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 Meas [...]re this way upon these Scales, being far more troublesom and uncertain, then on the single Line of Numbers with Compasses. Whereas the Line here treated of, is so easie, speedy to work, exact, and also so intelligible, [Page 2] 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 Halfes and Quarters, but Numbred thus, 4.5.6.7.8.9.1.2.3.4. Which 1.2. and 3. most commonly signifie 10.20. and 30. Though sometimes, (when there is occasion of Measuring any thing so small) they signifie 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 In [...]hes; 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 Girt be above 40 Inches, yet shall it be exactly Measured by this Line. As also all Flat Timber, that is, such as hath bredth and depth, may be speedily Measured hereby, the Mean Proportional [Page 3] 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 shewn, and thus Numbred, 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 shew 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 [Page 4] the second Chip, and Measure to the other end in feet and half-feet, (for I never knew any Buyer Measure in less Dimensions, then half a foot in the length and content, nor less then a quarter of an inch in the Girt,) then back again half-way, 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 g [...]ven in Foot measure, and the Girt 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 Girt, the third; whereof 12 and the Girt 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-feet; And in Inches, halfes, and quarters of Inches; [Page 5] 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 Girt in Inch-Measure, as is before said.
To come therefore to the Rule, set 12 on the Girt Line (marked as before) to the Length on the Line of Numbers; Against the Girt 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.
VVhen the Girt 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 easie, you will have the most frequent use.
2. VVhen the Girt 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, &c.
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, &c.
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 [Page 3] Numbers is 1 Load, the 2.3.4. &c. following 2.3.4. &c. loads directly. Then the odd tenths over and above, must be accounted 4 foot, each tenth the halfes 2 foot, &c.
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 [Page 9] line being clear for the ordinary and frequent use, I am loth 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 W [...]ongs, Knees of Timber, Studds, Joysts or Sparres, of smaller Dimensions, as also to shew the universality of my line, I shall set them down. And therefore,
When the Girt is less, then four Inches.
I have before said that 1.2. and 3. on the Girt-line, sometimes signifie themselves only, as in this Case, wherefore set 12 to the length; If the Girt 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.
[Page 10]But if your Girt 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 Girt is four Inches or above, and the Content Amounteth not to 1 Foot.
In this, case set 12 to the length in the [Page 11] second length of the line of numbers, so shall the Content be in the first le [...]gth, 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 Bredth and Depth.
Having measured the length in Feet, [Page 12] as before, Measure the bredth 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 it self 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 bredth, 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 [Page 13] numbers standeth 13, 36 or 13, a quarter and half quarter, on my line neer enough.
Or set 8 ½ on the girt-line against it self 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 neerer 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, [Page 14] speed and exactness, that any single proportion is wrought with, on the double Scale of numbers.
There are also Railes 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 bredth 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 [Page 15] this 41.57 is the leng [...]h 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 judgment of them that have seen and understood both wayes; 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 len [...]th would be measured in Feet and Decimals of Feet, the side of the square (if it be square) or the bredth 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 [Page 17] 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 bredth standeth the Content (or by setting 12 to the bredth, 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 [Page 18] them is so troublesom, as there is no induring 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 Halfes and Quarters of Inches, is ready for the Measurers use. The Timber in this County of Suffolk, (and for ought I know elswhere) not onely what is for Building Ships of all sorts, as also what is Shipt for London, or elsewhere, being always measured the length in feet, and the quarter of the Circumference or Girt, in Inches, Halfes and Quarters, and not otherwise.
Whereas on the Line of Numbers, the large Divisions are subdivided into ten Parts, where want the Quarters actually, [Page 19] and after into 5, where there are wanting both Halfes 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-feet. 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 glewed 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 [Page 20] 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 bredth 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 Moveable, the other fixed.
On this Loup'd 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 Loup'd 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 moveable Rule be to your right hand, when [Page 21] 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 Joynt-Rule besides, to measure the Girt 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 moveable or furrowed Rule be an inch longer then 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 Shouldrings, that the Loup being Fixed, it may also be immoveable. One Pin going through on one side the said Screw-Nut, the other on the other. [Page 22] Then there being room towards the outside of the moveable Rule. Let there be put on the same Flat on which the Girt-line is, 12 inches, divided into Halfes, quarters and half-quarters, but Numbred from the Loup, 13, 14, 15, &c. to 24. at the end.
On the other Flat of this moveable Rule, next the outward edge, let be 12 inches divided, as next before, into halfes quarters and half-quarters. But numbred from the said end to the Loup, with 1.2. 3.4. &c. to 12 at the Loup.
So any Girt 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 moveable Rule.
Or it may be annexed to the Carpenter's Two-Foot Joynt-Rule, having two Loups fixed to the immoveable Leg, the Spline being also glewed into the said [Page 23] 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 Joynt-Rule, to begin at the double end with 1.2.3. and to 24. at the single end, subdivided into halfes, 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 [Page 24] 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, &c.
To divide the Girt-line.
Prepare a Diagonal Scale of one hundred in the Integer, ten Integers whereof [Page 25] 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 complement of 4 from the beginning, so shall you have 10 Figured, 1. Then may you set of the Divisions beneath ten by their Arithmetical Complement; 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 halfes and quarters, not into Decimals, 25 must be accounted the quarter, 50 the half, and 75 three quarters.
The Complement Arithmetical of 4, 3.979 shall give you ten.
[Page 26]The Complement 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 troublesom to make, yet named by the Author J. W. with several hard Names as troublesom to speak; I here offer the ingenious Surveyour one in little more then half the Bredth, and [Page 28] long as he please, without one Prick, and but four short Lines more than his of the same length, yet of as easie and certain use as his or any other.
Let the bredth 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 Numbring 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 [Page 29] 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 Cypher: as also put a Cypher 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 Cyphers.
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 [Page 30] 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 Ʋse.
If the place of tens 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 tens 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 Chaines 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 finde after a very little practice to be no trouble, but very certain and exact. And being in a small Volume, it is not troublesom. It will be also made in as much less time then the other, as so many hundred Pricks, which are as above is said, 20 Chaines no less then 1760: in every [Page 32] Chain there being 80: so the longer the more. Which Considerations of time and trouble, will render this cheaper, and being as easie and exact as any other, will I hope be at least as well accepted.