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-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-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-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-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-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
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-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-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 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
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
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
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-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
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
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
ground of nine or ten acres for it often falls out that if a piece of ground be ten acres yet all of it will not be overflowed so that if you bestow any great cost we may say materiam superabit opusâ— yet this I have seen in one of these dry years in a meadow near Hartford that one man having a piece of ground encompassed with the river flowing it made five pound of an acre of his first crop where his neighbour made scarce twenty shillings an acre of the ground adjoyning although naturally in other years before as good Yet this is not comparable to land-flouds for these partaking of a slimy and muddy substance being brought into meadows or pastures in the spring either by drains dams turning of town-ditches sewers high-ways streets filths do both moisten and fat them wheras the river-water fats nothing so much as Virgil hath it huc summis liquuntur rupibus amnes Declivémque trahunt limum And in another place Et cùm exustus ager morientibus aestuat herbis Ecce supercilio clivosi tramitis undam Elicit illa cadens raucum per levia murmur Saxa ciet scatebrÃsque carentia temperat arva And doth not all the world know how the river Nilus fats with his slime the whole land of Egypt But now having by drains and dams brought your water to the highest part of the ground that you would slow you shall cut a little trench as level as you can ghuess by the eye which in your ground let not be above nine inches broad and seaven or eight inches deep so going not above a pole at once laying your turves on the lower side of the trench and close by it with the grass downward that if you think good you may put them in again or carrie them away and now let in so much water as will fill up that trench If you have the water run over at the last end a little it is the better that so stopping your trench 〈◊〉 a turf your water may run over in any place But if you are risen so that the water will not follow you then you should have a spade for the nonce with a long crooked handle crooking up like a fire-shovel that therewith you may deepen your trench and take out the moulds and then go a little lower the next time still making the water to follow you as you go to the further-side of the ground then according as the ground falls you may make a cross-trench one or more in the middle or at ends four or five pole downward and at every four or five pole make trenches the same way you did at the first till you have done so that you shall need no water-level for this work unless perhaps you need it to try whether it will come to the ground or no. If you are to bring it over some ditch or brook where the water is lower then your water-way then must you either make a bridg over it or else shoot four boards and nayl them together and make a trough which may lie both under the ditch and through the mounds of the ditch CHAP. XXVII Of drayning of grounds THe drayning of grounds is often found to be as advantageous and profitable not onely in arable but also in low meadows and woods and bogs upon hills as the flowing of them if not far more by reason more grounds for the most part will be drained then flowed both in less time and with less charg The Instruments for this work may be a plow spades scopets shovels and bills and forks In some Parishes they have a town-plow that will hold eight or nine yoke of oxen and a couple of horses afore for boys to ride on to guide them and three or four horses with drivers on them others to hold the plow one one while another another while booted up to the middle others following with bills forks spades scopets shovels that if any grass or turf-ground fall in after 〈◊〉 plow some may cut it to pieces with their bills and others throw it out with their forks but in plowed grounds with spades scopets and shovels thus yearly about All-Saints do they serve their pease-stubble barley-stubble and low meadows especially commons But this plow must have a piece of wood either screwed or cotered to the right-side of the beam somewhat toward the fore-end of it to make another coulter-hole that in sward-ground you may put in another coulter that may cut both sides of the furrow and let the ground-wrist be five or six inches broad and the broad-wrist be longer and stand out broader then the ground-wrist by an handfull to throw both earth and turf a good way off But if you are in clay-ground you may make a broader point then on stones or gravel but howsoever let there be a whole pan and a finne-share Thus if you will make any new drain ditch for quick-setting brook or river first set up your mark at each nine or ten pole on both sides for the riders to guide on the horses then plow once all over that breadth and throw out the moulds then set your horses single and with any other lighter plow plow again and throw out till you are deep enough thus may you do more in an hour then in three days otherwise Likewise I have known divers high-ways where one furlong hath abutted upon them and another run long-wise by the side of it where the way hath not been above a pole broad that the plow continually carrying out moulds upon it hath so raysed that linsy-side that it hath been so linsy that not a loaden cart hath gone on it in harvest or hay time since the memory of man yet the most necessary harvest-way this have I mended and made level with mine own plow and mine own people in two hours a quarter of a mile together and the like have I done to raise a road-way in the middle by plowing and throwing up both sides Also I have known one Mr. Field of Aspley-bury in Shidlington parish in Bedfordshire who there with his plow made a larg moat onely by plowing and throwing out the moulds and making a ware for the horses to go in and out The same man also being at an especial friends house in Hartfordshire his advice was requested about cleansing of a brook which was filled with stones driven down the hill by land-flouds neither could they dig it with spades nor strike in a mattock if they did the water would fly in their faces and the cold water overflowed the banks winter and summer and spoiled all about he gets a strong plow with a narrow-pointed share and plows one hour in the fore-noon and gets good store of labourers with forks and shovels and throws out what the plow had raised and then to plow another hour in the afternoon and thus made quick speed without trouble or let Another time the same man stock'd up a wood and having onely stockt up the