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.

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 [Page 5]

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 [Page 6] 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.

[Page 7]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 Water­line, 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; [Page 8] 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 ha [...]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.

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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 [Page 10] 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 [Page 11] 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 [Page 13] 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 [Page 14] 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 ⅘ 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 ⅓, 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 [Page 15] 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 [Page 16] 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.

By this Proportion the Moulds being made and Sir­marked to the body of the Vessell, and that they must be marked, or ordered, to finde the decrease of her bulks [Page 17]

body in the Midships, and to come to her way Abast, that the Water may pass to her Rudder to make her Stere, repaire to the Draught, and first set off her Risings thus; Example, We will begin at Timber 3 Abast, and his Rising is 7 inches: therefore draw a line pa­rallel [Page 18] to the Base, or Ground line F G, as the line 3 3; 7▪ Inches, from it then take the narrowing of the Floare with the Compasses off 3 also, and it is here 4 Inches, shewed by the little Spot, or Cross, in the Rising line 3 3, then seeking for the Narrowing at the breadth for Timber 3, there is none that sheweth that she keep­eth the same breadth at 3 still, 20 Foot, but seek for the height of the breadth, and it will lie higher at 3, then in the Midships, by 6 Inches, signified by the little marke in the line A I, a little above I, at the point 3; then for the breadth at top of the Side, finde that at the point 3, in the line V W, drawn to that end, and you will finde that it is narrower there by 2 Foot 7 Inches, then at the breadth, or Tumbleth Home, so much at the height, 24 Foot signified by an Occult dark line, drawn from the top of the Poope to the Foarcastle, to order▪ the height of the Head of the Toptimber Mould, an­swering to the Narrowing of the same, at the line V W; and this point for 3 falls at the little Cross Marke 3, in the upper part of the figure: For the next Example we will set off on our Platforme the rising narrowings of Timber 6, and 6 risth from the Keele 1 foot 7 inches, as you see the parallel▪ line 6 6 for breadth, the same still at the breadth, but the height of the breadth is high­er by one foot, then at the Midship, signified by the mark at 6, in the line; at the breadth, the Tumbling home, 1 foot▪ 7 inches and a halfe, at the height of 25 foot 4 inchos, at the point 6, and so proceed of all the rest, be­ginning at one till you come aft▪ to the fashion Pieces; when you have set off all the heights of Risings, nar­rowings of the Floare, narrowings of the Breadth, height of the Breadth, at the Breadth of the Vessel, [Page 19] and also of the Head of the Toptimber: Then at each point of the Floare, still in a Naile, or a Gimblet, or some such thing, as suppose we begin here at 3, stick one in the Midship line at 3, another in the little Cross, at the narrowing of the Floare at 3; another at the height of the Breadth at 3; another at the little cross, at the head of the Toptimber for 3; then if you have a lower Futtocke Mould, and an upper futtocke Mould, otherwise a navell Timber Mould, and a futtocke Mould, naile them together with small Nailes, and lay the Sirmarks of the floare Mould, and futtock Mould to the Gimblet that sticketh at the shortning of the floare; for by this meanes the floare Mould and futtock Mould is hauled downward: then make a mark at the cross, in the Midship line C D, setting to the marke of 3 for Timber 3, which will be the shortning of the Floare; then be sure the Navell Timber Moulds touch the Gimblet at the breadth, and at the narrowing of the floare, keeping the lower Sirmark thereto; and make a marke on the Futtocke Mould, at the upper Gimblet, for the rising alow lifteth up the Moulds high­er; and if there be any Crossing at the foot of the Navell Timber, and Head of the Floare Mould, marke it, and set to the marke 3 to it, that you may know to lay them together again, and keeping the Futtocke Mould fast, lay to the Toptimber Moulde the breadth Sirmarke of the Toptimber Moulde, to the Gimblet at the breadth, so have you no more Sirmarkes on the Toptimber Moulde but one, and guide the head of him till a line stretched from the Cross, at the head of the Toptimber, till it compareth with the right part of the Toptimber Mould, then regard the Crossing of the [Page 20] foot of the Toptimber Mould, and the back of the futtocke, and marke it, setting to the proper Marke 3 to it, that laying those markes together again, they may finde their own places again, so having finished for this Roome 3, take up the Moulds, and remove the Gimblets to the next, as to 6, here in our Example, and stick the Gimblets at all the markes of 6, then lay down the Mouldes again, laying down the floare Moulde to the Sirmarke of 6, on the narrowing of 6, and to the Gimblet, sticking on the Midship line of D C, and right on the same line, at the crossing, make a marke on the floare Mould, which will be the nar­rowing of the floare; then lay down the futtocke Mould, the Sirmarke on the foot to the Gimblet, on the narrowing of the floare, and keeping the Mold to touch the Gimblets at both places, make a marke for the breadth Sirmarke at 6, on the futtoke Mould, and set to 6; then lay down the Toptimber Mould, the breadth Sirmarke thereof to the Gimblet, sticking at the height of the breadth, that the backside of the up­er end may randge faire, by a right line from the cross at the uper end of the Toptimber at 6, by the back of the Toptimber Mould, a straight line may compare therewith▪ then keeping fast the Mouldes so till you have marked the crossing of the foot of the Toptim­ber Mould, by the back of the futtocke, marke it on the foot of the Toptimber Mould, and set to the marke of 6, so that when you are in any other place, as in the Woods a hewing of a Frame, where you to every place his Timber, you may be able to lay your Moulde together, and moulde it according to your Draught: We will lay down the taking of one bend of Timbers [Page 21] moreafte, where the breadth is narrowed, as at Tim­ber 13, take his rising off, and measure it by the Scale, and it will be 6 foot 8 inches, which set off on your Plat-forme, and draw thereto a Parallel line, to the Ground line A B, as is the line 13 13, then take off the narrowing of the floare, as at 13, it is 2 foot 2 in­ches; set that off on the line 13, from the line E F, as at the little cross thereon, then take off the narrowing of the Breadth at 13, and it will be 8 inches; draw therewith a little parallel line, parallel to I O, as is the parallel line 13 13, then seek the height of the breadth, as at 13, it will be from the uper edge of the Keele 12 foot 3 inches, and crosses the parallel line, at the low­er end of it, just then for the tumbling of the Top­timber it will be 3 foot 3 inches, and at the height of 27 foot 7 inches, at the little Cross 13: Now for the order of the hollow Mould, the little round piece of an Arch, in the Scegg of the Vessell, as it were, take off all the Risings, and mark them on the Rising Staffe, on one edge, that they may be known from the other Ri­sings; as here, for Timber 13, take off the hollow Ri­sing, which will be at 1 foot 10 inches, set it off on the rising Staff, at 1 foot 10 inches from one end, and the use of it will be in Moulding, set off the height of this hol­low Rising on the middle line of the Timber, when the Mouldes are laid to pass, and strike a line from this Ri­sing, on the middle line, untill it breakoff on the back of the Moulds, then lay the hollow Mould to the low­er part of the britch of the Timber, and at the halfe breadth of the Keele, and so bear in the other end till it just touch the streightline, made by the hollow Rising, and the back of the Moulds, and this mouldeth the [Page 22] lower part, or britch of the Timber, and bringeth in the hollow very faire; the same orders may be obser­ved afoare, as abaft, on the other side of the Moulds, and marked with letters, to be known from them abaft: Then for the height of your Waals, you may marke a marke at every third or fourth Timbers, which you re­solve to make frame Timbers; I say, you may make a marke at every third or fourth Timber, for the height of the upper edge, or lower edge of the Waale, and so bring on the Waale fair by those markes on the one side, and with a level finde the height of the other side by the former.

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

[Page 23] by the side B C, the height of the rising 60 inches, and so cometh 345, and 3 [...]6/60, which is abreviated ³; unto this 345 [...]/ [...] 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/ [...] inches, and something more, near [...]/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.

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:

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[Page 25] Now this half Chord in our Work is the length of the Rising line, and the height of the Rising on the Post is that in our Work, which he represents by the name of the Versed sine, where remember to multiply the length of the Rising line by itself, if it be a Rising line, and divide by the height of the Rising, and to the di­vision add again the height of the Rising, so have you alwayes the whole Circle, divide it by 2, so have you the length of the Sweepe.

CHAP. VIII. How to Extract the Square Root.

KNow then that a square number hath its sides equall every way, as are the sides of 4, repre­sented by ⸬ pricks; and you see that every way of all the 4 sides it containeth 2, and so 2 times 2, make 4, which is the squaring of a number, so you see ⋮⋮⋮ 9 pricks is a square, or 9 is a square number, whose side is 3, and 3 times 3 make 9, but 2 times 3 is not a square number, as you see :::, being but 2 one way, and the other way 3, that make but 6; so then all the numbers between 4 and 9, are not square numbers: by the like reason, a square, made of the Next square number 4 is 16, for 4 times 4 is 16, as by the Pricks you may see it repre­sented here, every of the 4 sides con­taining 4, make a squared number of 16, and all the numbers that are between 9 and 16, as 2 times 4, or 3 times 4, are not squares, but have a fraction annexed to them; so also any number betwen 16 and 25, are not squares, as 4 times 5, or 2 times 5, or 3 times 5, these are not square numbers, but 5 times 5 is a squared number, and ma­keth 25, where note, that to square a number, and to extract the square root, is two different things; for when we say, to square a number, is to multiply it in it self, or by it itselfe; or

[Page 32] when we say, or speake of a number squared, it is a number multiplied in it self, but to extract the square Root, is to finde the side of the square in a number gi­ven, or the extracted square Root is the square Root found in any given number.

Thus you may conceive of the Squares of 6, for 6 times 6 make 36; 7 times 7 make 49; 8 times 8 make 64; 9 times 9 make 81; 10 times 10 make 100: there is all the squares made of the 9 Figures, ex­pressed by this little Table annexed, as against each Figure is the square made of them, as 2 times 2 is 4, so is 4 a­gainst 2, as you see.

Now to extract the square Root from greater numbers, as from 144 proceed thus, write downe the summe given, as followeth, and make a quo­tient on the right hand, as you see, then set pricks under every other figure beginning at the right hand, and set pricks towards the left hand, under every other figure, so in this number 144, consisting of 3 figures, there is 2 pricks, and so many figures must the quotient consist of; then begin at the left hand of the summ, and say, or enquire for the greatest square in the figure, or figures, over the first prick, at the left hand, which here is but 1, therefore you can take but 1, for 1 is alwayes the Square, or Cube of 1, therefore write 1 in the quotient, and substract that 1 from the 1 over the left hand prick,

[Page 33] and Cancell it, nothing remainining, write a Cipher over it, as you see, so have you one figure of the quoti­ent, then double your figure found in the quotient, as 2 times 1 is 2; write that 2 under the figure between the next prickes, which is the Divisor for the second figure, then say, how many times 2 can I have in 4, over the Divisor, I say 2, therefore I write 2 in the quotient, saying, 2 times 2 is 4, which substract from the 4 over head, Cancell the Divisor, and the 4 over head, and write a Cipher over it, then square the last figure found in the quo­tient, saying, 2 times 2 is 4, which substract from the 4 over the prick, and so resteth 0, therefore cancell the 4, and write Ciphers over head, signifying, that the number given to finde the roote of, is a just square number, the roote or side is 12, the proofe hereof is by Multiplication of the quotient in it self, as 12 by 12 make 144, which, if it be the same with the summ gi­ven to be Extracted, it is rightly done▪ if it do not a­gree, it is not true.

CHAP. IX. A Description of the Table of Squares.

TO save the Practitioner a labour of Extracting of Roots, for here they are ready done to thy hand of purpose, and all the use of Arithmetick required is onely Substraction, as Example in the Figure of the Sweep foregoing, being found to be 203 inches, as you saw it found before, which is, I say, alwayes one side of the Triangle, made of the side DI, then know­ing the length of [...]I, 132 inches, which is the distance of the point, of which the Rising is sought at; seek in the Tables, under the Title of inches, at the head of the Tables, for 132, you will finde it in the second Page, and the twelfth line; and right against it, in the same line, under the next Title of Squares, you have 17424, the square made of 132, which Substract from the Square made of 203, which is 41209, which is found in the second Page of the Tables, and the third line: Now the other number 17424, Substracted from 41209, so resteth 23775; seek the number nearest to it in the Ta­ble, under the Title of Squares, which you will finde in the second Page, 34 line, you finde not just the same number, for in stead of 23775, you finde 23716 too little by 59, and the Root answering thereto, is in the same line, under the Title of inches, towards the left [Page 40] hand, which is 154; now if you take the next square lower to the left hand 35 line, it is 24025, 250 too much, so you may see it is nearer to the 34th line, because there it was too little but by 59, so that you may see it will be ¾ of an inch less then the number of inches, belonging to the 35th line, and about ¼ of an inch more then the numbers in the 34th line; so that you see it is answered, the third side D 0 is 154, and ¼ of an inch, which Substracted from the whole Sweep 203, leaveth 48¾ inches for the Rising, so you have no need of extraction of the Rootes by these Ta­bles, it is already done to your hand; the Columne that is between the inches and the squares, and written feet in­ches in the head, is to shew you, how may feet, and inches of the foot any number of inches is; as here, the number 203 inches sought, and found in the Tables, in the second page, and third line, just against it, in the same line, between that and the squares, is 16—11, shewing that it is 16 feet and 11 inches; or if the square were given, as 41209, found at the second page, and third line, next toward the left hand, you have 16 foot, 11 inches; and if you seek for it in inches, in the third Columne toward the left hand, and the same line, you have 203 inches: Thus is it very ready to reduce inches into foot measure, or feet into inches.

CHAP. XI. Shewing, how to Hang a Rising line by severall Sweeps, to make it rounder aftward, then at the be­ginning of the same.

IF any be desirous to have a Rising line rounder aft­ward then it is at the foar part of it, they must proceed thus; first Work by the Sweep that they would have first, and then begin again, and finde the other Sweep, that they would have the roundest; An Example of this will make it more plain, as in the following Figure will appear.

Let D E represent the length of a Rising line E I, the height thereof 8 foot, on the after end thereof; first I finde the Sweep that Sweepeth it, by Multiplying of 20 foot the length, which is 240 inches: for if you look in the Tables, under the Title of Feet-Inches, for 20 feet, you will see in the next Columne, toward the left hand, 240, over head is written Inches, signifying, that in 20 feet is 240 inches; and just against it, and in the same line, toward the right hand, under the Title of Squares, you will see written 57600, signifying, that the square of 240 is 57600, these numbers you will finde in the second Page of the Tables, and the last line, the seventh, eighth, and ninth Columns.

[Page 54]This squared number 57600, made by the Multiplication of D E, 240 in­ches, must be divided by the height of the Rising line assigned E I, 8 foot, or 96 inches, so remaineth in the quotient 600, to which must be added the height of the Rising, as is afore taught, and they make 696, which is the Diameter of the whole Circle: the half thereof is 348 inches, which is 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,

[Page 55] 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.

[Page 56]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

[Page 57]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.

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.

[Page 58]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.

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 [Page 60] 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 [Page 61] 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 [Page 62] 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 foot long and 34 foot in bredth, as the bredth added to the length, and the half bredth added together, make 165, that divided by 5, yields 33, and so many yards is the length to be of that Mast, the fore-mast must be a yard shorter at the head, that is to say besides the height of the step, which commonly in most ships the step of the fore-mast standeth higher from the bottom of the ship than the step of the Main-mast; the foremast must be shorter by that difference, and one yard more, or the bigness of the ship considered, 4 foot shorter at the head, or besides the difference below,

The Top-masts two thirds of the length of the lower Masts.

[Page 63]The Main-yard to be 2/ [...] and [...]/22 of the Main-mast, as in the Mast aforementioned of 60 foot long, two thirds of 60 is 40, and the 2/12 of 60 is 5, added to 40 make 45, for the length of the main yard.

The foreyard to be 6/7 of the Main-Yard, as the Main­yard being 45 foot, divide 45 by 7, so cometh 6 in the quo­tient, and a fraction remaining of 3, signifying 3/7, so that the 1/7 of 45 will be 6 and 3/7, you must take 6 times so much, a [...] 6 times 6 makes 36, and if you take 6 times 3/7 make 18/7, that is, two whole numbers, and 4/7 remaining, which ad­ded to 36, make 38, and 4/7 of a foot for the length of the fore-yard.

The Top-sail Yards must be half the length of the lower Yards, the Mizne Yard usualy is made of equal length with the fore-yard, the Crosjack yard, of equal length with the Main top-sail yard, and the mizen Top-sail yard to be half the length of the Crosjack yard.

The mizen Mast to be of the length of the Main-top mast from the upper Decks, and so much longer as is the height of the ship between Deck, the Boltspreete to be of length equal to the fore-mast from the upper Deck of the Fore-castle upwards.

For the bigness of these Masts, to a yard in length, ¾ of an inch, or else ¼ of an inch to the foot, and so of yards like­wise, only the Boltspreet somthing bigger, would be the better if he be made as big as the fore-mast.

The Spritsail yard in length [...]/ [...] of the Boltspreete, the Spritsail to psail yard as of the rest, to be 1/2 the spritsail yard, the mizen yard in bigness, but [...]/ [...] inch to a yard: And di­recting my discourse to Young-men that desire instructi­ons, I will avoid troubling of them as neer as I can with Arithmetick, therefore I will shew them the sweeping out of Mast and Yards, for the filling up their Quarters accor­ding [Page 64] to circles. Thus, make a half circle equal▪ in diamiter to the bigness of the Mast, in the partners, or if it be a Topmast, equal to his bigness in the Cap; as suppose for to make a Mast 60 foot in length, then by the former directions ¼ of an inch for his bigness to a foot, rendreth him to be 15 inches

thorow, but for a Main-mast it is alwaies better that they be made bigger, to everie 6 inches ad ½ of an inch more, so then this Mast will be 16 ¼ inches, I make a sweep of 16 ¼ inches, as from A to B, supposing the feet of the small scale, to be inches, draw, the Sweep or Arch A C B, 15 inches from A to B, than at the Centre draw a line perpendicular to A B, as from D to C, divide the perpendicular into four equal parts, with the compasses, & set off 3 of them, on the perpen­dicular from D to E, and through that point draw a line pa­rallel to A B, as is the line f g, which shall be the bignesse of the Mast at the Hounds, then middle the space between D & E as at h, and draw the line i k, which shall be the big­ness of the Mast at the middle, then two other lines drawn again through the middle between D h & another between h E, shall be the bigness of the Mast in the quarters, so then take off from the sweep, the bigness at each place from the midle line D C, to the arch, & in like māner middle the mast [Page 65] from the Partners to the Hounds, and quarter it, and strike a middle line from end to end, and at each place set off the thickness given you by your Sweep, for the length of the Heads of the Masts, you may allow to every foot 1 inch ¼ of an inch from the head to the uper part of the Crostrees, the length of the Trestle trees to be 1/3 of the Ships breadth, and in depth halfe the thickness of the Head, at the Hounds, and for the thickness, halfe the thickness of the Head, at the very end of the Head of the Mast, for yards you may draw the Sweep of them to their bigness at the Slings, and let the ends of them be but one third of the bigness in the Slings, accordingly draw your sweep, and fill him out in the quarters, according to the Circle, which I shall leave now to your practice, hoping, what I have spoken shall be well taken of the ignorant, who desire instructions.

CHAP. XIV. Concerning Rowing of Ships, when they are becalm'd.

I Have here invented a meanes of Rowing of a Ship, by the heaving at the Capstane, where will be many benefits; First, of a greater purchase of strength, for it is evident, that 10 Men at a Capstane shall heave a Ship a Head, when 30 Men shall not Haall her a Head by hand, nay 50; neither shall they be so soon tired, for that Owers are a great weariness to the Armes, beside a double motion of the body, as when the stroak is fetched, to way down the Ower, that the blade may be elivated out of the Water, where it must be kept so, untill another

[Page 66]

[Page 67] stroak be fetched, and then great strength put to the Ower by the Armes, or else heavy bodies, will not be moved: beside, if you have never so many Owers as you can put, they all fetch their stroak at once, but when Rowed by hand, one is likely to fetch a stroak before another, so that much of the strength is lost by a disagreement in the la­bour: But to proceed to the description of this inven­tion.

Let the two lines, C D, and C D, represent the sides of the Ship, 16 foot broad, as is the line C C, 16 foot long, by the Scale of the Draught; and let the two long squares, d d, and d d, represent the two Bitt-pins, with the Cross-piece of, let the Black, between the two Bit-pins, represent a Roule, or Windless, with a Surdge in the mid­dle, as is the Surdge of a Crab, or Capstane; in the two ends of this Roule let there be placed two Winches, as you may see represented by Cranks, a and a; let there be made a hollow place in the Head of the Bit-pins for these two Winches to rest in, that they may turne round in them, and bide in them: then let there be two pieces of Timber, equall in length, to the space of the Ship you would have filled with Oares, represented by the two black lists, marked b b, and b b; then let there be fitted two small pieces, made of good Ashe, or some good strong Wood, of equall length as is the two black Lists, n L, m L, fastned into the pieces of the frame, as at the points L and L, by a Boult, but so, that they may play on that Boult, and the other ends must be with a Hoale made in the ends, put over the handles of the Cranks, at n and m, then in the two long pieces for the frame let the Oares be fixed, as at the points 1, 2, 3, 4, 5, 6, 7, of each side of the Ship representing 7 Oares of a side, they may be fastned in the Frame, by a Mortis made therein, and a Tenent on the Oar, made to go slack, in that the Oar may play, and have liber­ty [Page 68] to fetch a Stroak, in the middle whereof must be placed a Iron bolt, to fasten him, and keep the Oar from launch­ing in and out, and on the Roughtre, or side of the Ship▪ as in C D and C D, must be placed Thoule pins to each Oare, as in Boats that Row; then must you have a Halser splised together, in manner of a Viall, that must take two or three turnes about the Roule, in the Surdge, as you may imagine, at the middle of the Black Roule, or notch therein, and pass from thence to the Capstane, with two or three turnes there also; then this Viall also, reeved thorough some other Blocks, as in manner of Snach block, and these blocks placed between the Capstane and the Roule, you may thereby increase that purchase so, as that it may heave very easie, and with great strength, so as to be able to Row a Ship a Head in a calme, or in little winde, two, threee or four leagues, a watch or more, according as the Ingine shall be better or worse fitted; for if you marke in the Figure of the Work, and suppose the Viall Reeved, and by heaving of the Capstane, shall turne the Roule, as the Crankes goeth round, it shall carrie with it about, and then the small pieces shall cause the frame to pass forward to and again, to fetch a stroake with the Oares.