TThe first thing wée will begin withall is to find the length of the mayne mast, for any ship whose length at the keele, the breadth at the beame, and the depth in hold is knowne, which is done two severall wayes: The first, which is the most Rationall way, is to adde the breadth and the depth of the ship together and double it, and divide the product by 3. and the quotient is the length of the Maine Mast in Yards. Example in the ship we have propounded, the bredth 29 ½ the depth 13 foote, those two added is 42 ½ the double of 42 ½ is 85. that divided by 3. the quotient is 28 1/ [...] Yards, that is 85 foote, but we have propounded out Mast to be but 84 foote.

A second way is thus, adde the length of the Kéele, the breadth of the beame and the depth together, and to that Sum adde the difference betweene the breadth & twice the depth, and multiply the whole Sum by the breadth at the beame, and the product divide by the former whole Sum, and the quotient is the length of the Mayne Mast in Yardes. Example in the Ship we have propounded, the length of the Keele 75 foote, the breadth of the beame 29 ½ foote, and the depth 13 foote added together the Sum is 117 ½ unto which adde the difference be­twéene twice the depth 26 and the breadth 29 ½ which is 3 ½ and the whole Sum is 121. which multiplyed by 29 ½ the breadth at the beame and the product is 3569 ½ which divided by 121. the former whole Sum the quotient is 29 ½ Yards, which is a yard more & better, then it was the other way, but it is too long, and therefore we commend the first way for the more rati­onall way, and doe perswade those that have occasion to make use of that way.

[Page 10]Now having found the length of the Mayne Mast in this manner for any Shipp; we have set downe a Table of the lengths and thicknesse of all the Mastes and Yards of the Ship we have propounded by meanes whereof, after the length and thicknesse, at the partners of the Mayne Mast for any Sip is found. The lengthes and thicknesse of all the o­ther Mastes and Yards may be found by our Table as fol­loweth: Suppose a Ship 63 foote by the the Keele, 25 foote breadth at the beame, and 11 foote déepe in hold, we desire to know the length and the thicknesse of all the Mastes and yards; and first for the Mayne Mast, the breadth at beame 25 foote, the depth 11 foote, their Sum 36. their double 72. which divi­ded by 3 the quotient is 24 Yardes, the length of the Mayne Mast, which is 72 foote. To finde the lengths and thicknesse of all the other, you may doe it by the Rule of Thrée, the lengthes in féete and the thicknesse in inches, and the proporti­on is from the lengthes and the thicknesse of the Masts and Yardes, for they are but a lineall proportion: That is:

As, 8, the length of our Maine-mast in the Table is to 72. the length of the Maine-mast found so is 28, the thicknesse of our Mayne-mast in the Table to 24. the thicknesse of the Maine-mast found at the partners; the thicknesse or the Di­ameter at the hounes must be ⅔ two third parts of that which it is at the partners which in this, is 16 inches thicknes or Di­ameter. Or this proportion of the lengths of the Mastes may be abreviated, for it is as 7 to 6. so is 28 to 24. and so we may pro­céed to finde all the rest, as 7 to 6 so is 75 our foremast to 74. the length of the foremast required; and so wee may procéed for all the other lengthes and thicknesse both of the Masts & Yards: but because this is some-what troublesome, and every one is not able to worke the Rule of Thrée in numbers, wee have considered of a more easie and spéedy way for the performing of it, which is by an opening scale, having two lines drawne, one on each side from the center, each line divided into 150. parts: and each part into two parts, whose use is thus, take 72 from the Center on one side of the scale in your Com­passes the length of the Maine-mast found, and put it over in [Page 11] 84 and 84 the length of our Maine-mast in the Table, and kéeping the scale still at the same distance without altering it take the distance over with your compasses betwéene 28 and 28 the thicknesse of our Maine-mast in the Table, and measure it on the side of the scale from the center, and it will end in 24. the thicknesse of the Mast sought; and take it over in 75. the length of our fore-mast and it will end in 64 the length of the fore-mast required, and take it over in 25. the thicknesse of our fore-mast and it will end in 21 ½ the thicknesse of the fore-mast required, and in 74 the length of our Maine-yard in the Tables, and it will end in 63. the length of the Maine-yard required, and in 24. for the thicknesse and it will end in 21 the thicknesse required: and so procéed for all the rest of the lengths and thicknesse without altering the scale, and you shall finde 56 the length of the bowsprite and 19 thicknesse, and 53 the length of the fore-yard, and 17 ½ the thicknesse, and 44 the length of the Mizon-yard and 13 thicknesse, and 45 the length of the Mizon Mast, and 15 the thicknesse, and 43 the length of the Spritsaile yard, and 14 the thicknesse, and 36 the length of the maine Top-mast, and 12 the thicknesse, and 31 ½ the length of the fore Top-mast, and 11 the thicknesse, and 31 the length of the maine Top-saile, and Crossieck yards, and 9, the thicknesse of the maine Top-saile yard, and 6 ½ the thick­nesse of the Crossieck yard, and 27 the length of the fore Top-saile yard, and 7 ½ the thicknesse, and 23 ½ the length of the mi­zon Top-mast, and 6 ½ the thicknesse, and 18 ½ the length of the maine Topgallant mast and 6 the thicknesse, and 17 ½ the length of the mizon Top-saile yard, and 4 ¼ the thicknesse, and 17 the length of the fore Top-gallant mast, and 5 the thicknesse, and 16 the length of the main Top-gallant yard, and 5 the thicknesse, and 14 ½ the length of the fore Top-gallant yard, and 4 ¼ the thicknesse, and 14 ½ the length of the Spritsaile Top-mast, and 4 ¼ the thicknesse, and 12 the length of the Spritsaile Top-saile yard, and 3 ½ the thicknes: By this meanes we have performed the finding the lengthes and the thick­nesse of all the mastes and yardes belonging to our supposed ship of 63 foote by the kéele, 25 foote by the beame, and 11 [Page 12] foote déepe in hold, with wonderfull ease and spéed, very exact­ly; and now we will goe forwards, first to finde the sizes of our Rigging: secondly, to find the quantitie of Rope of each size that will serve our turne to rigge the ship compleatly: and thirdly, to find the length of each Rope, that we shall have oc­casion to make use of in Rigging: all which shall be performed with as much ease and spéede as the former was for the mastes and yardes, (number for number.) Héere note by the way, that wée could have given the lengths of all the mastes and yardes by proportions from the length of the maine mast, and so from one to another, but because our way that we have propounded is far more easie and speedy in performance, I rather make use of it, then of the other way.

Now first for the sizes of our Rigging wee are to consider that it is but a lineall proportion betweene the Diameter of the maine mast in our Table, and the Diameter of the mast found, which proportion is, being abbreviated, as 7 to 6. so is one inch one tenth part the smallest Cordidge in our Table, to nine tenths of one inch our smallest Cordidge for out supposed ship of 6 [...] foote by the keele: and here we are to note that it is the circumference of the Cordidge that we find, all which is performed without altering the scale, but let it remaine at the same opening it was at, to finde the lengthes and thicknesse of the Mastes and Yards. As for the smallest Cordidge of one inch, and one tenth part, take the distance over betwéene 11 and 11. which measured from the center will end in 9. and more almost one halfe, which is 9 tenths of one inch, & then put it over in 13 and 13. for our second size Cordidg of one inch and 1/10 in our Table, which measured from the center will end in 11. which is one inch, and one tenth part for our second size, for our supposed ship, and so procéeding on in the same manner for all the rest of our sizes, taking for one inch, and 1/10 parts 18 and for two inches and 1/10 parts 22. and for 2 inches [...]/10 parts 26. and for 3 inches 1/10 part, 31 and so in like manner for all the rest, and taking for 14 inches, 140.

But here it may be obiected that the greatest Cordidge in our Table is but 14 inches, and the extent of our scale is but [Page 13] to 150. how then shall we do if we were to fit a ship, whose size of Cordidge would goe beyond the end of our scale? To which I answer, it may be done thrée wayes: first, it may be done by the Rule of Thrée in numbers, or else, secondly, (which is more pertinent to our way of performing) by the scale, which is thus, I have a Ship to be Rigged, the thicknesse of whose Maine-mast at the partners is 35 inches, I demand the size of the maine stay, the size of the maine stay in our Tables is but 14 inches, this that we seeke for must be more, the propor­tion betwéene the thicknesse of the Masts is as 18 to 35, which is as 4 to 5. In this case because our scale goes but 150. wée take the distance over betwéene 70 and 70. which is halfe the size of our maine stay and measure it from the center, and it will end in 87 ½ that is halfe the circumference of the Maine stay required which being doubled is 175. that is 17 inches and one halfe, the circumference of the maine stay required.

A third way by the scale, we may take the distance over be­twéene 14 and 14, as the scale is numbred, which measured from the center, will end in 17 ½ the size of our maine stay re­quired.

But to goe forwards to find the rest of the sizes of the Cor­didge for our supposed Ship of 63 foote by the kéele.

For our Cordidge of one inch [...]/10 in our Table, wée shal find by the scale one inch 6/10 parts, & for 2 inches 2/10 parts, wee shall find one inch 2/10 parts, and for 2 inches 6/10 parts, wée shall find 2 inches 2/10 parts, and for 3 inches 1/10 parts, wée shall finde 2 inches [...]/10 parts, and for 3 inches 5/10 parts, wée shall find 3 in­ches [...]/10 parts, and for 3 inches [...]/10 parts, wée shall find 3 inches [...]/10 parts, and for 4 inches 4/10 parts, wée shall find 3 inches 8/10 parts, and for 4 inches, [...]/10 parts, wée shal find 4 inches 1/10 parts, and for 5 inches 2/10 parts, wée shall find 4 inches 4/10 parts, and for 5 inches, 6/10 parts, wee shall find 4 inches [...]/10 parts, and for 6 inches, 1/10 part, wée shall find 5 inches, 1/10 parts, and for 6 inches, 5/10 parts, wée shall find 5 inches 5/10 parts, and for 10 inches, 5/10 parts, wée shall find 9 inches, [...]/10 parts, and for 14 inches wee shall find 12 inches [...]/10 parts: so now we have sized all our Cordidge for our supposed ship of 63 foote by the kéele, [Page 14] for Rigging proportionable to the sizes of the Cordidge in our Table.

The second thing concerning the Cordidge is to find what quantitie of each size will serve to rigge our supposed Ship of 63 foote by the keele. You may sée in our Table wée have set downe the Sum of the number of Fathomes of each size at the end or conclusion of the size, as for the first size of one inch and one tenth parte the Sum is 23 [...]. Fathomes, but because this number is greater then the length of our scale, we take the tenth part of it, and so we take it over betwéene 23 ¼ and [...]3 ¼, the scale remaining still at the same angle, or opening it was, at the first, and measuring it from the center, it will end in very néere 20. which being againe encreased or multiplied by 10. it will be 2 [...]0 Fathome for the Cordidge of the least size, to rigge our supposed Ship compleatly.

For our second size which in our Table is 691. Fathome, wee shall find 59. which is 590 Fathome, and for our Third size which is in the Table, [...]51. Fathome, wée shall find 30. which is 300. Fathome, and for our fourth size▪ which is in the Table 838. Fathome, wée shall finde 71 ½▪ which is 715. Fathome, and for our fifth size, which is in the Table, 728. Fathome, wee shall find, 62 ½, which is 625. Fathome, and for our sixth size, which is in the Tables, 764. Fathome, wée shall find 65 ½ which is 655. Fathome, and for our seventh size, which is in the Tables, 36 [...]. Fathome, wee shall find 31 ½ which is 315. Fathome, and for our eighth size which is in the Tables, 85. Fathome, we shall find 72. which is 72. Fathome, and for our ninth size which is in the Tables, 168. Fathome, we shall find, 14 ½ which is 145. Fathome, and for our tenth size, which is in the Tables, 182. Fathome, wée shall find 15 ½ which is 155. Fathome, and for our eleventh size which is in the Tables, 220. Fathome, wée shall find 19. which is 190. Fathome, and for our twelfth size, which is in the Tables, 232. Fathome, wée shall find 20. which is 200. Fathome, and for our thirtéenth size, which is in the Tables, 321. wee shall find 27 ½ which is 275. Fa­thome, and for our fourtéenth size, which is in the Tables, 43. [Page 15] Fathome, wée shall find 37. which is 37. Fathome, and for our fiftéenth size, which is in the Tables 23. Fathome, wée shall find 20. which is 20. Fathome, and for our last size, which is in the Tables 16. Fathome, wée shall find 14. Fathome.

But here it will be obiected, that in our Tables wée have put downe too much varietie of Rigging, and that there is not so much required for every ordinary ship: for answer whereun­to, and what course to take, where any man is not disposed to have his ship so compleatly Rigged▪ as wée have propounded, goe to the Tables, and take out the numbers, that are against the Cordidge of every Size, that you intend to make use of, and adde the numbers together, then take over the distance in your Compasses from the scale, of the whole Sum, or the tenth part as you havr occasion, as is before directed, and mea­sure it from the center, & you shal see the number of Fathomes required of that size, although you rigge not your ship so com­pleatly as wée have propounded, alwayes remembring the Scale must remaine still at the same opening it was, at the first.

YOu are to take notice that these last Cords and Ropes are sized and their lengths are proportioned according to our Ship that we have propounded of 75 foote by the Keele, for which our former Tables are made. Now it remaines that wee speake somewhat of the sizing of Cables.

Your sheat Cable is commonly so many halfe inches about as your ship is bredth in feete at the midship Beame.

Now our propounded Ship to which our Tables are made is 29 ½ foote at the midship Beame, therefore the Sheate Ca­ble must be 15 inches about, and to finde the sizes of the rest of your Cables, you may do it by the weight of your Anchors in this manner.

Suppose your sheate Anchor be 15 hundred weight, and your Cable 12 inches, and you have another Anchor 9 hundred weight, you desire the size of your Cable for it.

For the answer to this and the like demands, I have cau­sed two lines to be put downe on the side of the scale; the one of equall parts containing 385 parts, and the Tens and Fives drawne out, and it is numbred at every 50, thus, 50, 100, 150, &c. The other line of unequall parts begins at 1, and ends at [...] and is numbred to every unite, and each unite is divided from five to tenne by fives, and from tenne to [...] by tens, each unite into ten parts.

First I take 9 upon the opening scale from the center, the weight of the second Anchor, and put it over in 15, and 15, the weight of the first Anchor, and kéeping the scale so, I looke against 12 in the unequall parts, and in the equall parts a­gainst it are 72. then I take the distance over upon the opening scale betwéene 72, and 72, and measure it from the center, and it ends in 43 ½ Lastly, I looke 4 [...] ½ in the equall parts, and a­gainst it in the unequall parts is 9 1/10 that is 9 1/10 inches the Circumference of the Cable for the Anchor of 9 hundred weight which was required.

Or otherwise the Cables may be proportioned from the burthen of the Ships in this manner.

Suppose that a Ship of 300. Tun have a sheate Cable of 15 inches about, what shall be the Circumference about of the [Page 19] Sheate Cable of a Ship of 115 Tunne? Here because the greater number of Tuns is more then is upon our scale, wée take one quarter of 300. which is 75. and one quarter of 115 which is 29 néerest, and the proportion is all one: so I take 29. from the center and put it over in 75, and 75, and so kéepe the scale. Next I looke against 15, in the unequall parts, and against it in the equall parts is 112 ½. then I take over the di­stance betwéene 1112 ½ and 112 ½ & measure it from the center and it ends in 43 ½ then I looke against 43 ½ and in the une­quall parts, against it are 9 3/10 that is 9 3/10 inches, the circum­ference about of a Sheate Cable for a ship of 115 Tunne ac­cording to the former supposition, and as it was found before; and so the sizes of all the rest of the Cables may be found from one ship to another after the same manner.

It may be obiected that the staies of the middle masts may faile to hold in proportion according to the lengths of the midle masts in all ships, because the distance betwéene the maine mast and the fore mast may not be proportionable in all ships according to their lengths, wée suppose it to be so, yet our scale performes it exactly.