and nayl their great ends together within five or six inches of the top with one nayl onely that they may open and shut like a pair of tongs also you shall take a joynd-stool and cushion and having put the neck upon the foot and the Pandoron on the pin of the neck close the three feet together with your right-hand and lay them on the cushion and with your left hand under-set the neck with the tongs opening and shutting them as need is or setting them nearer or further from you as need is all with the same hand and turning it aslope with the right hand Then having first placed the sights at the beginning of the degrees turn it till by the edges of both sights you see one of the stars you desire then keep the Table fâ—st there and move the sights till by them you see the other star voti compos â—ris CHAP. XXI Of taking of altitudes terrestrial by the Quadrant THere are divers ways whereby these altitudes may be discovered whether they be perpendicular as properly they signifie or Hypotenuses or bases for all of them are comprehended under the notion of Altitude because the bases may be as well found by the help of the perpendiculars as perpendiculars by the help of bases and any of these may be found severall ways by the Pandoron either as it is a Quadrant or as it is a Geometrical Quadrat of eitâ—er of which we will lay down some Problemes and first as it is a Quadrant Probl. I. A distance being given and the angle of the base to finde an altitude Measure the distance AC â—00 and the angle A 9 degâ—â— 0 min. by your Pandoron the Complement wherof is the angle B 60 d. 20. n. ergò as fine ABC 60 d 20 m. 993898 is to the line AD â—00 230103 so sine BAC 29 d. 40 m. 969496 to CB 114 03. 205700 II. Likewise the height CB given to finde AC the distance As BAC 29 deg 40 min. 969496 is to CB 114 03. 230103 so B 60 deg 20 min. 993898 to AC 200. 230103 To finde either of them by the scale and compasses having the angle A and distance AC First draw the line AC set from A toward C 200 of some scale of equall parts upon C erect a perpendicular and upon A make an angle of 29 deg 40 min. which line will meet CB and you shall finde CB 114 feré So measuring the height CB and the angle B and plotting it you shall have AC 200. III. The height BC and angle A being given to finde the Hypotenuse AB As A 29 deg 40 min. to BC the height 114 03 so ACB 90 deg to AB 230 17. To finde it by the scale Draw the line AC let it be 200 of equall parts upon C erect the perpendicular BC and on A make an angle of 29 deg 40 min. so the Hypotenuse AB wil be 230 17. The part of the distance DA in the same diagram being known to finde DC or AC Let AD or EF be 90 foot and I desire FG or DC but I cannot measure it for impediments therefore first take the angle of altitude B at both stations A and D at AI finde A 29 deg 40 min. so that the angle CBA is 60 deg 20 min. at DI find the same angle D 46 deg and DBC 44 deg subtract 44 deg from 60 deg 20 min. resteth ABD 16 deg 20 min. then say As fine ABD 16 deg 20 min. to AD 90 foot so is BAD 29 deg 40 min. to DB 158 â— 10. Then again As 90 to BD 158 â— 10 so is DBC 44 deg to DC 110 which added to 90 AD makes AC 200 as afore By the scale thus draw the lines AC and AB ad infinitum making the angle 29 deg 40 min. then set 90 feet from A in the line AC to D where you found the angle DBC to be 46 deg because the angle CDB is 44 for they are the complements one of the other therefore plot the angle BDC and it will be 46 deg and the BD 158 4â— then from B let fall a perpendicular upon AC and it cuts it at C making DC 110 and AC â—00 as before To let this perpendicular fall divide either AB or DB into two equall parts and with the compass at that wideness set one foot in the intersection and the other in the line DC at C and there falls the perpendicular BC and the end of the line AC Likewise any part of the altitude being known the rest of it may be found by turning the height into the distance and the distance into the height Secondly As sine DCB 118 deg vel 62 deg Compar 0054164 to BD 600. 2777974 so sine CBD 4 deg 8843588 to CD 47½ the Castles height 1675726 But this will not be found very exactly by plotting by reason of the meeting of the acute angles the lines running so far one in another especially AD and BD that you cannot distinguish their intersection and thus also we have not onely found the height of the Castle 47½ but also the rest of the hill line by measuring AB 200 a part of the same line and up an hill also for if you add BCD 118 deg to CBD 4. deg they make 122 which subtracted from 180 deg rests 58 deg the angle CDB Then say As CBD 4 deg Compar 1156416 to CD 47½ 1675726 so CDB 58 deg 9928420 to BC 776 2. 2760562 which added to AB 200 gives the whole line 976 2. And now if you intend to begin your mine at B. your best way is to go 10 or 12 foot first in BG line as you ghuess half the breadth of the fort to K and thence draw the line KL parallel to BC which two lines are of equal length Elem. 1. prop. 26. and then keep that line up to the top for that must be your line of direction that if by occasion of some rock or other impediment you are forced to raise or sink or go side-ways you may by help of this line drawn on paper with a large scale keeping account stil how far you are gone in the said line and by help of the Quadrant at each station be able to plot how much you are above or below your line of direction and by help of your Needle to finde how far you are gone side-ways but your best way is to draw one line for ascents and descents and another for variations side-ways besides your line of direction and it will not be labour in vain also beside both these lines to set down in a note-book the inches raised by themselves above the line of direction and the fallings by themselves that so you may subtract the summ of the lesser from the summ of the greater just as in conveying of water whereof we shall speak anon Likewise set down the variations on the right-hand by themselves and those on the left by themselves and against
of them without going again into the field I Shewed before in Chap. 2. the manner of keeping your field-book by help of that and this you may readily obtein your desire All the field-books that ever you fill with notes page them all writing at the top of each page the name of the Parishes or Parish wherein the land â—â—th contâ—ined in that page and at every beginning of a new man set down his name and likewise at the beginning of every new field furlong or parcell in a furlong set down the name of the close field furlong or parâ—ell Also write on the cover of your first book A on the second B on the third C c. Then reserve four and twenty pages at the end of your first book A which shall not be paged or else make a little book by it self and on the cover thereof write INDEX and on the top of each page write A B C c. in Alphabetical order Then under each severall letter write first the Towns name beginning with that letter secondly The mans name for whom you measured thirdly The books name in which you wrote it and fourthly The pages either all of them or at least the first and last And whereas you may think this way will not be so beneficial â—o you as to go measure it again for that you may do as you see good you need not finde it unless you will Besides that you deserve pay both for surveying plotting and notes as if you had measured it And if you will measure it again these notes will do you no hurt See an example P. Purton 〈◊〉 Norton lib. C. pag. 31 32 33 34. Panchurch Rob. Audley lib. B. pag. 64. ad 76. Putford Tho. Dennie lib. K. pag. 97. ad finem Refer this following to pag. 85. line 13. But if you would bring water to your house from a conduit where you desire to place a cock as high as you can and that without Instruments First begin at the conduit and dig a trench near a foot deep there but as you go farther off let it be still shallower for five or six pole in length more or less according to the fall of the ground so that the water may but just follow you and when it begins to run over there stay it and begin a new depth as afore but he sure the fall of it be down-right like a stair and so go on till you come where you would be then add the fall at the conduit and all your stairs together and so high may you set your cock above the level of your trench FINIS ¶ An Appendix to my Faithfull Surveyour WE have in the book it self spoken of measuring such things as are measured by observing Instruments as the Pandoron plain-Table Quadrant Quadrat Theodelete Circumferentoâ— viz. of measuring of land taking of Altitudes and Distances taken by the chain here we will speak of such superficies as are done by a two-foot-rule as board glass pavement wainscot and of solid as stone and timber forbearing those things that seldome or never come in question as globes regular bodies and the like First Because land-measure and those seldome meet together in one man Secondly Neither would I have the book to be of two big a price and Thirdly Because my little time I have hath need to be spent to the best advantage for the common good CHAP. I. Of making the Rule FIrst I would have the Rule whether it be of box or of brass whether joynted in the middle or streight out to be just two-foot-long by some standard of brass kept by the Clerk of the Market and not as I have seen some that have been half an inch too long Let it be an inch and an half broad at the least and a third part of an inch thick with a square stroke struck round about it just in the middle of the length thereof Let one edge be besild off which serves that if you have occasion to draw lines with a pen if you turn that side downward you need not fear blotting if your rule chance to be blackt with inke if you rubb it well with sorrel that will fetch it out Through the midst of this besill strike a Gage-stroke an another along the midst of the other edge divide the rest of this side beside the besill into eight equall parts with seaven Gage-strokes In the 4 next coâ—umnes save one to the besill you may place all the under-measure of this Table of board-measure following which will not fall in a scale upon the rule viz. all inches halves and quarters from one inch to six or if you will to ten inches in small spaces the inches of the breadth of the hoard in the column next save one to the besill the feet required to a foot foreward at the breadth in the next the odd inches in the third and the Gentesmes in the fourth And adjoyning to this Table toward the middle of the Rule in the first of those four columnes seâ— one inch divided into ten equall parts and each of those into halves and each of those halves into five or suppose them so divided so is it divided into 100 parts or Centesmes from which inch you shall take off all your Centesmes with your compasses that are to be set in any of your scales For making the scale of board-measure Before you can make this scale you must have one column on the otherside the Rule next the besill parted into three small parts with Gage-strokes and divided in the middle of the length of the rule into two equall parts or feet whereof divide one of them into ten equall parts and each of them into ten more and each of them suppose at least to be divided into ten other so shall that fooâ— be dvided into 1000. and this Gunther calleth foot-measure which must be reckoned both wayes first from the beginning of the rule to the middle thus 1 2 3 c. and backward again and thus 11 12 13 c. and because the other foot makes ten of these inches and these ten make twelve of them therefore divide the other foot into twelve equall parts or inches and each inch into eight parts and number it from the end toward the middle with 1 2 3 4 c. but from the middle to the end with 13 14 15 c. and this he calleth inch-measure By help of this inch-inch-line and the inch aforesaid and by help of your Tables for board and timber-measure are made your scales for board and timber-measure And this Table of board-measure is thus made First for all whole inches divide 144 by the inches of the breadth and you have the inches forward to a foot If any thing remain after division it is the Numerator of a common Fraction whose Denominator is the Divisor to which remain annex two ciphers on the right hand and divide again by the same Divisor and you have the Centesme desired Example
length of that trapezium also add your two breadths 60 and 7 together make 67 for every middle breadth of each station-line must be twice added save where you have two severall breadths fall in one place as in the line CD where you have the length 200. twice together the half of 67 is 33½ by which multiply 472 facit 15742 to be set against the latter breadth 7. Then go to the second line BC where the first length is 100 the common breadth 3½ gives 350 and so go on according as the example gives then if you add all those primes or square links into one summe you shall finde it to be 40346 that keep till you have cast up the triangles within the station lines and likewise all the other slabs Therefore I draw a diagonall from A to C which will be the base to both triangles and half the length is 504. the perpendicular falling from B is 514 that from D is 494 the summe of both is 1008. then these multiplied the summe of both perpendiculars by half the base or the whole base by half of them it gives 508032 which added to the summe of the borders 40346 it makes that first close to give 548378 square links in all Now to bring these links into acres you need but onely cut off the five right hand figures the rest to the left hand are acres viz. five acres the reason is there are 25 links in the length of a pole that squared gives 625 square links in a pole and that multiplied by 160 the poles in an acre gives 100000 links by which divide your summe of your links or for the five cyphers cut off five places the rest are acres and the five so cut off are the numerator of a fraction of an acre whose denominator is â—00000 So 548378 gives five acres Now to bring these five figures into poles you may either divide them by 625 the primes in a pole or else multiply those two of the five next the left-hand always by six and set them a place nearer the right-hand and then add those two which you multiplied and the two which are under them together and increasing them so many unites as are sixes in the next two and you shall have 7 pole and 253 links If now that when you have cast up a close you have more then half 625 primes remaining ordinarily it is accounted for a pole if lesse then for nothing But if you have more closes adjoyning you may reckon it with the next close Suppose your ground hath the out-side of this form whose station-line is AD you may set it down in words thus in your note-book At A it is 10 to the brook from the station-line 0 at B where I have gone 20 pole in the station-line there is a square line to a crook stroke with the edge of the table in which at 15 on the left hand is 20 at 28 is 25 on the left hand and 15 on the right hand at 44 is 28 on the right hand at 56 is 33 on the right hand at 70 is 0. on the left and 30 on the right hand then at 30 in the station-line is 10 at which 30 also I strike a station-line forward which when I have stroke it I finde the fore-most acute angle by my scale of chords to be 70 degrees that also I enter in my book by help whereof and a diagonall line from angle to angle I can draw the plot of any ground though many years after without going to it again And after the same manner you may plot and set down single lands in the common-field or a close that is narrow and long CHAP. VI. Of measuring a Wood. THe difference of measuring a wood and pasture is in these two things First in pasture you measure on the in-side but woods on the out-side Secondly in pasture all your trapezia are to be added to that within the station-lines unlesse your station-line be in the close adjoyning but in this to be subtracted CHAP. VII Of dividing or laying out of ground OF this there are three degrees each more difficult then other The first is when the length of a ground is given and a given quantity desired as if you would lay out two acres of grass in a pasture which is 36 pole long and you desire the breath First I turn my two acres into square links it is 200000 which I divide by 900. for 25 times 36 is 900 it gives 224¼ the which if you divide by 25 the links in a pole it gives 8 pole 22¼ links in breadth and this needs no plotting Or if you would do by the foot-chain say two acres is 320 pole that divided by your length 36 gives 8 pole and â—2 36 which abbreviated is 8 9 and to know how many half-feet that is because there are 33 half-feet in a pole therefore I multiply 33 by 8 facit 264 that divide by 9 gives 29 half feet and 3 9 or â…“ that is 8 pole 14 feet 8 inches Secondly In pasture-ground suppose a pasture with crooked hedges is equally to be divided between two men First I plot it and find it 52 acres 2 roods 10 pole that is 26 acres 1 rood 5 pole a peice I ghuess as near as I can to strike a line over the middle of my ploâ— but measuring one end upon the plot I finde it wants 264 pole of his due therefore I measure the length of the dividing line which I finde to be 56 poles Now to work by the decimal chain I multiply 264 my poles wanting by 625 the square links in a pole they make 165000 likewise I multiply 56 pole the length by 25 the links in a poles length they make 1400 by which divide 165000 it quotes 117 6 7 that is 4 poles 17 6 7 links But by the foot-chain if you divide 264 by 56 it quotes 4 poles and 40 56 which to bring into half-feet multiply the numerator 40 by 33 the ½ feet in a pole facit 1320 which divide by 56 it gives 28 half-feet and 16 56 of a half-foot in toto 4 pole 14 feet 2 inches almost And so much must you remove your dividing line at both ends and this may be done as well on the out-side as on the in-side Thirdly To divide a standing wood of 200 or 300 acres and to drive a streight line from a mark on one side thereof to any mark on the other though the wood be twenty years growth and a hill in the midst A rare secret Be sure to plot and measure enough or more then you desire to take out of it and where you intend your dividing-line shall come there in your station-line on the first side set a mark keeping also good marks at every station so going on till you be sure you are far enough on the other side also Then draw your dividing-line by ghuess keeping one end thereof still upon the mark in your station-station-line then
come near to the truth and may indifferently serve in case of letting because it always is a little under the length as will easily appear in this diagram If an hill run streight along a ground if by one side it will be a mere declining level if through the middle it will be two declining levels and that line so running along the top will be a line of level and equal to the line of level under it therefore if you add both ends together as you measured them by the chain and multiply half of them by the length of that line you have the content if it be of equal height at both ends But if it be unequal at both ends though it be a declining level and have more then three angles your best way is to part it in severall triangles whose Hypotenuses and perpendiculars you may finde by either of the two former ways without measuring them by the chain Thirdly If you have no Quadrant nor plain-Table at all save onely the chain and any board of a foot or 14 inches long with one streight edge of ten or eleven inches broad draw a streight line close and parallel to that side and near one end thereof stick a pin in the line with thread and plummet hanging on it then if you are at the bottom of the hill and look upwards turn that end with the plummet from you but if you are at the top turn it towards you and as you espie the mark let a stander by on that side the plummet is on lay his hand gently on the bottom of the board and with his thumb press down the thread there holding it till you have made a prick right under it in a good large tran first drawn with 60 of some large scale of chords whose center shall be the hole where the pin sticketh then take with your compasses the distance between the said prick in the said tran and the beginning of the said tran and apply it to the same scale of chords you drew the tran by it gives the complement of the angle ascending viz. the dâ—grees of the angle descending But if you are at the top and look downward it gives the complement of the top-angle and degrees of the bottom ascending But if you will but erect a perpendicular upon the same center and take the distance between the prick and it it gives the contrary CHAP. X. Of reducing a plot from a greater to a lesser ALthough there are several ways of performing this as likewise of a lesser to a greater whereof there is great use in turning statute-measure into the eighteen-foot pole c. we will lay down onely this one generall rule Or Secondly If you desire a plot equall to another you may oyle a paper drie it well then put it over the other plot that it stir not through which you may see the lines on the neather plot then draw them with your pen on the oyled paper then take it off to prick it then pounch a new paper draw it Or Thirdly Having drawn a line representing AB in your new plot take the line AB off the old either all or ½ or according to your desired proportion set it on the new Also take the proportion of the line AE and set one foot in A and tran where you think E will fall in your new Take also the like proportion of the distance of BE and set in the said tran and so you have E the same 2 distances will set out D also D and B will set out C and so you have all your angles then draw their lines and you have your plot desired CHAP. XI Of measuring pasture-ground by the chain onely and that as speedily and exactly as with any instrument whatsoever and with less help though in misty weather to plot shut and prove the plot thereby also ABout the midst of one of your longest station-lines and some known length in the same as at X in the first or third close chap 3d pag. 2â— set up a mark and mark it in your book both with its proper length letter then having measured round about the ground on the inside or at least all but the last side if you have more then three angles in stead of measuring it from angle to angle viz in the first close from A to C or from B to D you shall measure from C to X and from X to D so making a triangle the more then otherwise which two subtendeâ—ts will easilie be run whilest you can set up the Table once so you shall need less help by one to carry your Table for that is wholly one bodies work and these two subtendents must be set down at the latter end of your notes of that close in your field-book Then if you measure the last side AD having plotted the rest if that AD on the ground and AD on the plot agree all is right neither ever need you divide any more lines then one in the whole ground or close throughout so that at least none of the station lines strike outward for then it must be accounted as another close so much of it till the last line that strook inward being continued streight out do meet with the other plot again See more chap. third Now to plot such a ground measured by the chain onely suppose it be the said first close chap third first I draw the line AXB making a mark at X and another at B secondly you must either take the subâ—endent XC setting one foot of the compasses in X tranning where you think C will falâ— or else take the station-line BC with your compasses and set one foot in B tran at C and then take the other of these two last lines viz. XC setting one foot on its proper mark X and with the other make a prick in the said tran and so have you placed C in his right place then draw the line BC next take CD with your compasses set one foot in C and tran where you think D will fall then take the subtendent DX set one foot in X and make a prick in the said tran and that sets out D then draw the line CD and because D is your last station and that A and D are both set out already therefore draw also the line AD now if AD on the plot and AD in your book agree then all is right else not So that in this kinde of plotting there are onely these three positures First draw a station-line secondly tran with a subtendent thirdly prick with the next station line Nevertheless in great larg plots it will be needfull to use a good larg pair of compasses because you must take the whole length of your lines with them In which case a pair of beam-compasses with a beam of deal willow or sallow or some such soft wood is best of all of 17 or 18 inches long with a piece of an
be shown with indico and azure or black-lead for seas a greenish sky-colour of indico azure smalts white-lead and verdigrease CHAP. XVI To measure all manner of ground by the Pandoron or any other graduated Instrument THe Pandoron is an Instrument compounded of First an ordinary foot with three legs for a plain Table Secondly a Table and folding-rulers like it save that it is a true square Thirdly the box and needle Fourthly it hath on one corner a centre in which is a screw-pin on which a moveable ruler with sights turneth Fifthly in the two out-sides furthest from the centre is drawn the Quadrate for terrestrial altitudes and distances Sixthly next to it is the limbe of the Quadrant both for celestial and terrestrial altitudes and distances whether upright flat or aslope Seventhly Gunther's Quadrant for your own latitude for houres both of night and day and Azumeths and divers other problems Eighthly Fale's Quadrant for Planetary houres Ninthly a circle and scale for finding the declination of a plain Tenthly a neck of 14 or 15 inches long to put on the top of the staff the Table being taken off with a pin on the side to hang the Table on to take all manner of altitudes and distances aslope Eleventhly a beam of 6 or 7 foot long about two inches square of deal and a trough on the top gouged all along half an inch deep to fill with water for a water-level having a sight at each end having a lath crossing the beam in the middle above and below 6 foot long fastened with screw-pins and brackets above and below with an hole in the bottom of the middle of the beam in stead of a socket to stand on top of the three-foot staff So that there is nothing that all or any observing Instruments can do but this doth it By this you measure land as by the plain-Table then if the weather be moist or in hilly ground you may uncover the Table and work by the Quadrant whereby you may save the charge of hill-ground sights which are as costly as all the rest of the Instruments Besides which if you know how to work by the Quadrant you cannot be ignorant of working by the Theodelete or semicircles the difference being onely this that they take onely at once which if it be above 90 degrees by the Quadrant you first take some part of it and then the rest of it afterward yet all at the same station and then plot it by your scale of chords Indeed by the Circumferentor you take all the angles by observing the cutting of the south-South-end of the needle and then either plot the angles by a protractor and the lines by a scale of equal parts or else you may plot the angles either by your scale of chords or by the Circumferentor it self both which I hold better ways then the first So that there being nothing desirable in an observing instrument but this giveth it it so pleased Mr. Hender Roberts the Lord Roberts youngest son a Gentleman every way fitted with a genius for the Mathematicks whom I cannot name without honour who had the first of them to give it the name of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 omne donum So that in shewing the use of it as it is a Quadrant we shall with the same labour shew the use of all graduated Instruments in measuring of land and as for working by it as by the plain-Table we refer you to the ten first chapters of this book Now therefore for working by the Quadrant yet herein we will speak of nothing but what is within the station-lines contenting our selves for the rest with that which hath been spoken before in the use of the plain-Table all the difference consists in three things first the taking of the angles secondly in keeping the field-book thirdly in plotting Now for your plotting it first draw the line AB set out 20 of your scale of equal parts upon it then take always 60 off your scale of chords set one foot at the end of your 20 in B and with the other foot tran always from the last line which here is AB towards the place where you think your next line BC will fall Then take your angle B which is 60 and set it in the said tran from the line AB forward there make a prick and from B through that prick draw the line BC ad infinitum In which line set out â—8 of equal parts there make a prick for your station C. Then take again your 60 of chords set one foot in C and tran from the last line BC toward CD Now because your angle C is more then 90 and that your compass tran at 60 therefore first set out that 60 in the said tran to B and because there wants yet 46 of 106 therefore take those 46 with your compasses and set them on forward from 60 there make a prick and draw your line CD through it and so of the rest So that there are but these things first draw a station-line secondly tran your angle with 60 of chords thirdly prick out the degrees of that angle CHAP. XVII In measuring by graduated Instruments to know if your plot will shut or no. Because in working by graduated Instruments you always plot at home but never in the field and that if any thing be mistaken in the field as oft it comes to pass to be so then will not your plot shut at home therefore either you must look to your needle at every plantation or else you must measure all the angles which by the plain-Table you need not do therefore with such Instruments the needle is more needfull then with the plain-Table and yet the Circumferentor will hardly help you herein neither though you work all by the needle unless you work by taking angles by it which is the slower way Now having measured all the angles if on the inside of a ground because all the three angles of a right line triangle are equall to two right angles or 180 degrees and that there are so many triangles save two as are angles therefore if you reckon so many angles save two for each of them 180 and finde that and the quantities of all your angles to agree there is great hope your plot will shut else not As if there be a triangle they must all make 180 if a quadrangle 360 if a pentangle 540 an hexangle 720 a septangle 800 an octangle 950 but if you measure on the out side as a wood then every outward angle is the complement to 360 of its inner angle therefore to take all those complements is your best way both to prove and plot it by and less labour if you are far from your mark and not to go to it again it oft-times will quit your pains lest you are forced to spend perhaps an whole days-work about that you have done or at least would have done already to prove your angles after this manner CHAP. XVIII
us a better CHAP. XXV Of Instruments for conveying of water and their use IF your distance be not above an 100 poles or thereabouts you may hang your Pandoron or Quadrant on the pin of the neck and then set up a staff or rather let one hold it upright with his face toward you at the head of the water moving a sheet of paper up or down as you standing 8 or 10 pole off in the water-way shall direct him by the signe of your hand till you having there set up your Instrument and plumb'd it truly level you see either through the sights or over side of the Quadrant the nether edge of the paper having first screwed the ruler fast and placed the thin edge thereof precisely upon the upper Horizontal line of the Instrument now take not your stations above 10 pole at the most from your standings both in regard of the refractions of the air which will deceive your sight as also for that though your Instruments be never so true yet if you fail either in your plumbing it or in laying your ruler but one tenth part of an inch false which is easily done you will fail so many tenths as are Tables lengths between your Table your staff which if your Table be 18 inches Radius and your station ten pole will come to eleven inches in that distance enough to marr your whole work Now he having placed his paper let him bring it staff and all to you without stirring it and then you having a two-foot rule and a stick in your hand about four foot and an half long measure first the height of your sights above the ground also from the bottom of his staff to the nether edge of the paper if both be alike then those two places are level if not then see which is most and how many inches there are odds if his be more then yours then your ground is risen more then his so many inches as the difference is but if you are more then he then you are lower and then the water will run or else not For it will never run higher naturally upward unless your former falls do countervail your rise Having thus found the difference you must in a note-book make two Tables one for the risings and another for the falls at each station with their titles of rising and falling over them and the number of inches at each station and the number of the stations on the left hand and you may do well also to measure the distance with a chain and set down on the right side the distance from the spring-head and at each station to observe some mark And having all done you must cast up the Tables each by it self the inches of the falls by themselves and the ascents by themselves then subtract the lesser total from the greater if the descents be most it will run so that there be no station in the way that is higher then the spring-head which if you suspect cast up both your Tables onely so far and you may easily know Yet if it should that will not cut you off altogether for though you cannot help your self by digging deep yet it is hard if you cannot by going about Having thus measured and found the difference you may for triall-sake exchange places and let him stand where you stood and do you stand at the fountain If there you finde the descent to be the same as you did before all is right and that you will hardly do unless your Instrument be both very large and very exact But now you must know that there is a difference between your being between the spring-head and him and his being between it and you for now if he be most he is lowest for always he that is most is lowest Now if you will you may either your self go on forward and let your assistant stand or rather your self stand there still if you remove not to prove as I said and so you may take two distances at one station especially if you have two assistants and all you three are in one direct line so if you keep your work in a streight line if two assistants stand in the water-way if you stand in the middle in a right-line if you see to one of them you see to the other without stirring the Instrument any ways Again so far as you go in a direct line if you have once set two marks level you may easily by them set up a third and fourth as far as it goeth in a streight line and when it turns then use your Instrument as afore Also it so falls out that water is to be brought out of some pond or level water if you bore holes in two boards like trenchers and sharpen sticks of equal height with white papers on them if the boards lying in the water two assistants hold the sticks that you may set up a third in a streight line with them with a mark upon it agreeing level with the other marks if they are too high remove them lower but both alike or your own higher contrá onely take just notice how high the two are above the water and then go on with a fourth and fifth so long as you go in a streight line and then use the Instrument as afore Also it may happen that you desire to bring water from some spring or head but you have neither level nor level water nor streight water-way but you suppose it will run and the way is not long and you would willingly try First then begin at the head and make a little trench of three or four pole long towards the way that it will run streight whether this be streight or crooked it matters not then let run so much water as may onely fill this trench if you finde it dry or shallower of water at the head then at the other end it shews the ground to be falling then do the like with three or four poles more still making the water to follow you till you be gone three or four pole in your streight line then having fill'd it that the water may stand level at both ends stick up two sticks one at one end the other at the other of equal length about four foot above the water then go on 10 or 12 pole in the same line where set up a mark so that you standing behinde it and looking to the middle mark either all the tops or all the bottoms according to which you measured your equal heights may agree then if that stick be longer beneath the mark then the other two it shews descent if any rising places be in the midst you may easily finde their rise by setting up a stick and measuring it as before CHAP. XXVI Of flowing of grounds MIne intent is not here to describe the manner of making engines sluces Cochleas mills c. to mount the water withall as being too great a charge for a small piece of
Let a board be seven inches broad I desire to know how many inches forward makes a foot Divide 144. by seven it gives twenty inches or one foot eight inches â— 7. Now to bring â— 7 into centesmes annex two ciphers to the remain four it makes 400 which divide again by seven it gives â—â— 100. But for half-inches reduce the breadth into an improper Fraction as 6½ is 1â— 2 then multiply 144 by the Denominator 2 it gives 288 so that you must always divide 288 by the Numerator or number of half-inches of the breadth of the board which is 13 so have you 22 or one foot ten inches 15 centesmes But if your breadth be an odd quarter or three quarters First reduce it into quarters and divide 576 by it so ◠¼ is 27 quarters therefore divide 576 by 27 it gives 21 inches or one foot nine inches 9 27 or 33 centesmes The Table followeth A Table shewing how many feet inches and centesmes of inches forward are required to make a foot of board measure at all breadths both whole inches half-inches quarters and three-quarters from one inch in breadth to 36 inches Quar. Board feet inch cent Quart feet inch cent Qu. inch cent quar inch cent 1 0 12 0 0 8 0 1 6 0 15 9 60 22 6 55 1 9 7 20 1 1 5 46 1 9 44 1 6 47 2 8 0 0 2 1 4 94 2 9 29 2 6 40 3 6 10 29 3 1 4 46 3 9 14 3 6 33 2 0 6 0 0 9 0 1 4 0 16 9 0 23 6 26 1 5 4 0 1 1 3 56 1 8 87 1 6 19 2 4 9 60 2 1 3 16 2 8 73 2 6 13 3 4 4 36 3 1 2 77 3 8 57 3 6 6 3 0 4 0 0 10 0 1 2 40 17 8 41 24 6 0 1 3 8 31 1 1 2 5 1 8 32 1 5 94 2 3 5 15 2 1 1 76 2 8 22 2 5 88 3 3 2 40 3 1 1 35 3 8 12 3 5 82 4 0 3 0 0 11 0 1 1 9 18 8 0 25 5 76 1 2 9 88 1 1 0 80 1 7 81 1 5 70 2 2 8 0 2 1 0 51 2 7 78 2 5 65 3 2 6 31 3 1 0 25 3 7 68 3 5 59 5 0 2 4 80 12 0 1 0 0 19 7 58 26 5 54 1 2 3 41 1 0 11 76 1 7 48 1 5 48 2 2 2 18 2 0 11 52 2 7 39 2 5 43 3 2 1 4 3 0 11 29 3 7 29 3 5 38     Qu. Inch. Cent.       6 0 2 0 0 13 0 11 8 20 7 20 27 5 33 1 1 11 4  1 10 87 1 7 11 1 5 28 2 1 10 15  2 10 67 2 7 2 2 5 24 3 1 9 33  3 10 46 3 6 94 3 5 19 7 0 1 8 57 14  10 29 21 6 86 28 5 14 1 1 7 86  1 10 11 1 6 78 1 5 11 2 1 7 2â— Â 2 9 93 2 6 69 2 5 5 3 1 6 58  3 9 76 3 6 62 3 5 1 Q. I. C. Q. I. C. Q. I. C. Q. I. C. 29 4 97 31 4 65 33 4 36 35 4 12 1 4 93 1 4 61 1 4 33 1 4 9 2 4 89 2 4 58 2 4 30 2 4 6 3 4 84 3 4 54 3 4 27 3 4 3 30 4 80 32 4 50 34 4 24 36 4 0 1 4 76 1 4 46 1 4 21    2 4 73 2 4 43 2 4 18    3 4 69 3 4 39 3 4 15    Now to place this Table upon the rule divide the second third fourth and fifth columns next to the besill at one end into small squares that may hold two figures a piece in which set over-most the inches of the breadth in the second the feet required in length at each inch half inch and quartern In the next the odd inches and in the next the odd centesmes and this you must do to six inches you may do it to ten inches if you will Then at the end of ten inches set one inch divided into ten equal parts and each of them into halves and suppose each half into five so will it be supposed to be divided into an hundred parts as before Then from six inches to 36 you shall set all in the column next the besill with small strokes after this manner First I begin with six inches and a quarter to which I finde in the Table there belongeth one foot eleven inches four centesmes that is eleven inches four centesmes from the middle cross stroke of the rule But because my compasses will not reach so far I onely take 56 centesmes from the former inch which makes it just two foot from the same end which I set the under measure at Another example let be 9¼ for which I finde in the Table one foot three inches 56 centesmes First I take with my compasses 56 centesmes from my inch of centesmes and prick it down upon a line upon a paper Also with my compasses I take three inches in the foot-line of inch-measure on the other side of the Rule set that distance also on the paper at the end of the 56 Centesme in the same line then take with your compasses the whole length of both set one foot in the middle-cross-line of the Rule and in the said scale and the other toward the beginning of the Rule and it gives the length correspondent to nine inches and â— 4 from the stroke to the end of the Rule Thus do with all the rest marking each whole inch with its proper number to 24 also 30 and 36. And now before we proceed to shew you the making of the Table of timber-measure we will first shew the measure of boards CHAP. II. Of measuring of boards with the Rule THere are divers ways of measuring of boards of which the fundamental way is this 12 inches in length and 12 in breadth that is twelve times twelve or twelve inches square which is 144 inches make a foot of board therefore multiply the inches of the length of the board by the inches of the breadth and divide the product by 144 you have the content in feet If any thing remain divide it by twelve it gives the odd inches or twelve parts of a foot for an inch is the twelfth part of a foot let the foot be what it will Example Let a board be 13 foot five inches long that is 162 inches long and nine and an half broad these multiplied give 1529 and an half which divided by 144 give ten foot 89 square inches and ½ remains which divided by 12 is 7½ ferè inches of board Secondly If you multiply the length in feet 13 feet 5 inches by the breadth in inches 9½ first 9 inches by 13 foot is 9 foot 9 inches half of 13 is 6½ and 6 square inches and 9 times 5
the basis on which the other are built or scale by which they are made Secondly For the Diameter Archimedes gives this rule Multiply the Circumference by seven and the product divide by 22 so have you the Diameter so on the contrary Thus our circle 88 multiplied by seven gives 616 which divide by 22 quoteth just 28 as afore Thirdly For the square within the circle this is the rule The square without the circle is double in content to the square within Or thus The content of the square within the circle is to the content of the circle as 7 to 11 First therefore by the content of the square without we found the Diameter or side of the square to be 28 that squared or multiplied by it self is 784 the content thereof Therefore the content of the square within is but ½ 784 that is 392. whose square-root is 19 31 39 as afore Secondly by the content of the circle for which Archimedes saith half the Diameter multiplied by half the Circumference gives the content so 44 the half of the Circumference multiplied by half the Diameter 14 gives 616 the content of the circle This therefore multiplied by seven makes 4312 which divided by eleven gives 392 just as afore Fourthly For the square equal to the circle having by this last rule found the content of the circle to be 616 we need but extract the square-root thereof which is 24 40 49 which doth discover a most monstrous and a most gross errour in measuring round timber of which hereafter CHAP. VII Shewing the manner of placing these upon the Rule FIrst To set out the Diameter you may take the nether part of the third column of the besil'd side to set it on from the middle square stroke of the Rule Then Gunther in his Vse of the line of numbers in broad-measure Prop. 11. hath this proportion Having the Circumference of a circle to finde the Diameter As 3143 to 1000 so is the Circumference suppose it 47 ⌊ 13 to the Diameter 15 so that if you take 47 ⌊ 13 in your circle-scale and set in that column from the middle square downward so shall you set out 15 in that distance run that distance as oft as you can to the bottom of the Rule which will be 4 times more divide each of them into 3 equal parts and the uppermost third into 5 equal and number all the other great parts save that with 5 10 15 c. or if you will you may double 47 ⌊ 13 that is 94 26 and take it from the circle-scale set it there they will be 30 then half it and they will be 15 then third it into fives 2. To finde how to proportion the square within the circle by the Diameter Let the Diameter be the Radius 1000 then will the chord of 90 degrees which is the side of the square included be the natural sine of half 90 viz. 45 degrees the sine whereof is 707 therefore then because I would divide my scale into even sines if therefore I take 7 times 5 that is 35 the proportion will be 707 1000 ∷ 35 49 ⌊ 50. or 49½ therefore if you take 49½ on the Diameter and set it on the scale of chords and divide it into 7 equal parts and that part next the end into 5 small parts numbring all but that with 5 10 15 c. you have your scale of chords or square within the circle Or if you think it troublesome to divide it into 7 equal parts you may take 6 times 5 that is 30. and say 707 1000 ∷ 38 42 ⌊ 43 so then you may take 42 ⌊ 43 of the Diameter and set on your scale of chords and then divide each of them into halves and each half in to 3 parts Otherwise thus The content of this circle according to Archimedes is just ½ the content of the square of the Diameter Suppose the Diameter 24 the square thereof is 576 the half whereof is 208 the root whereof is 17 ferè then say If 17 in chords require 24 Diameter what shall 40 in chords or any other even number of fives Answer 56½ therefore take 56½ of the Diameter and set it in the scale of chords which because it gives 8 times 5 first divide it into halves then into quarters then into eight 3. It may also be made by this Rule of his The area of the square within the circle is to the content of the circle as 11 to 7 so that the circle begin known the content is thus found ½ the Diameter multiplied in ½ the Circumference gives the content of the circle which if you multiply by 7 and divide the product by 33 it gives the content of the square within whereof take the square-root and you have the side desired therefore 19 ⌊ 8 88 ∷ 20 88 ⌊ 9 or as Mr. Wingate hath it in Problem 33. of his Appendix to his Rule of Proportion 225 1000 ∷ 20 88 ⌊ 9. So that take 88 ⌊ 9 from the Circumference and set it on this scale and divide it into four fives and this scale may be set on the lower half of the besil'd edge 4. Having the content of the Circumference to find the side of the square equal Take the square-root thereof so we found before that the Circumference being 88 the content is 616 whose square root is 24 ⌊ 40 49 that is more then 24¼ or more easily because as Gunther hath it the Circumference is to the side of a square equal as 1000 the Radius to 282 therefore say 282 1000 ∷ 20 70 ⌊ 9. Therefore take 70 ⌊ 9 of the Circumference and set it in the scale of the square equal it gives 20 of that scale with which distance set out all the twenties the side will bear dividing each 20 into four fives and the last into five little ones and numbring them by five as afore and this scale may be set in the over part of the third column nexthe square edge Errour in round timber to take a quarter of the circumference for the square 5. And here I must acquaint you with that monstrous errour in measuring round timber which I spake of before which is this to gird the piece about and to take the fourth part for the square thereof as suppose the piece be 80 inches about then by this account the square should be but 22 inches whereas in the last section we found it to be above 24¾ whereby the full fifth part of the timber is lost to the seller which notwithstanding the most of them know to be extream false by reason that when they have hewed it they make a great deal more of it then they did before it was hewed But what is their excuse Even this they say That will scarce pay for the hewing and it is but sap and bark I answer The goodness or badness of any thing is considered in the price but neither in the measure nor the manner of measuring
one so that you may understand as many ciphers with it as shall be requisite so that it may signifie 1.10.100.1000 and then if one signifie 10 the next two will naturally signifie 20 but not always Now to take and set the number 2 in his right place take a Table of Logarithmes of absolute numbers and look either the Logarithme of 2.20 or 200. and take the three next figures to the Characteristick which are 301 then with your compasses take 301. viz. three inches no tenth part of an inch and 1 10 of a tenth part or Centesmes of an inch and set one foot in the nether-most cross stroke where you set the first one and turn the other upward in the same column and there set your 2 likewise with the same numbers set one foot in the middle cross stroke where you set the middle one and turn the other upward toward the uppermost one and there set your 2 also likewise do with 3 whose Logarithme is 477 id est 4 inches 7 tenths 7 Centesmes also with 4. And these figures for the making of this line we will call hundreds the next subdivision tens and the least Centesmes But now because we will suppose your compasses will not well reach beyond the figure 4 whose Logarithme is 602 that is above 6 of those inches therefore first let us set on the tens so far on both feet and then the rest of each foot afterward Next set out each fifth tenth so far because you must mark them with longer strokes then each single ten so then you must not account the next of those fifths to 1 as 5. for then you will account the one for nothing but you must account it for 15. or 150. and so take the Logarithme thereof which is 176. Likewise 25 or 250 is 398 which you must take with your compasses and set in their places in in both feet and in like sort shall you do with all your single tens accounting that next â— not for 1 nor 2 but for 11. Or instead of taking them off with your compasses strike out all the first foot with a fine small striking squire of brass laying it upon the Log. in the line of foot-measure and then set out the other foot with your compasses by this Now for the rest of each foot look out the Logar of your numbers and take the distance between it and the middle cross-stroke and with that wideness set one foot in the upper 1 and where the other falls there is the place of that number Example I would set out 70 the Log. is 845 I take the distance between it and the middle-stroke of the Rule or the Arithmetical complement of it 154 and set it both from the upper stroke and middle-stroke downward and you set out seventy But your over-foot may bear unites to 20 and from thence to 40 divide each tenth into five and from thence to the end into two To make the line of sines First you must know that neither the line of sines nor tangents enter the Rule till 35 minutes where you see the two next figures to the characteristick 8 are both ciphers there also the characteristick changeth from 7 to 8 for your characteristick shews what foot you are in therefore since we reckon the minutes onely by tens our first number or division upon the Rule will be at 40 minutes of the first foot shewn by the characteristick 8 for 9 is the last and therefore belongs to the last foot so that whereas you see that the Log. of one minute hath 6 the characteristick 463 the three next figures therefore one minute would be above a foot and half before the entrance on the Rule and likewise would the first minute of the tangents be Now the Logar of 40 minutes hath beside the characteristick 8 the three first figures 066 feré therefore take off 0 inch 6 tenths and 6 centesmes or 5 centesmes and 7 millesmes if you caâ— ghuess so near and set them from the nethermost cross-stroke at the beginning of the line of sines forward And thus do for all under two degrees be it sine or tangent but from thence to sine 5 degr 45 min. or tangent 5 degr 43 min. As suppose the sine of 4 degr whos 's Logar beside the characteristick is 843 you shall take the distance between 8 inches 4 tenths 3 cent and ten inches and apply that distance from the middle-stroke down-ward and so of the rest of the quarter But for all both sines and tangents in this first foot you may by their Logarithmes strike them with a square as you did the line of numbers Now for the upper-part shewed by the characteristick for all sines and tangents to 20 degr as suppose the tangent of 20 degr the Logarithmes of 20 degr tangent is 56 set it from the middle-stroke forward but from thence to the sine of 90 and tangent of 45 degr as the sine of 40 whose Logar is 808 take the distance between it and the middle-cross-line and apply it in the line of sines from the upper cross-stroke down-ward then number all the whole degrees to ten with 1 2 3 and after that in the sines with 20 30 40 c. to 90 and the tangents with 10 20 to 45 and back with 50 60 to 80 degrees Lastly for making the sextant of chords Set a pair of beam-compasses with a beam of willow deal or sallow near half an inch thick and â— 4 broad make a little nut of good tough wood with a mortes in it that the beam may slide in it to and fro indifferently stiff and in all places alike with a short prick or little piece of an aule-blade in one end and another longer in one edge of the beam hard by the end so long from the beam as the other point is If it goeth not stiff enough to stand and tran with at any place make the mortes a little the deeper one way to put in a wedge or else help your self with a screw-pin then go to some smooth loft boards opening your compasses to 23½ inches and with that wideness tran an arch that may be two foot long at the least and with each foot of the compasses make a prick in the said arch and set it likewise upon the Rule then divide that space in the arch into two equal parts which will be 30 degr a piece and each of them into three apiece which will be 10 degr apiece and each of them into two which will be five apiece and each of them into five simple ones Then take them off from the floor and set them on the Rule one after another and number them with 10 20 30 40 50 60 and this will be wonderfull beneficial in Dialling and also in many other things as to divide a circle into any number of equal parts or to make an angle of any number of degrees or to finde the quantity of any angle and so by the line of foot-measure you may also divide a streight line into as many parts as you will Now as I have shewed the use of all the lines on the other side of the Rule and also of both the out-side lines on this side so for the other three I must content my self to shew you the use in general for if I should descend to particulars all the paper in Cambridge would be too little to hold them First therefore you see already that as by the line of foot-measure and Table of Logarithms these lines are made so may you by these lines finde the Logarithme of any absolute number tangent or sine as if it were by the Table of Logarithms Secondly By these two lines of numbers and foot-measure may be resolved all questions whatsoever that common Arithmetick can resolve And more for hereby may be resolved all questions of Interest Purchases Annuities c. Thirdly By these three lines of numbers sines and tangents is resolved the whole doctrine of Triangles and whatsoever may be performed by them either in Measuring Dialling Geography Geometry Arithmetick Navigation Cosmography Astronomy c. But because gentle Reader I would have thee learn now to go alone I will commit these to thine own consideration knowing that that chicken that will peck up never a corn but what the hen puts in the mouth will never be a fat chicken Now if the Rule of three is accounted of all men worthy for its excellency of the name of the Golden-Rule which is but the least part of the use of one of the lines of this Ruler then justly may this Ruler be called the Golden-Ruler FINIS Hom. Odyss 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 v. 230. Horat. Ep. 1. lib. 1. * Herbam porrigere Prov. How to set themselves right in a line To plot a plot taken by graduâ—ed Instruments For finding how high you may set your cock in a house see the last page of this Book Street-earth Soot Salt Pigeon-dung Folding of land Rags and Horn-shavings Malt-dust Lime Ashes Chalk c Burning of queach c.
angle upon the same line as if it were the end of it and then making a new plot at home your own reason will direct you better then I can shew it for it is easier perceived upon triall in the field then expressed by word or scheme but then you must lay down none but station-station-lines and angles 3. The most common help that Surveyours use is to remove the paper nearer one end of the Table and then with a piece of mouth-glue which they usually carry with them they glue on what paper they think they shall need and then fasten it down with the rulers again 4. If your plain-Table be also a Pandoron or have a semi-circle or a Quadrant you may at any time either in this case or case of moist weather take off your paper and help your self thereby as shall be shown hereafter 5. By the chain onely and your field-book whereof also hereafter in its place Eightly Before you begin you must know that both at the beginning and ending of every station-line and every crook of the hedge both inward and outward you must measure the nearest distance between the station-line and the hedge for all breadths must cut the station-line squire-wise and so make two right angles at the station-line and that is the best way and so doing all the pieces on the out-side the station-line will be either rectangle triangles or else compounded of an oblong and a rectangle triangle the area of both which is found by adding the breadth at both ends together and take ½ of it for the common breadth which multiply by the whole length and you have the content And sometime your best way to finde the shortest distance into an angle is to set up the Table right in the station-station-line if standing at the fore-mark you see by the edge of the Table the backer mark and then standing at the backer end you see the fore-mark then are you right in the line If now withall one or both of your other sides look right into the angle then are you right And all these lines must be entred into your field-book which fall perpendicular upon the station-line every one in their order on the right side of the line and on the left side right against each of them their correspondent lengths how far each of them is off from the last station Or else you may strike a station-line into the angle and so make scalenum triangles but that is not so certain and asks more labour Ninthly Before you go forward you must propound to your self a mark to go upon on the farther side the ground or if it be quite beyond the ground though it be a mile it matters not so that standing at A you may see it clear from the hedge yet as near to the hedge as you can whether it be parallel or no care not If you can see no such mark neither near the further side nor beyond then either you must send one before to stick up a stick with a cloth or paper on it or to stand there till you come with some white before his breast And moreover see if you can see some other mark between him and you right in the same line be it either flower weed grasse dung c to be a guide for the fore-man to keep him right in the line that carrieth the fore-end of the chain Tenthly Whereas you must have ten sticks about a foot long apiece whitled and sharpned at the great end let two take the chain one at one end the other at the other let the former take the sticks and let him be sure to lead streight in the line which for his guide therein he hath these helps First he must always be right in the line with his two marks before him till he comes at the first Secondly after he is come at the first let him every time he sticks down a stick look backward to set himself right in a line with those two And thirdly if there be no middle-man let the hindmost standing at A guide the foremost right in a line to B and after the first chains length let the hindmost guide the foremost and the foremost the hindmost for if the hindmost see the foremost right in a line between him and B and the foremost see the hindmost right in the line between him and A then are they both in the right line between A and B. Then to go forward let the foreman take all the sticks and tell them at the beginning at each change and at the end for the most common mistake is the losing or mis-telling of a stick and carry all save one in his left hand and that one and the chain in his right and let him go on streight in his station-station-line not looking behinde him till he feel the chain check him then stick down that stick and away as fast you can run and as you go shift an other stick into the right hand ready to stick down again In the mean time the hinder-man first holding the chain in his right hand at A let him look the chain be not tangled and away on till he come to the stick and then clapping his ring of the chain to the foreside of the stick let him take it up with the same hand he carrieth the chain and away after his leader And when the sticks are all run and that they are not yet at the end of that station-station-line let the fore-man run one chain more holding still the ring in his hand and at the end thereof set his toe there standing still and let the hinder-man take up the tenth stick and hold that still in one hand and the other nine in the other and deliver the nine to the fore-man setting his toe to the fore-mans then let the fore-man tell the nine and if they be right away if not you must measure all that course again and seek the stick for you know not which of you lost it and so going to the end of that station-station-line or within so much of the end of it that you may have libertie to set up the Table and see to the further end of the next station-station-line as you did at A without any incumbrances which if you work by a diagonall scale may be in any place but if by a plain scale you had best to have it at some even poles and because by Gunther's chain of an hundred links which is the best way you work not by the diagonall scale by links but by the foot chain by the decimall scale and by poles and parts of poles Set that length in your note-book on the left side of the line close by the line and a Bright under A and on the right side the line write station Then go on still in the said line till you come to the out-side of the ground which in pasture will always be beyond the station but in woods short of it Set down that length
also on the left hand and the breadth from the station-line at the end thereof to the hedges you came by on the right and then draw a line crosse over your book and so at the end of every other station-station-line But you must not forget that all along as you come you take as I said before the breadths from the station-line to the hedge both at the beginning and ending and every crook both inward and outward with their correspondent lengths and to set them down as afore Also if a fair plot in colours be required it will be needfull to set down the true lengths of each station line to every mans hedge that shoots upon your plot beside the ornaments that you may shew part of their corners as also in case they are their grounds that imploy you in it And sometime also if you are to measure two closes being together and that you would come forth upon that point in the station-line it will also be needfull to set it down in your note-book and often save labour marking it with an X. Now if you begin at A and have two closes lie there together to be measured then take up your Table there and having turned the length of the Table to the length of the ground and proportioned the A of your Table to the A of the ground set up your sights with the ruler upon the Table and having screwed it fast turn them upon the Table till you see the mark at B. Also see some mark in the close adjoyning on the further side or a mile beyond and because I see just there begins a triangle on the right hand which falls short of the length of the other line therefore I draw a third station-line from A representing the right-side line of that triangle so I leave that close till I have made an end of the other so having drawn my line AB I go to measuring it by Gunther's chain and I finde at O of the line AB are five links to the hedge I enter them as afore At 200. I crosse a path which I enter next on the left side but because there is no crook in the hedge right against it therefore I take no breadth but write path-gap At 437. the breadth is 60. I set them down because here is both a crook and right against the parting of two closes that shoot upon this thirdly it is right against a gap to come out from the further end of the first line in the second close whereby measuring that and 75. links of another station-line and setting up the Table twice that close will be measured as shall be seen anon fourthly it will be a good place to make choise of to save us some labour in teaching to measure by the chain onely as shall be shown in its due place Hence I go on to 900. there I choose my next station both because if I do go further my next station-line BC will be incumbred with the hedge as also I shall have no ground to set the Table on but here I take no breadth being the hedge goeth out streight to the end onely I set down 900 station and then measure streight on to the out-side 907. where the breadth is 8. so I set down 907. on the left hand and 8 on the right out that is without the ground Then having finished AB I strike a line crosse the book and set up my Table again at B and having made choise of my scale which I made no use of till this second station I take off 900. with my compasses from the scale and set it in that first station-line from A where I make a prick and a little roundle round about it as also at A. And here I write B and now that which was forgotten at A do now viz. one thing was to take notice what degree the South-end of the needle bore upon at A for if there be no errour it will bear upon that degree quite through the plot unlesse you remove the paper And a second thing is if you are to give in a fair plot in colours it will be needfull to strike a meridian-line through the plot unlesse you lay the North-end of the needle upon the Flowre-de-lice which in case a fair plot be required I confesse is the best way for so you shall draw your plot in the field according to the four windes whose borders shall be parallel to the edges of the Table I confesse in such a case as the third figure if there be a trapezium on the out-side of my station-line such as CDEF suppose my ordinarie station-line to be AB sometimes I use this way Right against the hedg CD I set up the Table at A and having placed the Table in his right situation I strike these three lines AD AE and AF and then measure on from A to B and then set up again and then again I strike BC BD and BE and never measure any of those six And after the same manner if I have a good large triangle on the out-side of my station-line if my station-line be one side thereof But in this case when I come at home if I determine to keep my note-book and to draw a plot of it 20 or 30 years after I then draw the like figure in my field-book in its proper place with the length of each line and the scale I wrought by I once was asked by a famous Mathematician but I forbear to name him what instruments I use to measure by I told him sometime by the plain-Table sometime the Theodelete sometime by the Quadrant c. Quoth he There is a deal of lumber indeed I 'le carry nothing but an high stool a field and with two sticks a cross I 'le stand upon that in the midst of the field and take the distances to every angle and I 'le measure three acres to your one I gave him his saying risum teneatis amici but truly I could not But let us to our work again Having now at your station B drawn all the lines you will draw and drawn a line cross your field-book go on to measure the station-line BC where the breadth at 0. is the same which was your distance in your last station-line between 900. the station and 907 out viz. 7. set it down on the right-side of the down-right line under the overthwart line in your book and 0. in the left-side then go on at 700 0. at 350 0. at 560 a square stroke into the angle 30. at 563 a station C 568 out Now having finished this line take again the distance between BC 563 upon the same scale you took your 900 and set it on your plot from B. Then if you did not set up at A or if you did not draw the line DA when you were at A but that there wants two outside-lines to draw still then set up your Table again at C and laying your ruler on the
line BC turn the Table till through the sights you see the mark B which if you do then see if the south-South-end of the needle do strike the same degree it did at A and B if not there is some fault which most commonly is in the last line save one and must be rectified before you go further But there is a second way of triall infinitely better which is this Having placed CB line right upon B lay your ruler upon the two pricks C and A if then through the sights you see A all is right if there be a fault it is commonly in the length of the last station-line save one which if you came contra Solem and your sights look on the left hand of A your book is more then your plot vice versâ If you have rectified it set out your next station-line CD and measure as afore and make your station if you can see A at the very end and can go free from all impediments else make it short as afore And then begin to measure that CD line having drawn a line cross the book say at 0 5. at 200 40 at 200 10 at 656 out station 12. Where you see because I need not to set up my Table any more for there is but one line more to measure therefore I drive the station-line CD to the very outside so I take the whole length of the line where my breadth is 12. This length 625 I set on the plot from C to D where I make a prick within a little circle and write D then before I measure the last line DA upon the ground I measure it first upon the plot setting one foot of the compasses in D and the other in A and then applying that distance to your scale that will give you the true length of the line DA before you measure it So that when you have measured it if the line on the plot and the line on the ground agree then all is right and this we call the true shutting of a plot which if it agree within a pole or 20 links most Surveyours count it well shut I think it too much neither do I remember that ever I missed so much in all my life I once measured a wood called Horsley-wood in Luton-Parish for Judge Crawley where one Master Lawrence was my Antagonist for Sr. Robert Napier he puts me to measure it and he goes by and takes the angles as I drew and set them down in his field-book but seeing that we were forced to make 14 station-lines and hilly ground too he offered to wager five shillings that I should not shut within five pole I offered to accept it in regard whereof at the last station I giving him the distance on the plot would needs set my Table to try what hopes that gave me and finding it stroke right upon my A I then offered to take his wager to shut within a yard but I miss'd not a foot We two had been four times Antagonists for the same men before one after another and our greatest difference was never but five pole at a time in sixty or seventy acres An Example We will give you now an example of the Field-book and plot of three closes lying together partly reall and partly supposed Chesterton Cambridgeshire June 21. 1656. Measured by me G. A. three closes called Church-closes I for A. B John Dampot for C. D. upon purchase S L. directour I begin with the East-close at North-West going contra Solem. Links in length Links in breadth A 0 5   200 a path  X right against a hedge 435 60 14137 B 900 station   907 out 7 15742  0 7   100 0 350  356 0 00000  560 into angle 30. 3150 C 563 station   568 0 out 120  0 5   200 40 450  200 10 these 2 breadths are both in one place D 656 out station 10. 4560. A 0 0   500 0 0000  740 meets A 15. 1837  745 out the N. W. close   enters    all the borders 40346 Subtende  CX 674  D X 756  N. W. close enteâ—s at 5 from A Westward A parallel by the North hedge of 15. next station-line AE Next station-line AFG A 0 0  F 650 50. stat-lin F E G 825 60   850 out 0.  GX  Turn South  G 0 30   75 25.3 d close enters 3d close enters   75 25   400 25  X 900   1200 140   1500 200  H 1550 station   1575 out   0 25   300 160   500 160  I 800 station 56  956 out 0  0 156   300 60   860 against C  1340 out 0. against X Subtend from out to X 1090. thence to l. 947. Here you see in this plot the station-lines being pricked lines are not drawn parallel to the hedges or out-sides of the ground if we should do so how many stations should we make in stead of that line I L Likewise we must make three for CD yet these are nothing to Hockley-brook Besides in working this way my station-lines cut one another more perpendicular then any other way whatsoever which is much to be regarded in working by the plain-Table The onely way to take an acute angle is with graduated instruments to take the quantitie of the angle and to calculate it by sines and tangents by the doctrine of triangles but he that goeth that way to work may chance to measure ten acres whilest another doth an hundred Adde hereto that I can more easily see every crook in the hedge in going round then any other way CHAP. IV. Of plotting at home and of severall ways THey that use to go parallel to the hedges do seldome use any field-book but plot as they go by the plain-Table because they suppose themselves to go in the hedges and therefore allow a parallel from the hedge but if at any time they cannot go parallel by reason of houses waters bushes or the like then they are much troubled and must of necessity plot as they go for want of a field-book whereby they spend much more time abroad both they their helpers then they need which they themselves might do in half the while at home besides that the least mist drives them out of the field for though they could measure by the chain onely which I am sure was never heretofore published by any but hath ever been thought a thing impossible to plot and prove a plot by of which God willing hereafter yet can they no way help themselves for want of a field-book also the form whereof being already laid down unto you together with the plot to which it belongeth being compared together will direct you better then many words yet because I desire to make all things so plain
that we may be sure you can stick at nothing we will lead you through one line and then turn you foot-loose First therefore if you have not yet done in the field and the weather serves your helpers are ready then take your plot off your Table and cover it with a new sheet of paper and away into the field lose no time there especially if you are far from home for you may plot cast at all times at home but you cannot always measure in the field But if otherwise then take your Table from his foot the socket from the Table your plot still upon it lay your field-book before you and take your scale and compasses in your hand and begining at A both of your book and plot seeing 5 which signifies 5 linkes in breadth is right against A on the right-side of the line and that you go contra Solem which gives the hedge you go by to B on the right hand therefore take those 5 with your compasses from off the same scale you laid down your station-line by and set them from A to the right hand which although you work by a scale of 8 or 10 in the inch you cannot take with your compasses therefore ghuess at them and then make a prick Next take with your compasses your next length on your left hand which is 200 that set in the station-line from A that is set one foot in A as you must doe likewise with all the other lengths and the other where it falls in the said station-line toward B but because there is no crooke of the hedge either inward or outward save only the path which shewes that there you cross'd the path therefore onely draw a stroke or two if it be broad cross the station-line Then take your next length 435 and set it likewise in the station-line from A towards B and for that right against it you have 60 breadth therefore take 60 and set on the right hand of your station-line and because I see also hedge it tells me that a parting hedge of two closes shot right against that 60 therefore I give a little touch with my pen till I come to set out the rest of it in the other closes My next length being my station 900 B is set out already Lastly because my last length is 907 that is 7 beyond 900 and that the breadth against it is 7 also therefore take 7 with your compasses and set it both forward and on the right-side and thus have you pricked out the hedges against this station-line Now you must draw lines with your scale and compasses from pricke to pricke and then with ink so these parcells between the line and the hedge must be additions to that within the station-lines to this first close but subtractions from the other where one station-line serves to two closes as that part of AB from A to 435 doth both for this and the next CHAP. V. Of calculation or casting up The figures or parts to be measured are either squares oblongs triangles or trapezias such as are compounded of an oblong and a triangle For the square and the oblong one rule may serve both viz. multiply the breadth in the length Triangles are of divers sorts we make use onely of two the rectangle and the scalenum the rectangle without the station-lines the scalenum within For the rectangle and trapezium one rule will serve both at least those trapezas which have two right angles at the station-line Add the breath at both ends together take half for the common breadth multiply it by the length these breadths and lenghts our book will give us For scalenums within the station-station-lines the way is thus Look how many angles your station-lines do make so many triangles will there be save two by drawing diagonall lines from corner to corner these diagonalls are fittest for your bases unless if it be a single triangle then commonly the longest side Take the length of your base therefore with your compasses and apply it to your scale and what it gives set it down take also the shortest distance between the angle opposite to that base and the base it self apply it also to the scale and what it gives set down also now take half the base and all the perpendicular or half the perpendicular and all the base and multiply one by the other so have you the content of that triangle But commonly where there are more angles then three one base will serve two triangles and add both perpendiculars together and take half of both and the whole base or half the base both them and multiply so have you the contents of both triangles And thus shall you cast up all your out-borders just as you found them by the chain many times the bases of your triangles also So that by this way it is impossible to fail much if any heed be taken whereas by the common way of plotting without a field-book it is almost impossible to come near the truth especially working by so small a scale as I have known some do mixing those crooks without with the triangles within so that they lose wholy the benefit of their measuring by the chain not taking one line as they measured it they trust rather to taking up their out-side lines by the scale and compasses then to their chain yet they will confess that with the scale of 32 in the inch which I have known a famous Artist use in no great ground that they cannot distinguish a quarter of a pole So a quarter miss'd at laying down and a quarter at taking up there is half a pole miss'd in the length of each perpendicular and as much in each base and these multiplyed I see not but a man may pase a ground as near the truth as they And thus in general We will now come to the particular parts and first of the outsides We shewed even now how an oblong must be measured by multiplying the breadth by the length and likewise the rectangle triangle and trapezia by adding both ends together and taking the half for the mean breadth Now therefore in the first close begining at A subtract the first length 0 out of the next against which you find a breadth viz. 435 there remains the length of that rectangled trapezium 435 and for the breadth of it add the first breadth 5 10 the next 60 it makes 65 the half whereof is 32 1 2 which multiplied by 435 gives 14137 the content of that trapezium to be set against the latter of the two numbers or breadths 60. Where note by the way that you shall never have any other fraction to multiply by but ½ and for that you must work from the left hand to the right saying Half 4 is 2 half 3 is 1 half 15 is 7 as here you see Then again take your last length 435 out of 907 for you have no breadth at 900 rests 472 the
measure that part upon the plot as in the former ground and add or subtract from your dividing-line as before save that here you need not remove the further end if the difference be but small but double the breadth at the last But if you rather think fit to remove both ends your best way is to do it first on your plot and make that perfect and then draw your new line quite through to the station-line on both sides But there is the mysterie how shall I give directions how in my absence to drive a streight line cross the wood from a mark in this station-line to a mark in the other on the other side through standing wood of 20 years growth and a hill in the midst as once I laid out 60 acres of Wilsteed-wood being 160 acres between Sr. Thomas Hillersden and Sr. Oliver Luke and another time in a wood at Hytchin But not to detein you If you work by the plain-Table look which side is clearest from impediments that you may go some 10 or 12 pole outward from the wood then set up your Table at that point in your station-line that your dividing-line falleth upon laying your index on the last station-line turn your Table till through the sights you see either your last station before that if it be not too near and having lengthned out your dividing-line as far as possibly you can lay your index upon that lengthened line turn your back to the wood sending one before some 10 or 12 pole let him there move to and fro sidewise as you shall direct him by looking through the sights and then at both your standings drive good stakes or lay stones or make holes so a line driven through the wood continued streight with these two will carry you to your first mark in the other side if you did not remove that end or if you did then to that mark where now you must set it so that look how much you removed it forward or backward in the plot so and so much must you remove it here also and then set a good mark here also But if when you have placed your Table on your station-line as before there is but little space left to draw your directing-line you may and indeed far better lay your index all along your dividing-line and by it direct your man CHAP. VIII To measure arable-common-field-ground IN divers countreys much arable lying in common fields lyeth in small parcells some places an acre some places half an acre and some places a rood and that so crooked that none will desire a plot of such ground yet for as much as a man in time may have his rood grown to half a rood by his neighbours plowing of it away and to find at any time afterward if it be so diminished or not and in what place you shall set it down in your field-book in this manner Chestâ—rton East-field in Broad-oake-furlong Begin on the East-side of the furlong three lands per estimate three half-acres TA on the East GD West coppy of Dame Anne begin North at 0 106 at 400 163. at 400 more 101 at 346 out 100 conteining 134500 that is one acre 55 pole 125 links One rood more in the same furlong RN. East J.D. West free of S. John's begin South at 0 24 at 400 27 at 300 more 28 at 244 more out 30. Content â—25526 that is one rood one pole feré Note that in this kind of ground where we say at 0 we mean two or three pole within the land 's end for there is no certainty in taking the breadth at the very end for the turning up the plow will get or lose egregiously Moreover in such ground the best way is the leader to take all the sticks anew every time you take a breadth which had best be not above 400 or 500 especially by the foot-chain at 16 or 17 pole as easiest for account unless the measure or decrease of the land requires otherwise CHAP. IX Of hilly-grounds IF a ground have the bottome and top-lines both level and both sides rising alike it is to be accounted but as a declining levell and to be measured as a level ground But suppose a ground be level at one end and both sides and rising in the middle and a hill rising along up the middle as the Lady Farmer 's Washrods-wood in Westoning-Parish in Bedfordshire or perhaps two hills rising one towards one side and another towards the other and a levell run through between them this is far more troublesome For if you shall begin to measure and plot your two levell side-lines and levell end-line first and then measure your line at the other end it will not lie between the two side lines by a great deal Again If you should shove out those side-lines that you might lay that line at the length you measured it you would drive the hedges into the adjacent grounds and make them too little as shall apear But if you are to give a fair plot of a Lordship where divers grounds border together your plot must be according to the form and yet you must write down the true quantitie too And because we cannot represent a round solid upon a flat paper therefore we must content our selves onely with the lines of level for our plot which how they are obtained we will here shew three ways First by a Quadrant or a semi-circle choose which you will they work both alike made for the same purpose made by Mr. Hayes at the Cross-daggers in Moore-fields the use of it is thus Suppose you stand at the foot of an hill and setting a mark at the top of equal height with your eye to the ground setting it level on your Table by help of the plummet you see through the sights the mark at the top of the hill you then look what degrees are cut in the limbe which I finde suppose 34 then I measure up so far as the hill keeps that scantling of rising suppose 35 pole keeping the edge of the standard at the 34 degree of the limbe I finde that 35 of the standard cut to the 29 line of the plate which is the line of level that you must plot though you have gone 35 all these I enter into my field-book If the hill still rise you must set again and as it rises or falls so you must alter so far as it goes level plot it as level and what is hilly plot it as hilly And what is here said of going up the same understand of going down But never go about to cast up by this plot though you have shut it never so true as indeed in such a case it is very ticklish therefore in this case we may well allow to miss a pole or two in shutting and yet account it well done too But for casting it up this way that it is measured helps not to the finding the true quantitie though the extending that last line doth
awl-point near one end and a sliding button to be moved pretty and stifly up and down and to be stayed with a screw-pin or wedge at any distance with an other short point in the end thereof Now we will shew you how to continue your plot out of one ground into another that so you may lay all the grounds of a Lordship together in one entire plot by the chain onely and that we will do by severall rules for the understanding thereof we will refer you to the plot in the latter end of the third chapter as also in the end of the book The knowledge whereof consisteth in four rules in the obtaining the first station line in the close which you go unto As for example First Suppose I would go out of the first close at A and would plot the station-line AG now because in plotting these kinds of grounds you must always reduce all into triangles therefore standing at A you may measure two chains length in the line AF or AG likewise two chains back-ward from A towards B in the line AB in the first close then measure the distance between those two lengths and plot them after this manner First your best way is though you have measured but two chains length a piece yet in stead of two take the double if the station-lines be long you may triple that distance setting one foot in A and extending the other towards B there make a prick in that line and tran from thence with that wideness where you think the line AF or AG will fall then look what the distance was between the two lines at the end of your two chains a piece if doubled before then double again that distance upon your scale and set it in the tran from the line AB in the first close to the line AF in the second and draw the line AFG through that prick ad infinitum Thus have you got a line in the second close by help of a part of the line AB which in this kinde you must always take viz. that station-line whereof the whole or part belongs to both the closes But because in this case you must always mete through the hedge from the two chains of one close to the two chains of the other therefore to avoid the trouble of cutting a hole through the hedge if there be ever a gap gate or stile near unto those lengths you may take more or less of those two lines as you please now because here is a gap at two chains and an half from A in the line AB you may measure two chains and an half of either of them or two and an half in that and three in the other as you please and measure the distance upon the ground between those two pricks then you may double all three distances upon your scale as afore and set out the proper distances between those two pricks as afore and then draw your line AG upon your plot in the second close But Thirdly because we have measured the distance between A and X in the first line which is one side of the triangle of that second close and likewise have measured from A to G on the second side and have a gap also at X therefore if you measure GX you will have all the sides of that great triangle which you may use as afore-said First you have the line AX already placed Secondly take the length of AG with your compasses upon your scale and with that wideness set one foot in A and tran where you think G will fall Do likewise with the line GX taken also upon your scale set one foot at X and the other is the foresaid tran and there is your center G. And after the same manner may you go out of that close into the great close from G by help of the line AG. Now having the line AF or AG you may easily set out the triangle AFE as you did AXG. Likewise you set out the triangle that is between the the line XG and the hedge between the two closes onely by the distance of G to the entrance of the great close A second way of going out of one close into another is when I have a station near the middle of a station-line and that there I would go into another close For example Suppose I would go out of the great close into the first close right against the station-line BC in the first from L in the station-line of K then when you come right against BC the station line lengthen that line BC back-ward into the great close from L to M two chains length measure also two chains lengths in the station-line IK and measure two chains lengths from L to I back again and measure the distance between two chains of the one and two chains of the other and that gives you the quantitie of the angle KBC Then from the line LK you may take from your scale four chains length and you may tran from the line KL towards the line LC or BC with one foot set in L and double the distance of the two pricks in the other close and take that with your compasses and set from the line LK to the LC and where it falls draw the line LC ad infinitum After the same manner might you have drawn a line by the South-side of the hedge by BC or LC Also so might you at X in the first close have gone either into the great close or into the little close by drawing a station-line on which side of the hedge you will A third way is by continuation of such a station-line as shoots upon the corner of a close and thus suppose you would go out of the great close into the little close at K if you had but continued your line LK to A and this is the easiest way of all A fourth way If on the West-side of the hedge AK there were a spinny wood of two or three pole broad all along by the sides thereof and that you desire to go out of the first close into that little close but there is no gap save onely you can strike a squire-line from the station-line AB at either end of A K then may you both at A and at X erect a perpendicular into the first close ward and then may you continue those two perpendiculars so far as you shall need them till you are free from the spinny and may draw a line from one to the other by the spinny side and truly plotting out either perpendicular from the last station-line CHAP. XII To measure a wood by the chain onely BEcause a wood cannot be measured on the inside and herefore no subtendents can be taken as they may in pasture-ground we will therefore endeavour how to do it by taking of angles with the chain But in all this that hitherto we have spoken of measuring by the chain onely we would have you to understand that we
have onely spoken spoken of measuring and plotting of the station-lines for as for measuring casting up and plotting of the out-sides that is the same as before serving as well to this as to the Table And as for measuring hilly-ground we have shewed before in chap. 9 that also may be measured by the chain alone save onely any sorry board with one streight edge it matters not greatly whether it have a streight edge or no. If in measuring the out-sides you go upon a station-line as in the line AFG of the second close chap. 3 from which you desire to strike a perpendicular into an angle First ghuess at the place so near as you can where it will fall there set one of your counting-sticks set another 80 links backwards directly in the station-line another at 60 from the first stick into the angle then let one hold one end of the chain at the stick that was set backward and the other at the stick set in the angle-angle-line if they two meet just at the chains end I mean Gunther's chain of 100 links then is it a true perpendicular into the angle if it fall short you are not far enough if gone then you are too far If a ground be very large or bushy you may measure it on the out-side like a wood or measuring a chains length or two of each station-line and their subtendent on the inside from the angle Thus have we shewed you how to measure all manner of ground by the chain onely for which I expect as much thanks at the instrument-makers hands as Culpepper at the Colledge of Physitians And indeed I was determined to have published it above fourty years agone had not Mr. Allen and Mr. Thomson disswaded me from it upon this reason That if ignorant people see the most famous Artists go so to work they will be ready to judge that he that goes with a plain pair of poles and a square board to set out a square withall is a better workman then he And indeed I cannot deny but that they judge according to their tools which they see rather then according to their skill they see not Whereupon I have forborn till now considering I am even dropping into my grave and considering that my Saviour would not cease casting out devils because he was thought to do it through Beelzebub no more will I longer forbear this it being so lawfull and honest and beneficiall to a Common-wealth And truly had I regarded mens sayings I must have given over surveying long ago or else to give over profession for that I was judged by no small fools to work by the devil for that I could tell a distance before I measured it CHAP XIII Of taking distances by the chain onely ALthough we have shown the measuring of all manner of land by the chain yet since we are speaking of the use of it I hope you will not think your time ill-spent to read a lesson or two more that will be effected by it Let there be two forts C and D of a good distance asunder beyond a river a mile or two broad to tell the just distance how far they are asunder how far each is from A and each from B and the breadth of the river First I draw the line AB 40 pole a tenth part at least of the greatest distance let it run parallel but streight by the river 9 or 10 pole off then from AI set out both backward from A to E directly backward in the station-line six pole and six from A to F in AC line then E and F are four pole asunder Also I measure from B to G and from B to H 6 a piece and 6 between them also and from A toward B and D 6 piece and they are 4¾ asunder and from B toward A and C 6 apiece they will be 3½ asunder but it is best to draw your station-line with a very small scale but set out your angles with a very great one then draw AD and BD till they meet at D likewise AC and BC till they meet at C and a right line from C to D for the distance of the two forts and another from B to K for the breadth of the river so shall you finde all your desired distances of you see them set down upon their lines your station-line AB being your common scale viz. 40 poles for if you take that line with your compasses look how oft you finde that length in any of the other so many furlongs or so many times fourty poles are in that line and what is more take it with your compasses and set one foot at A and the other forward in the said station-line or scale and it gives the odd poles But if you would onely take the breadth of the river KL observe a mark on the farther bank as at K then in your station-line at 8 pole long and 8 from the river measure their distance and plot that triangle continue your cross-line toward your mark then lengthen your station-line to a fourth or fifth part of the breadth of the river thence also measure 8 pole right toward the foresaid mark and 8 in the station-line backward measure their distance and plot it continuing the mark-line till it meet with the other so your scale to both the other will be the station-line as afore CHAP. XIIII To take the declination of any streight upright wall for Dialling by the chain onely TO do this you must finde out a meridian-line by any of these ways following First setting your back to the wall right under the plain where you will have the diall look by some true clock or watch just at noon where the sun is and set up two sticks a pole or more asunder in a streight line between you and the sun then go to the furthest and look back to the wall and just in that line make a mark on the wall for there shall you plumm down your meridian-line of your dial But yet take not up your sticks whereof let the furthest of them be 50 links from the wall Secondly if you neither have help of watch nor clock take a smooth board and lay it level stick upright a wier of 2 or 3 inches long in the midst of it and about nine of the clock in the morning lay the board at the foot of the wall aforesaid mark where the shadow of the top of the wier falleth there make a prick then take out your wier and set one foot of your compasses in that center and open the other â—o the former prick and there draw a circle and then set up your wier upright as it stood before neither deeper nor shallower then before you may apply a squire to it to see it stand upright or measure with your compasses from the circle to the top of the wier if it be alike all 4 ways If it be right set up two sticks right in a line between it
and the Sun as afore Then again about three a clock in the afternoon watch where the Suns shaddow falls just on the same circle again and then set up two other sticks so that they may meet in the same centre divide the space between the two furthest sticks into two equall parts and mark that for your meridian-line But lest the Sun should not shine when it comes to that circle you may make severall circles upon the board and stick up marks where the Sun comes at them forenoon and afternoon If both these ways fail this third way is better then either of them In the evening go Southward of the place where you would haue your diall three or four pole turn your face Northward moving Eastward or Westward till you see the North-pole and the place where you will have the meridian of your diall both in a line which by looking over the house you may the better do if you get one to hold a pole a slope with a line tyed to the end thereof and a plummet to it If now the line the meridian-place on the wall and the North-pole are all in a line you are right there stick up a stick till morning another right behinde it for just there is your meridian-line Now to know the pole you may easily ghuess at it near enough for it is a point in the heavens in a right line between the hinder horse of Charles-wain called Alliot and the polar-star so far off fâ—om the pole-star as the pole-star is from the next star to it so that if Alliot be just beyond the polar star then is the polar-star full North è contra A fourth way is this in some plain place near hand where you may see both ways set a mark go South two or three pole then move Eastward or Westward till you see the pole-star right beyond the first staff there set another or rather pitch two good stones like grave stones in Church-yards for so they will not onely serve for this business but also give the hour of the night to a minute by knowing the right ascention of the Sun and stars The use we make of it here is double first it helps us to set out the meridian-line every where near hand for if standing here at the North stone you see the Sun right over a stick or pole holden at the South you run presently set your back against the wall where you would have your diall and set up two sticks between the Sun and you you have a meridian-line desired Having a meridian in some open and plain place to finde the Azumeth set up a stick at the south-South-end of your meridian-meridian-line measure back in it 50 links there make your centre A thence measure 50 forward in the Sun-line measure the distance of those two fifties and plot it then take 60 off your scale of chords and do as in the last rule Having the Azumeth to finde the angle of the wall and Sun by help of the last figure Sometime you are in such a place where you cannot set out a meridian-line yet you may always set out an Azumeth or Sun-line which elswhere I call the angle of the wall and Sun Now finding your Azumeth as in the last rule come presently from thence not staying to cast it up or plot it but presently measure 50 by the wall and 50 in the Sun-line and their distance and then plot both the triangles and finde the degrees of both angles at the centre as afore so have you both the Suns Azumeth and the angle of the wall and Sun Then making a circle with two cross diameters first set out your Azumeth from the South if it was taken in the morning then on the East if in the after-noon on the West Then always reckon backward the angle of the wall and Sun in the course of the Sun and from thence draw a line through the centre representing the wall-line as in the last diagram the distance between that and the East and West line in the circle is the declination of the wall desired And although the Sun be newly gone off the wall or not yet come on by help of the shadow of the end of the wall and these former helps you may finde the declination Onely in stead of setting your Azumeth backward you must set it forward in the course of the Sun if you take it before it shines on the wall And all this may be done by a two-foot rule or yard or a boyes cat-stick CHAP. XV. Of colouring and beautifying of plots IN beautifying of plots it is necessary that you draw a square round about the plot the upper-upper-end whereof shall represent the North-side the nether line the South the right-side line the East but you must help your self to these by taking a meridian-line first in the field and drawing a meridian-line through the first plot Secondly Examine your former plot how many chains or poles your plot reacheth from North to South and from East to West and thereby make choise of such a scale that you may lay the whole Lordship within the said square according to the Northing and Southing and distance Or else you may draw your plot first by what scale you will and then draw the square afterward Thirdly Fill the out-borders between the square and the demeans at least such as border next to the demeans with the bordering hedges and names or owners names of the grounds Fourthly Whatsoever you write write it from West to East unless it be the proper name of some river or high-way or such like For if the North be upward the West will be on the left hand Fifthly Describe all houses ways rivers Churches wind-mills arbours great lone-trees gates stiles c. that fall within your plot as also the Lordship-house with other edifices in a corner by it self and the Lords coat in another corner the house being drawn in prospective Sixthly Describe at the bottom the scale that you drew it by adorning it with compasses ovalls squares and compartiments c. Seventhly Having drawn all your severall grounds and distinguished them with their hedges it will not be amiss first to pounce over the paper or parchment with some stanish grain and burnt Allome and a double quantitie of pounced rosen both finely searced and lightly pumiced thereby to preserve the paper or parchment from through-piercing with the colours Then lay on your colours in manner following being first ground and bound with gum-water very thin and bodiless Arable for corn you may wash with pale straw-colour made of yellow-ocre and white-lead For meadows take pink and verdigrease in a light green Pasture in a deep green of pink azure and smalts Fenns a deep green as also heaths of yellow and indico Trees a sadder green of white-lead and verdigrease For mud-walls and ways mix white-lead and rust of iron or with ocres brown of Spain for white-stone take umber and white water or glass may
To take terrestrial distances by the plain-Table or Pandoron aâ— by the Table WE have spoken of taking them by the chain onely in chap. 13. between that and this there is very little difference We will here suppose the same oppositions as there viz. two houses beyond a river between which I desire the distance also between each of them and each of my stations the chiefest difference is this that by this your best way is to have your station-line as near the river as you can which let be as before AB 40 pole long First set your â—nstrument at A and turn the sights to DC and B and draw their lines measure thence to B 40 poles there make a prick but lay down your 40 pole with a very small seale if the distances be long so that the 40 pole be little above an inch long Then set up your Instrument at B laying your index on your station-line of your plot turn it till through the sights you espie A then fasten your Table and one end of your ruler turning upon the center B turn the sights first to C then to D then draw lines whose intersections with the former will give you all your distances desired CHAP. XIX To do the like by the Pandoron as it is a Quadrant or by any graduated Instrument LEt the same example be propounded as afore and let your station-line be AB 40 pole as near the river-side as you can I set up the Quadrant first at A where I find BAD 110 degrees and CAD is 50 degrees likewise set up at B then CBA is 104 whereof CBD 50 this station-line 40 and these angles thus plotted extend you lines till they meet and their intersections will give you the desired distances as afore yet if you will bestow the time and pains to cast it up by the doctrine of Triangles you may come somewhat nearer First for the triangle BAD seeing that BAD is 110 degrees and the angle ABD 54 which make being added 164 which take out of 180 rests the angle ADB 16 degrees Now in the same triangle having all the angle and the line AB to finde the side AD. As the sine ADB 16. Comparithmes 055966 is to AB 40. 160206 So sine 110 degrees that is sine 70 997.99 to 136 3 10 BD. 213.61 Also to finde AD As sine ADB 16. Compar 055966 is to AB 40 pole 160206 so sine DBA 54 degrees 990796 to 117 4 10 AD. 206968 Then in the triangle CBA CBA is 104 and BAC is 60 these added together make 164 which taken out of 180 leaves the angle BCA 16 degrees Now to find BC. As sine 16 d. Compar 055966 to AB 40 p. 160206 so is sine CAD 60 993753 to BC 125 and 7 10 209925 Also to finde AC As sine ACB 16. Compar 055966 to AB 40 160206 so sine 104 that is sine 78 998690 CBA to AC 140 8 10 214862 Lastly having the two sides AC 140 8 10 and AD 117 4 10 and the angle CAD 50 in your triangle CAD to finde CD As the summ of the sides 258 1 10. Compar 658804 to the difference of the same sides 23 4 10 236922 so is the tang of ½ the sum of the angles unknown 65 to the tang of ½ their difference 11 degrees 033133 which add to 65 d. ½ facit 76 the greater 928859 angle D. But subtracted from it makes the angle 54 degrees and then as sine 54. Compar 009205 to 117 4 10 206967 so sine 50 degrees 988425 to CD 111 2 10 204597 CHAP. XX. Of altitudes and distances celestial by the Pandoron or Quadrant FOr taking of altitudes and distances celestial or altitudes terrestrial it is a matter of necessity that besides your Quadrant and three-legg'd foot you get also a neck or piece of close-grain'd wood whose Diameter may be about three inches or somewhat more Let the nether end be turned with a socket that instead of the socket of your Table you may put on that so that it may turn on the top of the staff as the socket doth having also a screw-pin in the side of it to hold it at any situation Also about two or three inches below the top turn it like a bowl in the midst whereof bore an hole with an inch-wimble to which fit a pin of the same wood so hard both driven in and glewed in that it stirs not but let one end thereof be so big and so long as to fit the brass socket that the socket may turn very stiff about it and let the little end of the pin reach past the hole of the bowl almost the depth of the socket and then you may fit that end of the pin either to that or any other Instrument by glewing upon it a piece of its own wood turn'd like a little salve-box then upon this pin put the socket of your Instrument and work as followeth To take the altitude of the Sun Take the string of your plummet in your hand and apply it to the edge of your Instrument and hang it plumb then screw it fast then move the ruler with sights up and down till the Sun shining through the sight next the limb the shadow of the thread run streight along the rule then look how many degrees are between the edge of the rule and the bottom of the limb so many degrees is the height of the Sun and this you may do by setting it on a stool To take the height of a star To do this having hanged your Instrument on the pin of the neck and plumbed one edge by the light of a candle look by the edges of both sights moving the ruler till you see the star desired in a streight line with them both then screw the ruler and take down the Table accounting the degrees from the bottom to the edge of the rule for the height of the star To take the distance of two stars howsoever situate If both be near the Horizon and near of one altitude and within 90 degrees of each other you need not use the neck at all but onely lay your ruler on the beginning of the degrees then screw it and turn the Table till by both sights you see one of the stars then fasten the Table and move the sights to the other star and the degrees on the limb of the fiduciall edge of the rule gives their distance If they be both in one and the same half of a vertical circle take both their heights as afore subtract the lesser altitude from the greater you have your desire If they are in severall halfs of the vertical circle take the complements of both their heights and add them together actum est But if they lie aslope and yet are within 90 degrees one of another then besides the foot and Quadrant or Pandoron get you two round sticks as big as your thumb about six foot long a piece sharpen their little ends
as they cut mows or hay-stacks with both like sithes and stabs also wheel-barrows and half-inch boards of six or seven foot long a piece If this coat of weeds be very soft you were best to nayl two boards together with ledges like a door but if it be any thing hard let them go single Then begin with your crones or drags and cleanse the out-sides with them first as far as you can reach and let the barrows carry it away out of your way then take your boat and spret and for want of a boat take a Brewers cooler and let two folk go into it and row your selves to the crust and laying your boards on it and you standing on them cut with your sithe pieces as long and broad as the board then take up that board as you stand on the other and remove it beyond it then take you the crones that stand on the bank and having fastened your haling-line both to the crone and to the stale of it by knitting a knot at the handle-end let them on the bank draw out those pieces which that they may do the more easily they may level a place about an handful above the water and pull them thither and then cut them smaller with their stabs and then draw them up Now then having thus gone round and cleared it from the sides round about pitch all your crones into one side of the core or crust and trie if you can draw it to the bank-side for these kind of cores never grow to the bottom especially if the water be deep which if you so draw it then may you standing on the bank finish all with your crones But if you cannot move it then with your sithe-knife and help of your dores and boards you may slit it all along either in the midst or as much as you think you can move at once But now because you must move your boards and dores end-long which is harder to do then side-ways your best way is to have a hook at the end of your haling-haling-line and make a mortes at one end or both of each board and thus put the hook in the mortes of the hinder door and raising it a little at the end with a couple of chisils or such like draw it till it is entered upon the neather dore then having a board lie by the side of it stay your self on it till the hinder be drawn along upon the other and lie foremost and thus may you divide and draw piece after piece till you have finished CHAP. XXX Of cleansing of water SOmetime you are to bring water to an house but you have none but such as comes from noysome places now to purifie such water if you make a trench of a foot and an half deep and three or four pole long the longer the better and fill it a foot deep with hurlock or clunch cut in pieces as it were for the lime-kill then fill it an handfull higher with pebles then fill it up with gravel or earth it will so purifie it that it will be fit for brewing or the pot or laundressing or any thing else if you cannot get hurlock content your self with pebles Also it greatly mendeth water in a pumpe or well first to cleanse out the mud and then to put in clunch into it It will likewise purifie the water very much if you would lay clunch or hurlock as high as the water riseth in your well in the same form that they use to lay their bricks so will the water cleanse it self by draining through the body of the clunch CHAP. XXXI Of quenching an house on fire THe Instruments for this purpose not to speak of the water-squirt which will throw a whole hogs-head of water to the top of an house at once for that such are scarce to be had save in some great Towns or Cities are pikes spits mawkins pike-staves forks wet-blankets ladders buckets scopets pails c. and the materials water coal-dust turf-ashes wood-ashes sand horse-dung dust dirt and in extremity even drest-grain it self I know you will think it strange that I should mention pikes and spits dust sand and ashes but I speak on often experience that four men that know how to use these things will sooner quench a fire then 100 that go to work with ladders and buckets to strip houses and hooks to pull them down It 's a misery to speak it when the rude multitude are once come together every man will have his own way If it be a dwelling-house some will busy themselves to carry out brass pewter but their chief aim is at the monychest whilest others wait to take it of them and carrie it away others perhaps of more honesty but less wit will be ripping the house and so let the fire have the more air to burn the more violently that whereas they think thereby to save other houses that are near to it they use for the most part the onely way to fire them for the greater the flame is the more is the danger and the farther the sparks of fire will flie And now if you will vouchsafe the reading which is no great labour for you I shall endeavour God willing to give you such directions whereby you may with least loss least help and most speedily quench any fire wheresoever it begins or howsoever it comes The first rule is this If it be in house or chimney do not by any means open any vent to let it out especially upwards but rather stop all the holes you finde If the foot of a brick or stone-chimney be on fire discharge a pistoll twice or thrice upon it so foot and fire and all falls together If it be a wooden-chimney and that all the timber both ground-sells studs mantle tree beams and all are on fire at once then first with your pike-staff fork or spit rub down all the coal then throw on water and then ashes and all is done And thus did I my self all alone quench a fire at Westoning in Bedfordshire where coming that way accidentally and meeting a woman coming out of a yard wringing her hands and crying I asked her the reason but she gave me no answer whether it were for that I was a stranger to her or whether for grief she could not speak I know not but away she runs as fast as she could I fearing some such matter ran into the yard but finding the door lockt and hearing withall a fluttering of fire I took up an hogs-trough which lay there and ran against the door and broke it open and went in where I found a buck of clothes standing on a tre sole and a great many turves under it almost burnt out yet the buck had no hurt but they had fired the end-groundsels studs and all the timber of the chimney I having been at the Fullers earth-pits not far from Oburn to survey them had the foot of my plain-Table in my hand wherewith I rubbed down all the