TIMBER-MEASURE By a Line OF More Ease, Dispatch and Exactness, than any other Way Now in Use, By a DOUBLE SCALE. After the Countrey-Measure, by the Length and a Quarter of the Circumference in Round Timber. And by the Length and Side of the Square in Squared Timber, and Square equal in Flat Timber. AS ALSO Stone-Measure and Gauging of Vessels by the same Near and Exact Way. Likewise a Diagonal Scale of 100 Parts in a Quarter of an Inch, very Easy both to make and use. By HEN COGGESHALL, Gent. LONDON, Printed for the Author, and are to be sold by Robert Prick, at the Golden Ball in St. Paul's Churchyard next Cheapside, where you may have Choice of Books of Geometry, Perspective and Architecture; Likewise Italian, French and Dutch Prints. 1677. TO THE Reader. IF Thou delightest in Timber-Measure, or hast occasion for Much; Thou hast here a Line so Fit for thy Purpose, that thou canst not imagine, much less, wish a better. For what can be more ready and easy, then having set twelve to the length, to see the Content exactly against the Gird or Side of the Square. Whereas on Mr. Partridge's Scale the Content is the Sixth Number, which is far more troublesome then with Compasses. The Line is also so clear, that one cannot easily mistake any way. Also the Girt-Line being subdivided into Halfs and Quarters of Inches, renders this way more exact than any other way, by Decimal Division. But a Mean Proportional is also most easily, and exactly found hereon, whereby Flat Timber, or such as hath Breadth and Depth, as also Stone, etc. is also readily Measured hereby: Gauging of Vessels ●s likewise readily and exactly Performed by this Line. Besides, in great Pieces the Content is given in Loads and Feet directly, where the Load is Accounted 40 Foot. Lastly, being small or great, it is Measured (in a manner,) with equal facility. But I refer thee to the Book and Rule, not doubting of thy kind Acceptance, as it never failed of the Approbation of all such Gentlemen, and others concerned in Timber, who have seen and understood it, it being none of the least Commendations of it, that it is presently understood. THE DESCRIPTION And USE of a LINE of TIMBER-MEASURE. THE double Scales Contrived by Mr. Partridge, are well known, and deservedly esteemed; yet in this Point of Timber-Measure, they are not so useful; The Measure this way upon these Scales, being far more troublesome and uncertain, then on the single Line of Numbers with Compasses. Whereas the Line here treated of, is so easy, speedy to work, exact, and also so intelligible, as that a better cannot be desired. The Line begins at 4, and is unequally divided to 40, each Division subdivided into four, it representing Inches, with their Halves and Quarters, but Numbered thus, 4.5.6.7.8.9.1.2.3.4. Which 1.2. and 3. most commonly signify 10.20. and 30. Though sometimes, (when there is occasion of Measuring any thing so small) they signify themselves only. At 12 let there be four Pricks in a Rhombus thus As also there may be such another at 41.57, for an use hereafter mentioned. So that as far as 40 Inches; the Girts (by which name we call a quarter of the Circumference) are actually on the Line; Though beneath 4 Inches it is not accounted Timber. And if the Gird be above 40 Inches, yet shall it be exactly Measured by this Line. As also all Flat Timber, that is, such as hath breadth and depth, may be speedily Measured hereby, the Mean Proportional being found by the help of this Line more easily, then on the single Line with Compasses. Herein it excelling any other Measure now in use. This Line divided, as hereafter is shown, and thus Numbered, is to slide against the Line of Numbers in two Lengths, to which it is exactly equal, which as in other Measure is to be estimated as occasion requires. Ordinarily 1.10.100. Sometimes, 10.100.1000. And sometimes ·1 or 1/10 1.10. The first Estimate is always meant, if it be not otherwise limited. These things Premised, I shall show you the Use of this Line. To Measure Round Timber. TO which purpose you may take Notice, that in Measuring the length of a Tree, they begin at the Ground-end, at the second Chip, and Measure to the other end in feet and half-feets, (for I never knew any Buyer Measure in less Dimensions, then half a foot in the length and content, nor less than a quarter of an inch in the Gird,) then back again halfway, where they take the Circumference with a Cord, and Measure a fourth Part thereof (having doubled it twice) in Inches▪ and quarters of Inches. And this must be observed, that the length be given in Foot measure, and the Gird in Inch-measure, though it be one, two, three Foot, or more in length. This done, you have three Numbers given, viz. 12. which is always the first; then the length, which is the second; and the Gird, the third; whereof 12 and the Gird are always on my Line (which I shall therefore hereafter call the Girt-Line,) the Length and Content on the Line of Numbers. But you may Note by the way, that though Timber is Measured usually in feet and half-feets; And in Inches, halves, and quarters of Inches; and I never saw any Measured otherwise. Yet any man may Measure in less Dimensions if he please, or the Custom be so. But always the Length in Foot-measure, and the Gird in Inch-Measure, as is before said. To come therefore to the Rule, set 12 on the Gird Line (marked as before) to the Length on the Line of Numbers; Against the Gird on the Girt-Line, you have the Content on the line of Numbers. So that the lines being set to the length, you have at one View against any Girt his own Content at that length; As also, what is got or lost by adding or abating a quarter, or half an Inch, which convenience no other Way of Measure affords. Now there being several Cases in Timber-Measure, I shall set down the most ordinary, and give an Example of each, whereof this shall be the first. When the Gird is from 4 to 40, and the Content not above 100 Foot. 1. Example. At 9 foot length, and 15 inches Girt, what is the Content? Set 12 on the Girt-line, to 9 on the line of Numbers, against 15 on the Girt-line, is 14 and a little more on the line of Numbers, which is the Content, viz. 14 foot. 2 Example. At 35 ½ foot length, and 14 ¼ inches girt, what is the Content? Facit 50 foot. And of this way, being the most easy, you will have the most frequent use. 2. When the Gird being from 4 to 40, the Content is above 100 foot. If the length be not above 9 foot, the Content will not be above 100 foot▪ therefore, First, if the length be 10 foot or above set 12 to the length in the first, length of the line of Numbers; so shall your Content fall in the second length, But now 1 in the middle of the line is 100: the 2 following 200, etc. Example. At 18 foot length and 31 Inches girt, what is the Content? Set 12 to 18 in the first length against 31, you have 120 foot. Secondly, if your length be between 9 and 10 foot, and yet the Content fall beyond 100, as it may about 39 inches girt. Set 17 in the girt-line (in stead of 12) to the double length, in the first length: so shall the girt point out the Content in the second length, 1 in the middle of the line, being 100, etc. Example. At 9 ½ foot length, and 39 ½ inches girt, what is your Content? setting 17 to 19 in the first length, the Content will be found 103 foot. Or use the way directed in the next Case. Which is When the girt is above 40 inches. Having set 12 to the length, use the half-girt in stead of the whole, and observe the Content; for if the Load be▪ 40 foot, 1 in the middle of the line of Numbers is 1 Load, the 2.3.4. etc. following 2.3.4. etc. loads directly. Then the odd tenths over and above, must be accounted 4 foot, each tenth the halves 2 foot, etc. At 11 foot length and 51 inches girt, what is the Content? Set 12 to 11; against 25 ½ in the girt-line, you shall find four Loads and 9¾, which make 39 foot more. But if the Load be accounted 50 foot, then account your Number Pointed out by your half-girt, as it really and properly is, and multiply it by 4, which shall be your Content in feet, as in this Example, 49 ¾ multiplied by 4, maketh 199 foot. This Quadruplation may be avoided by dividing the beginning of the girt-line as far as 6, as those are between 3 and 4, viz. each into 10, and then subdivided into 4, and the beginning of the first length of the line of Numbers, as the beginning of the second length. But the line being clear for the ordinary and frequent use, I am loath to obscure it for that, which perhaps will not fall out once in a year or more, especially seeing the former way is unquestionably true. Although the two next propositions may seem needless, because under four Inches (some say six Inches) it is not accounted Timber, yet for that there may be occasion of measuring Wrongs, Knees of Timber, Studds, joists or Sparres, of smaller Dimensions, as also to show the universality of my line, I shall set them down. And therefore, When the Gird is less, than four Inches. I have before said that 1.2. and 3. on the Girt-line, sometimes signify themselves only, as in this Case, wherefore set 12 to the length; If the Gird be against any part of the line of Numbers, it shall point out your Content: but 1 in the middle of the line of Numbers will be but 1/10 of a Foot. But if your Gird falleth beyond the line of Numbers, remove 12 to your length in the 2 length, so shall you have the Content, 1 in the middle of the line of being 1 Foot. Example of the first. At 15 Foot length and 3 Inches Girt, what is the Content? Facit 94/100 or 9 tenths of a Foot. Example of the second. At 15 Foot length and 3 ½ Inches, girt, what is the Content? Set 12 to 15 in the first length of the line of Numbers, so shall 35 or 3 ½ point out 1 ¼ Foot in the second length. When the Gird is four Inches or above, and the Content Amounteth not to 1 Foot. In this, case set 12 to the length in the second length of the line of numbers, so shall the Content be in the first length, 1 in the middle of the line being 1 Foot, the Divisions in the first length being ninetenths of a Foot. Example. At 6 ½ Foot length and four Inches girt, what is the Content. Set 12 to 65 or 6 ½ in the second length, so against 4 you have ●2/100 a Foot, which is not ¾. So much for round Timber. Squared Timber. As for Timber that is squared, it is measured as the round, for setting 12 to the length, against the side of the Squa●e standeth the Content, which needeth no Example. To Measure flat Timber that is, such as hath Breadth and Depth. Having measured the length in Feet, as before, Measure the breadth and depth in Inches and Parts of Inches. Then find the mean proportional between them, which mean is the side of the square equal to the Base. Then having the length in Feet, measure it as next before. This me●n is found by the help of my line with much readiness and exactness. For, Set the greater number on the girt-line, to the same on the line of numbers, against the less on the line of numbers is the mean proportional on my line, or set the less number on the girt-line to itself on the line of numbers, against the gteater number on the line of numbers, standeth the said mean, on the girt-line. Example. At 10 Foot length, 21 Inches breadth, and 8 ½ Inches depth, what is the Content? Set 21 on the girt-line to 21 on the line of numbers, against 8 ½ on the line of numbers standeth 13, 36 or 13, a quarter and half quarter, on my line near enough. Or set 8 ½ on the girt-line against itself on the line of numbers, against 21 on the line of numbers standeth the same 13, 36. on the girt-line, as before. Then setting 12 to the length 10, against this 13, 36, on mine you have 12.4 Foot which is not an half. This mean in a Case of a Fraction, shall give you no trouble, for if with a Pencil, Chalk or any thing that maybe wiped off without damage to your Rule, you make a fine mark at this mean, and then set 12 to the length, and this mark without defineing it shall point out the Content. Thus, that which is done in natural numbers, by Multiplying the 2 numbers together, and Extracting the square Root of the Product, (though by the Logarithms a nearer way) and with the Compasses, by dividing the space between them upon the line of numbers into 2 equal parts, is here done with the same ease, speed and exactness, that any single proportion is wrought with, on the double Scale of numbers. There are also Rails rhree square for Pales, which were square, and then sawn through from edge to edge, which may be thus measured. If they were exactly squared, before they were sawn, measure them as if they were whole, and take half the Content. But if they had breadth and depth, or were not exactly squared before, take the mean proportional between half the Perpendicular and the whole Base, or between half the Base and the whole Perpendicular; which shall be the side of the square, and then measure as before. To find how many Inches in length make a Foot of Timber, at any Girt given in Inches, as far as 40. Set the girt on the girt-line, to 1 at the beginning of the line of numbers; against this 41.57 is the length in Inches, which make a Foot of Timber at that girt. So much for Timber-measure by this line, which how much it surpasseth the way by Compasses needs no more proof, than the judgement of them that have seen and understood both ways; this being preferred by several, as wel● Gentlemen as Timber-Masters, Carpenters, and Ship-Wrights, who have desired these Rules. Stone-Measure. Stone may be measured as square or flat Timber, only the length would be measured in Feet and Decimals of Feet, the side of the square (if it be square) or the breadth and depth in Inches and Decimals of Inches. Whereby the mean proportional being first found; the Content will be also found in Feet and Decimals of Feet, as in the measure of square or flat Timber aforegoing. Gaugeing of Vessel. The Gauge-pipe for Wine is marked on the Rule with W, of Beer with B. Wherefore having measured the length of the Vessel in Inches and tenths, as also the Diameter at the Bung and at the Head, first find the mean Diameter thus. Take the difference between the two Diameters, this difference Multiply by 7, add the Product to the less Diameter; so as the figure representing hundreds, be set under the unite-place of the less Diameter, and the rest forward toward the right hand, for a Centesimal, the same shall be the mean Diameter. Then set the Gauge-point against the length, in the line of numbers, and against the Mean-Diameter on mine, is the just content. Example. Let the length be 34: ½ inches. The Diameter at the Bung. 29.4 inches, the Diameter at the Head 25.3, inches. the difference is 4: 1; which multiplied by 7 makes 287, which I add to the less Diameter thus, 25.3 which 28.17. is the mean Diameter. 2.87/28.17 Then setting the Gauge-point of Wine or Beer respectively, (for example of Wine against 34 ½: Against 28.17. or 28.2. you will find 93 Gallons the just content. As for the double Scale of numbers, at 2 equal lines in each 2 lengths, though the measure of Board and Plank on them, be as the measure of Timber on this, by setting 12 to the length, and against the breadth standeth the Content (or by setting 12 to the breadth, and against the length stands the Content) for which cause, as also for working proportions of other sorts, I have caused them to be put on to the other flat of these Scales. Yet the measure of Timber upon them is so troublesome, as there is no enduring it, (I mean this way) the way by Compasses on the single line far surpassing it. For though the Compasses stand upon a fourth number, yet there is not the least necessity of determining what that fourth number is, which yet must be exactly defined on the double Scale, and so transferred from one line to the other. My Line also being actually divided into Halves and Quarters of Inches, is ready for the Measurers' use. The Timber in this County of Suffolk, (and for aught I know elsewhere) not only what is for Building Ships of all sorts, as also what is Shipped for London, or elsewhere, being always measured the length in feet, and the quarter of the Circumference or Girt, in Inches, Halves and Quarters, and not otherwise. Whereas on the Line of Numbers, the large Divisions are subdivided into ten Parts, where want the Quarters actually, and after into 5, where there are wanting both Halves and Quarters actually, (the Quarters in this case being hard to pitch on) and after into 2. This is no great inconvenience in my Measure, the Line of Numbers representing only Feet, viz. in the length and content, in which, as I said before, I never saw less dimensions taken notice of then feet and half-feets. But where the Custom is to measure to a quarter of a Foot, it may be done so, as well this way as the other. Concerning the Rules. Let them, as other double Rules, run between two Loupes, upon a Spline, either planed so, or glued into one, with a furrow in the other, and of one or two foot in length. If of one foot length, the Line of Numbers is ordinarily 11 inches precisely, and on this we may measure to a foot as far as 200 foot. But if they be 2 foot long, far farther to half a foot, the Lines being near 23 inches. As to that of a Foot my Advice is this. Let the breadth of each be about six tenths of an inch, let both the Loupes be fixed to that which hath the Spline on it, so the other shall always run in one Loup, whitherway soever you move it. And on this Account I call one Movable, the other fixed. On this Louped or Fixed Rule, let the Line of Numbers begin at the end next you, when it lieth toward your left hand, that this Girt-line may slide against it on the right hand. To the outward Edge of this Louped Rule on this flat, let the Foot be divided into 100 parts. In the other Flat, let the double Scale of Numbers be put on, but let them begin at the other end, so shall the movable Rule be to your right hand, when the beginning of the Lines are toward you, which I hold convenient. On this Flat to the left Hand, let the foot be into 12 inches; each into ten parts for Decimal Measure. So is it Fitted for any one that useth a Two-Foot joint-rule besides, to measure the Gird or any other measure. But if any Gentleman or other please to have this Fitted for other Measures, it may be conveniently and easily done thus. Let the movable or furrowed Rule be an inch longer than the other, that being drawn out to 2 Foot in length, it may be there Fixed by a small Vice-Nail through the Loup, which is at the end of the single line of Numbers, the Screw-Nut being let into the Rule before the Loup be fixed; it having also two Shouldring, that the Loup being Fixed, it may also be immovable. One Pin going through on one side the said Screw-Nut, the other on the other. Then there being room towards the outside of the movable Rule. Let there be put on the same Flat on which the Girt-line is, 12 inches, divided into Halves, quarters and half-quarters, but Numbered from the Loup, 13, 14, 15, etc. to 24. at the end. On the other Flat of this movable Rule, next the outward edge, let be 12 inches divided, as next before, into halves quarters and half-quarters. But numbered from the said end to the Loup, with 1.2. 3.4. etc. to 12 at the Loup. So any Gird or thing of one Foot or under, may be measured on this last. But if it be above, it may be measured on the other Flat, beginning at the empty Loup, and so toward the end of the movable Rule. Or it may be annexed to the Carpenter's Two-Foot joint-rule, having two Loups fixed to the immovable Leg, the Spline being also glued into the said Leg, and the lines of Numbers, and this line put on in every respect, as before. But let the Inch-lines be put on thus. On the Flat whereon the Girt-line is, let the inches be put on to the inner Edges of the joint-rule, to begin at the double end with 1.2.3. and to 24. at the single end, subdivided into halves, quarters and half-quarters: On the other Flat let them be put on in the like manner, but to begin at the single end. Also the Foot into 100 parts, and into 12 inches, each inch into 10 parts, maybe put on the single Rule toward the outward Edges, one on one Flat, and one on the other. There are two Properties which may be Noted on this Line, which (if there be no other use of them,) will try the truth of the Divisions. 1. Set 10 on mine to 1 in the middle of the Line of Numbers, which must be reckoned 100 So shall every division and subdivision on my Line stand against his own Square, on the line of Numbers, so that the square Root of a Number is easily found. 2. What number on mine, stands against 1 in the beginning of the Line of numbers; against the squares on the Line of numbers, shall stand the numbers, that are in Arithmetical proportion from the said number. As set 4 on mine to 1 on the Line of numbers. Against 4.9.16.25.36.49.64.81.100. on the line of Numbers. Stand 8.12.16.20.24.28.32.36.40. on mine. So setting five as above mine, against the said square, shall stand 10.15.20.25, etc. To divide the Girt-line. Prepare a Diagonal Scale of one hundred in the Integer, ten Integers whereof shall be exactly equal to the whole Line of numbers of 2 lengths, against which this Line is to slide, but there will not be need of above 7 of the said Integers. Having fitted the beginning and end of your Line to the beginning and end of the Line of Numbers. The end (at the beginning) shall be 4, the other 40. Set of the Arithmetical compliment of 4 from the beginning, so shall you have 10 Figured, 1. Then may you set of the Divisions beneath ten by their Arithmetical Compliment; but they must be set off from 10 toward 4. All the Divisions above ten shall be set off by their proper Log: Omitting the Judices, from ten toward 40. But because my Line is subdivided into halves and quarters, not into Decimals, 25 must be accounted the quarter, 50 the half, and 75 three quarters. The Compliment Arithmetical of 4, 3.979 shall give you ten. The Compliment Arithmetical of 9.75 neglecting the Index, set off from ten toward four, giveth you 9 ¾ it being, 0.109 0.222 giveth you 9 ½ 0.338 giveth 9 ¼ But then above ten, 0.107 giveth 10 ¼ 0.212: giveth 10 ½ 0.314.10 ¾ 0.414.11▪ Always neglecting the Index. A Diagonal Scale of 100 Parts in a quarter of an Inch. FINDING a Scale of this Nature in Wings Book of Surveying, made by Mr. Hayes being above three inches broad, and having in 20 Chains, and the Diagonal 1760 Pricks; which render it troublesome to make, yet named by the Author J. W. with several hard Names as troublesome to speak; I here offer the ingenious Surveyour one in little more than half the Breadth, and long as he please, without one Prick, and but four short Lines more than his of the same length, yet of as easy and certain use as his or any other. Let the breadth of the Rule be about one inch and eight tenths and an half, or 1.85 inches. Let the length be as you please, divided into transverse parallels equally, at a quarter of an inch distance for the Chain Lines. Setting of two tenths toward the left hand, for Figures for Numbering the Chains, draw the first long or Link-parallel, representing 0, draw 20 long parallels more, at about eight Cents of an inch equal distance from this and one another, which shall be the Link-parallels. Let those parallels that represent 5.10. and 15, viz. The 6th, 11th, and 16th from the Figures, or left hand edge of the Scale be only scratc'ht through the Chain-parallels, not drawn clean through, except through the Diagonal Integer or quarter of inch, being the uppermost, where they must be drawn through. On the top of the Scale over the said 5 and 15, stamp or cut a 5 over 10 a cipher: as also put a cipher between every scratch in the said Link-line representing 10. So will the Scale be divided as it were into two Scales, by the said row of Ciphers. Figure the Chain-lines as in other Scales from the Diagonal Integer downward. Divide the uppermost Integer at each end into five equal parts exactly. Draw Diagonals from 0 on the Left hand to the first on the Right, and from the first on the Left to the second on the Righr; and so on as in other Diagonal Scales. So whereas in other Scales you have your Diagonal Integer divided into ten one way, and ten the other; here it 〈…〉 divided into five one way, and twe●ty the other. And this is easily ma●● intelligible and certain in working 〈◊〉 it. The Use. If the place of ten in your Link● be 0.2.4.6. or 8. (which Figures or at least two of them, I would have set at the left end of the said Diagonal Integer against their respective Diagonals) then use the first or Left hand Scale. But if the place of ten in your Links be 1.3.5.7. or 9 use the second or Right hand Scale. For that Diagonal which is 20 in the first Scale, is 30 in the second, that which is 40 in the first, is 50 in the second, and so the rest. An Example of each. To take off ten Chains and 46 Links or 10.46. Chains, set one Foot of the Compasses on the tenth Chain-parallel, on the Link-parallel representing 6, in the first or l●ft hand Scale, and extend the other to the Diagonal of 40 in the said Link parallel of 6. But to take off 10 Chains and 56 Links, set one foot on the said Chain-line of 10, and the Link-parallel representing 6 in the right-hand Scale, and extend the other Foot to the said Diagonal, which is 40 in the first Scale, but 50 in this. This you will find after a very little practice to be no trouble, but very certain and exact. And being in a small Volume, it is not troublesome. It will be also made in as much less time than the other, as so many hundred Pricks, which are as above is said, 20 Chains no less than 1760: in every Chain there being 80: so the longer the more. Which Considerations of time and trouble, will render this cheaper, and being as easy and exact as any other, will I hope be at least as well accepted. H. COGGESHALL. Some Additional Notes. 1. NOTE, Relating to Page 7. line 9 TO what Number soever you set 12; 17 will stand against the double thereof, but it will stand a little over or beyond, because something less than 6 inches make a foot at 17 inches square; set therefore 17 so, and in this Example you shall find 10● foot near. 2. NOTE, concerning Gauging. Having the difference between the two Diameters in inches and tenths; On the double Scale of Numbers, set 1 on the first to 7 on the second; against the difference on the first, will be the Number on the second, to be added to the less Diameter, 1 in the middle of the second being one inch. If this Number be above 10, as it will be, if the difference be above 14 and an half; account 1 at the beginning of the first 10, so shall you have this Number on the second; 1 in the middle of the second, being 10. 3. NOTE, Relating to Page 21. line 15. In stead of the Vice-Nail and Screw-N●t there mentioned; a Pin that goeth full through will do as well, and is readier for use, therefore they may be omitted. The length of the movable Rule shall not need to be above 12 inches and an half. An Example of Stone-Measure. Let a Stone be 6 foot, and 35 centes long, 36 inches and an half broad, 5 inches and 7 tenths deep: Setting the breadth to itself, against the depth, you have a little short of 14 and an half, where make a fine mark with chalk or coal; Then remove 12 to the length, and this mark will point out 9 foot, and about two tenths, which is not a quarter. FINIS▪ ERRATA: Page 7. line 10. re●● of 〈◊〉 home to the, l. ●8. r. 103 foot near, l. 20 r. ●. When. p. ●●. ●. r. 4 fo●t ea●h tenth,. p. ●. l. 15. r. ●. When. 〈…〉. r. in the first length▪ p. 10 l 10. r. 5. When. p. 1●. l 5. 〈…〉. p. 1● l. 5 d●l● and. p. 14. l. 17. r. The use of the division at 41.57. p, 15. l. 17. r. ten●●s ●f inches. p. 1●. l. ●. r. Gag● point. l. ●. r. of Beer with B or A. l. ●●. ● Content in Gallons. p. 24. l. 16. r. on mine. l. 17. r. squares. Licenced. May 25. 1677. And Entered according to Order. ROGER L'ESTRANGE. These RULES with all other Mathematical Instruments, are made by Walter Henshaw, at the Globe and Mariner, near the Hermitage-Bridge, near Wapping.