA and DB then I divide the Diagonall lines into 9 parts and set off 2 of them from the Corners A and B to the points e then I set off the Dead Rising which is 4 Inches one Inch to a Foot for halfe the breadth represented in the Figure above by the little line parallel to FG from which Dead Rising take with the Compasses the Distance that will draw a piece of an Arch from ◠to ◠and so as one foot of the Compasses stand in the line EF and exactly touch the points at the Dead-Rising at f or g and touch also the points e over which point falls at ⊙ in EF or ⊙ in HG wherewith I describe the Arch e F or e G which is by the Scale in the Draught 4 Foot 8 Inches then for the other part of the Side upwards seek for a Point in the breadth line IK at which if one foot of the Compasses be set and the other foot opened to the Extreame Breadth will also draw or signifie an Arch to meet with the other Lower Arch on the Diagonall line at e which is at the points ⊙ and ⊙ thus the point ⊙ between D and K neere H Sweepeth the contrary Side I e and so the point ⊙ between DI neere E Sweepeth the contrary side at K extend the same Sweepe also above the Breadth line above Water 3 or 4 Foot the length of this Sweepe is 12 Foot 9 Inches then set off the Tumbling Home at the Height of the two first Haanses at the Maine Mast and Foarcastle 2 foot of a side then draw a line from the said 2 Foot of Narrowing at the points o v till it break off on the back of the Sweep on either side This kinde of Demonstration I conceive most suitable to our following discourse of Arithmeticall Work I could have cited other wayes but I Judge this way sufficient CHAP. V. The Description of the Rising Lines aftward on and forward on with the Narrowing Lines and Lines of Breadth As also the Narrowing Lines at the top of the Timbers DRaw a Hanging line on the Draught from the Keele from the middle of the Keele to the height of the Water line on the Post which will be the Rising line as the line DE this line DE is supposed to be sweept or drawn by a Semidiameter of a Circle extended on a Perpendicular raised at the point E for if it be shorter then such a Semidiameter of the true Circle it will make a fuller line then it should be and so must not be so long or else it will make a breach at the beginning of the line this if the Centre be supposed to be Abaft such a Perpendicular that should draw a Rising line Abaft I say that it will shorten the Rising line and make it fuller then it should be or then if it be farther forward it will be straighter then a Circle and also be a breach at the beginning of the Rising line therefore it should be a Circle I say whose Semidiameter will be on the Perpendicular line at the beginning of any such Rising line on the Heele either Afoare or Abaft and the like ought to be for all other crooked lines as the narrowing lines Abaft or Afoare or at the Narrowing of the Floare or other Circular lines as Hanging of Waals and the like the way whereof I shall describe to finde the lengths of all such Sweeps by Arithmetick as also the true Rising Narrowing of any Timber according to exact peeces of Circles very usefull for the setting of Bows to trie whether they hang to a true Sweepe or no I shall demonstrate it I say in the following discourse and in this place end what I intend to say For Demonstration then At ¾ of the Keele forward I draw a Rising line forward to the height of the Water line forward on the Stemm as you see the line op and the little line between these two lines parallel to the inside of the Keele marked Eo is the dead rising 4 inches high as in the bend of Moulds it is parallel to FG the height of the breadth from the Mid-Ship forward is the lower Edge of the upper Waale but afterward on it is the pricked line between the Water line and the lower Waale on the Post which runneth forward to the edge of the Waale and hath Figures set to it to signifie the places of the Timbers marked 1 2 3 4 5 to 15 as you see answers to the Figures on the Keele and the Letters set to forward on signifie the places of the Timbers forward marked ABCD to L in the middle of the Vessel the places marked with a Cipher signifie the Flats which have onely Dead rising although they ought to have some of them something more Dead rising then each other and those that have least to be placed in the middle of the rest that so there be no Clings in the Buldge but that it have also a little Hanging in it it will seeme the fairer Then I draw a straight line parallel to the bottome of the Keele as is the line FG parallel to the line AB the Keele and distant 10 foot by the Scale which is the halfe breadth of the Vessell for this line signifieth a line stretched from the middle of the Sterne-Post to the middle of the Stem called by Ship-wrightes a Ram-line Parallel to this Middle line I draw another line straight marked nm and is 4 foot asunder from the Middle line to signifie the halfe length of the Floare thwartships as in the Bend of Moulds EF is distant from DC 4 Foote then I draw a Crooked line Abaft within this line nm to signifie the narrowing of the Floare to bring or forme the Vessels way Abast as you see the line ik Abaft and Afoare it is represented by the line lo then here in this Draught I draw a Sweepe or a piece of a Circle from the point G the marke of the Timber G on the Keele to the halfe breadth of the Stemm to the point G on the Stemm signifying the Sweep of the Harping and is Sweept by the breadth of the Vessell 20 Foot the piece of the Pricked Circle Abaft at the Starne which is drawn by a Centre on the line FG is the length of the Transom thwart the
Starne as is the Arch FS the length whereof is 8 Foot which doubled is 16 Foot for the whole length which is â…˜ of the breadth 20 Foot the length of the Sweepe that sweepeth it is the length of the Starnpost to the bottome of the Keele 14 Foot â…“ then the Crooked line from the end of the Transom or from the point S and toucheth the Keele at the point p this Arch Sp is the narrowing line Abaft at the breadth and the Crooked pricked line within the Keele marked with TR is a Rising line to order a hollow Moulde by the Timbers are placed at 2 Foot Timber and Roome as you may see by the Scale the line drawne from the Poope to the Foar-Castle marked by the letters VW is a line signifying the breadth of the Vessell at the top of the side from the top of the Poope to the Fore-Castle the top of the Poop is in breadth 10 Foot halfe the breadth at the beame the use of this line is in ordering of the Moulds to stedy the Head of the Top-Timber Mould to find his breadth aloft CHAP. VI. Shewing the Making and graduating or marking of the Bend of Molds REpaire to some House that hath some Roome or other broad enough to demonstrate the breadth of the Vessell and height enough for the top of the Poope in the length of the Roome or else if you cannot finde such a Roome convenient lay boards together or planks that may be large enough for your business as in the following Scheame you see First a long square made for the breadth of the Vessell as in the following Figure IABK then make the Moulds by their Sweepes and make Sirmarks to them for the laying of them together in their true places off first the Mould for the Floare being made you may make a Sirmarke by the line EF on the head of the Floare Mould and another on the foot of the Navill Timber Mould at the same place to signifie that those two marks put together they are in their true places and will compare so when any Timbers are Molded by them those Sirmarks must also be marked off on the Timbers and so in putting the Timbers up in the frame a regard being had to compare Sirmarks with Hirmarks each Timber will finde his own place and come to his own breadth and give the Vessell that forme assigned her by your Draught if it be wrought by it and so for all the other Moulds In making your Moulds that they may be smaller and smaller upwards and not all of a bigness you may measure the depth of the Side in the Mid Ships Circular as it goeth from the Keele to the top of the Side as here the Side as it Roundeth is 26 foot and in depth at the Rounheads or at the end of the Floare is one Foot as m m and at the other end at the head of the Timber is but halfe a Foot as at n n so then drawing two lines as the lines n m represents the diminishing of the Moulds in thickness upwards as those two lines representeth as if you would finde the thickness of the Timbers at the breadth take your 2 Foot Rule and measure the length from the end of the Floare at the point F to I at the breadth in the crooked body and it is 11 Foot 9 Inches signified at the Sirmarks there those two lines shew the thickness to be 9 Inches and so thick ought the Moulds to be at the breadth of the Vessell Now I have briefly touched the Demonstration of a Ship by Projection I shall now come to an Arithmeticall way farr surpassing any Demonstration for exactness CHAP. VII Arithmetically shewing how to frame the body of a Ship by Segments of Circles being a true way to examine the truth of a Bow LEt A B represent the length of a Rising line 12 foot long or 144 inches the height whereof let be B C 5 foot or 60 inches to finde the side D E or D A the radius of the circle A C whereto A D is the Semidiameter multiply the side A B 144 inches in it self and so cometh 20736 which sum divide 144 144 576 576 144 20736 by the side B C the height of the rising 60 inches and so cometh 345 and 3â—6 60 which is abreviated 3 unto this 345 â— â— must be added again the height of the Rising the side B e 60 which make 405 3 of an inch which is the whole Diameter of the Circle the half whereof is 202 1 â— inches and something more near â— 4 therefore we will avoide the fraction and account it 203 inches or 16 foot 11 inches which is the length of the Sweep or the side D E and so in all other Sweeps given whatsoever the Rule is generall and holds true in all things as to finde the Sweepe at once that will round any Beame or other piece of Timber that is to be Sweept remembring that if it be a Beame you are to finde the Sweepe you take but the half of his length 23 3 20736 345 6000 66 Example As if the Beame be 30 foot in length and to round one foot you must Work by 15 the halfe length of the Beame and turne 15 foot into inches by multiplying 15 by 12 so cometh 180 inches remember the length of the Rising line if it be to finde the Sweepe it must be multiplied by it selfe or the halfe length of the Timber must be Multiplied in it selfe as 180 by 180 so cometh 32400 which must be divided by 12 the rounding cometh in the quotient 2700 to which must be added the 12 again the rounding of the piece and so it is 2712 the whole Circle the halfe of this 2712 is 1356 for the length of the Sweep and so in all other matters where the Sweepe is required This I read in Mr. Gunters Book where he calls it the halfe Chord being given and the Versed fine to finde the Diameter and Semidiameter of the circle thereto belonging Example in the Draught foregoing Where the length of the Rising line is from the point E to the point i 32 foot and half the height thereof is the line D i 10 foot turne both Summs into inches as 32 foot multiplyed by 12 produceth adding the ½ foot 6 inches 390 inches length for the Rising line then turn the height of the Rising into inches as 10 foot multiplied by 12 produceth 120 inches from which 4 inches must be substracted because of the dead Rising is 4 inches so then the height is 116 inches Now multiply the length 390 inches by it self 390 maketh 152100. 390 390 000 3510 1170 152100 This Multiplication of the summ 152100 must be divided by 116 inches the height of the Rising and so cometh in the quotient of the devision 1311 inches unto this 1311 inches must be added the 116 inches the height of the Rising 116 1427 and it maketh 1427 which is the whole 112 3323 46344
29 foot as you may see by dividing it by 12 or else if you turne to the Tables and seek under the Title of Inches for 348 you will see in the same line toward the left hand 29 feet which you will finde in the third Page and the 28th line the seventh and eighth Column then I Work by that Sweep to 3 5 of the length of the Rising line or 12 foot of the same at the point C it is represented at which point I seek the Rising C B I seek in the Table for the Square made of 144 and I finde it in the second Page 24 line at the first Columne and toward the right hand under the Title of Squares I finde 20736 which is the Square made of 144 then I seek for the Square made of the Sweep or side A B 348 inches and I finde it in the Tables to be 121104 from this 121104 I Substract the other Square made of the side D C 144 being 20736 and there remaineth 100368 whose Root I finde in the Tables in the third Page and the 37th line and the sixth Columne 100489 which is too much by neare 121 but the other number afore it being much more too little the number answering hereunto is 316 inches and near ¼ Substracted from 348 the whole side leaveth 31 inches ¼ or two foot 7 inches ¼ for the Rising 0 30 57600 600 9666 89 121104 20736 100368 at the point C Now to make a rounder Sweep aftward on or at the other end of the line as from B to F which runeth higher up or Roundeth more as from I to F Here will be something more of trouble to finde the Sweep that shall exactly touch the two points assigned as from B to F then to finde the former Sweep Now the Demonstration wil shew it to be thus Let B and F be the two points to which the Sweep is confined to touch draw a streight line from B to F as you see and so you have a Right lined Triangle made of the sides B H the length of the line to be swept by the second Sweep and the side H F the height of the same together with the Subtending side B F then a streight line drawn from the middle of the side B F and perpendicular or square to the same line B F and extended till it touch the side D A the place where it toucheth shall be the Centre of the same Sweep as is the line G H passing through the middle of the side B F at the point O which to finde Arithmetically proceed thus finde first the length of the side B F as before is taught of two sides of a Right Angled Triangle given to finde the third side which will be found to be 134 ½ inches the halfe whereof is 67 inches ¼ from B to O then if a perpendicular be let fall from O to the line B H it will cut that Base line also in halves as at the point P being 48 inches then again finde the side O H and that will be in this Example equall to the side B O but in other cases it may not so fall out So then those two sides being known as the side O H 67 ½ inches and the side P H 48 inches and the whole length of the side K H 240 inches you may then Work by the Rule of Three saying if 48 the side P H give 67 ½ inch for the side O H what will 240 give for the side K H as thus If 48 give 67 ½ what will 240 240 2 67 144 1680 4640 1440 16080 335  48888 16880 44 If you Multiply the two first numbers together and divide by the first number you will beget in the quotient 335 for the length of the whole side G H. I here neglected the ½ inch in this Multiplication for the ½ inch should have been Multiplied into the 240 by adding to the Summ 16080 120 the halfe of 240 and it maketh 16200 which divided by 48 maketh 337 ⅓ inches for the whole side G H So then these two sides being found find the side G K thus as before is taught look in the Table of Squares for the Square made of the side 337 and it will be 113569 from which Substract the Square made of 240 the other side being 57600 there resteth 55969 as you may see for that number sought for in the Tables and you find the nearest number to it to be 56069 and the roote of it to be 237 for the side G K to which must be added the Rising of the point C B or K D which is all one and is as we found it before to be 31 ¼ inches added to 237 maketh 268 ¼ inches or 22 foot 4 inches shewing that at 22 foot 4 inches from the point D towords G will be the point where the Centre of the Rounder Circle ought to stand Then again you have the side G K found as before to be 237 and the side K B 144 and if you work as is taught before but remember that if the longest side be sought for as is now in the last side sought for G B being the longest side you must add the squares made of the other two sides together and the square of those two Summs shall be the longest side G B 277 inches that is 23 feet 1 inch which is the length of the second Sweep and so have you the length of the Sweep The same order you may observe to round your Sweep as often as you please 113569 57600 55969 237 31 ¼ 268 ¼ If any have knowledge of the Doctrine of Triangles it may be found more readier that I leave to those that know the use thereof Note also that when you seek for any number in the Tables take heed that you minde the number of Figures you seek for to agree in number with those that directeth you to seek for them As for Example In the other figures abovementioned 55969 they are in number 5 by their places as you see then repairing to the Table I finde 559504 but telling the Figures I see that they are in number 6 but should be but 5 therefore this number represented in the seventh Page and the 28th line and third Columne is not the place I seek for then I turne toward the beginning of the Table till I see that the Columnes of Squares contain but 5 figures and there seek the nearest number agreeing to 55969 and in the second Page 37th line last Column I finde 56069 the nearest agreeing to it which is the place answering to the other directory figures Note also That the Example of finding the Sweep aforegoing is laid down by the small Scale of the Draught by which you may trie it for your better directions And in that Table you may see that any farther then 70 foot being the end of the seventh Page I have not mentioned the Feet and Inches belonging to the number of Inches but have left
it out because they are of little use any further because that will reach farr enough for the length of any Rising line of any Ship whatever If any be desirous to convert any of the following numbers into inches he may do it by Dividing by 12. Thus I think I have spoken enough to the Ingenuous concerning the singular use of the Tables or of this way of Working by Segments o Circles CHAP. XII Concerning Measuring of Ships 60 20 1200 10 120100 I Shall say something concerning it the Shipwrights have to themselves a custome of measuring at London or on the River of Thames thus they multiply the length of the Keel into the bredth of the Ship at the broadest place taken from outside to outside and the product of that by the half bredth this second product of the multiplication they divide by 94 or sometimes 100 and according to that division the quotient thereof they are paid for so many Tuns as suppose in the former draught being in length 60 foot and 20 foot broad 60 being multiplyed by 20 the bredth produce 1200 that 1200 being again multiplied by 10 the half bredth produce 12000 if you divide by 100 you need do no more than cut off the two last figures toward the right hand which shall be the answer and rendreth the Ship to be 120 Tuns but if you divide the sum 12000 by 94 you wil have 127 2 3 of a Tun very neer but this cannot be the true ability of the ship to carry or lift because two ships by this rule of equall breadth and length shall be of equall burthen notwithstanding the fulness or sharpness of those Vessels which may differ them very much or the one ship may have more timber than the other in her building so shall carry less than the other But the true way of measure must be by measure of the body and bulk of the ship underwater for if one ship be longer in the floor than another of the same bredth and length she shall be more in burthen than the other as a Flemish ship shall carry more than a French or Italian Vessell of the same length and bredth Therefore I say the measure of the ship being known by measuring her as a piece of timber may be measured of the same form to the draught of water assigned her the weight of the same body of the same water that the ship swimmeth in shall be the exact weight of the ship and all things therein loading rigging victuals included therein then if the ship be measured to her light mark as she will swim at being lanched the weight of so much water being taken or substracted from the weight of the water when she is laden the residue shall be the weight that must load her or her ability of carrying called her burden by this means you may know the weight of the ship light and what she will carry to every foot of water assigned to her which cannot be done by no general rules in Arithmetick because of their great irregularity according to the differing minds of Shipwrights you may if you please first measure the content of the Keel and Post and Stem-rudder all of it that is without the Plank and under the water line and note it by it self then measure the body of the ship in the Midships made by the square made of the multiplying of the depth of the water line and the bredth then you may find the content of the want by the circular part of the ship under water being narrower downward and substract this from the whole content of the squared body of the depth of the Water-line and bredth of the ship and this shall be the solid content of that part of the ship I mean in solid foot measure of 1728 inches to the foot then proceed to the fore part or the after part of the ship and to 3 or 4 Timbers more find the mean bredth at the narrowing aloft at the water-line and alow at the floor and the mean depth and measure that piece of the ship as I told you of the middle part of the Ship and so measure the whole Ship by pieces and add them together and so many feet as it maketh so many feet of water shall be the weight of the said ship and the reason may be considered thus there is a ponderosity in warer but there is a greater in the ayre onely to the heaviest of things and there is a ponderosity in water it self but not so much as in other things more solid as in Iron Suppose a Gun or an Anchor of Iron it sinketh in the water but yet it is not so heavy in the water as in the ayre by the weight of so much water as shall make a body of the same water equal to the body of the Gun or Anchor in magnitude which weight substracted from the weight of the Iron body weighed in the ayre and so much must be the weight of it in the water Again if a body be lighter in weight than water of the same bigness it hath an ability of lifting in the water and can lift or carry so much as is that difference as a piece of cork or wood of firr-trees being lighter than water it swimmeth on the face of the water and refuseth to be depressed without more weight added to it Thus a ship being a concave body is made capable of lifting according to the greatness or littleness of this concavity respect being had to the greatness of the Timber put into it or the nature of it all which maketh a ship swim deeper or lighter in the water I have proved by the Thames water that fresh Water is lighter then salt water so then salt water being heavier than fresh causeth that a ship swimmeth deeper in the fresh water than in salt I shall not need to say any thing more concerning the mesauring for it will be understood by those that have any Judgment in the mesuring of triangles the matter it self being but a nicity rather than usefll I only touched it to shew those that are so curious minded which way they may accomplish their desires I shall forbear to give examples because it will much increase my Treatise and augment the Price which might prove more prejudicial to youngmen than advantagious CHAP. XIII Concerning the Masts of Ships FRom the length and bredth is gained the Mainmasts length and all the other Masts as wel as yards is derived from thence and there is different proceedings in this case according to the largeness of the Ships thus the main Masts of small Ships to be three times as long as the Ship is in bredth as a ship of 20 foot broad by the same rule must have a Mast of 60 foot long Others for greater Ships add the bredth to the length and to that the half bredth which some they divide by 5 and the quotient is the number of yards as a ship 114