DIvers are of that opinion, That if two pieces of land are of equal peripherie, that those two pieces are both of one and the same content. But that is easily discovered false; for let one piece of land lie in a true square; being a quarter of a mile square, or 80. poles square, viz. a mile in all; the content is just 40. acres. For every one knowes, that 40. pole long, and 4. pole broad; or 80. pole long and 2. pole broad, make an acre. Therefore 80. pole long, and 80. pole broad, must needs make 40. acres, and that 80. times 80. is 6400. pole, which divided by 160. (the poles in an acre) is just 40. acres. But in a Circle of a mile about, viz. 320. pole, if (according to Archimedes) we multiply the Circumference by 7. which is 2240. and divide it by 22. it gives 101 11/22 the diameter: now then, if we multiply half the diameter 50 and 20/22, or 50 and 10/11 by half 320. the Circumference, viz. 160. (which are also the poles in an acre) first 160. by 50. is 50. acres: then multiply 160. by 10. facit 1600. which divide by 11. it gives 145. pole and [...]/11. so that the Circle contains more then the square by more then a fifth part. And as in land, so in timber; and therefore that must needs be a false way of measuring round timber, to gird it about, and to take the fourth part thereof for the square, as plainly appears in this; that, when they have hewed it, they make more of it then they made before. Also a square is more capacious then an oblong; for every Shepherds boy can tell, [Page 2] that if he hath but 24. hurdles in his fold, and that it goes upon a rood, where he hath b [...] [...]ne at each end, and 11 on each side; his sheep will lie thicker a great deal, then if his fold goes six on each side, and end: though he knows not the pro­portion, yet he perceives a sensible difference; and so well he may as being more then three to one ods. For it is as 11 to 36. for once 11. is but 11, and six times six is 36. And for want of this knowledge many surfeit their sheep in summer, by lying too hot. If I may advise, they shall never lay sheep thicker, then to allow 20. foot of ground to each sheep, so that if you have rod hurdles of 8. foot a piece, viz, 64. foot; in one hurdle square I would not put above 3 sheep and ½; nor in slat hurdles of nine foot long, above four sheep; and so doing, if your 24. nine foot hurdles go square, it may hold 96. sheep, and your 24. eight foot hurdles 84. sheep.

Another great errour I have known maintained by a great Rabbi Surveyour; that in measuring a triangle, it holds good to take the half of any side for the base, and the whole per­pendicular from the angle opposite to that base, to the middle of that base, & vice versâ, and their product to give the con­tent. But this is demonstrated to be false thus. In this oblong figure ABCD, let the two sides AB, and CD be 30 a piece, and the two sides AC, and BD 40 a piece, so 30 multiplied by 40 gives 1200 the content of this oblong, which is divi­ded into two rectangle triangles, by the Hypotenuse AD, which two triangles ABD, and ACD are both equal; for that the sides AB, and CD are equal by construction, also the

AC and BD are equal by construction, and AD is common to both; therefore the two angles B and C are equal: likewise the two triangles ABD, and ACD are equal; per 4. prop. Element the 1. Axiom. the 7. Qua ejusdem sunt dimidia, inter se sunt aequalia: therefore either triangle must contain 600. Now in the triangle ACD, to discover the falshood we must first finde the length of the [Page 3] line ED thus. First, square the line CD, 30, facit 900. also square CE, 20, facit 400; then C being a right angle, and we seek ED, the Hypotenuse, we must adde 400, and 900, facit 1300, whose square root is ED 36 [...]/ [...]3, multiply this by 20, the half of AC, facit 721, 1/10, the content, too much almost by a sixth part, being it should be but 600. and so you shall finde it, if you multiply AC, 40 by half CD, 15. for the oblong AFHC, is equal to the oblong FBDH, therefore it is the half of ABCD Also the triangle DGH, which is taken out of the triangle DCA, is equall to the triangle AFG, added to it.

Or if you will, make AD the base, upon which you may let fal a perpendicular from the angle C; but then it must not fall on the middle of the line, except it be the base of an [...]sosceles trian­gle, but if you will needs finde the true place of the field where the perpendicular must fal, I know no instrument you can work by, be it plain-Table, Theodelete, Quadrant, Circumferentor, no not so simple as the chain alone, but you may set out a square by it; therefore set up your instrument in the station-line, go­ing forward streight in it, till you ghuesse that a line out of the angle will cut your sta [...]n-line squire-wise; which if you think you are far enough, set up your instrument there and first let it behold the mark you came from; if it doth not then behold also the mark you go to, you are out of your line, and must re­move it side-wayes which having rectified it that way, then see if it look right into the corner: which if it do, it gives you the place in the station-line desired, which is 32 from A, and but 18. from D, viz. at I, which is thus made good. As the base 50. is to 70. the summe of 30, and 40. the two other sides AC, and CD; so is the difference of the same two sides 10, to 14. which 14 being taken out of 50, the whole base, the perpendicular shall fall on the middle of the remain 36, the half whereof is 18, to which adde 14, it makes 32 from A to I, as afore; and that taken out of 50. leaves ID, 18, as afore. Now to finde the length of the perpendicular CI, if you measure it in the field you will finde it 24 pole, which is thus proved. Take the square of the side AI, 32, which is [Page 4] 1024. out of the square of AC, 40, viz. 1600, rests 576, whose square root is 24, the perpendicular desired. Now if you multiply 50 the whole base by 12. the half perpendicular: or 25. the half of 50. by 24, you have 600, as afore. Thus you see it double proved, that this way of taking the middle of the base for the fall of the perpendicular, is for the most part an extream false way: and the sixth part of the ground and more may be easily got and lost hereby: insomuch that I have known by this very errour above twenty pounds got and lost in one day between the buyer and seller, severall times, and by severall men. But whether Balls of London used this way, or worse, I know not, who was sent down by the Lady Morrison, to survey a Farm at Hardwick near Shefford in Bed­fordshire, whereof she had let a new lease for 21 years to one Childe at five shillings the acre. Balls makes of it 400 acres just: Childe thinks himself wronged, sends for me, desiring me to measure it, not saying a word to me upon what terms, or that it had been measured before. I set to work, and having done, I give in mine account for 322 acres. He asked me if I would justifie it. I told him, I accounted him as my friend, I would stay for satisfaction a twelve-moneth; let him keep my plats, if in that time I were disproved two acres, I would have nothing for doing it. Whereupon he works to the Lady to send another to measure it; but durst not let her know he had measured it, but that his reapers, and mowers, nor his seed ne­ver gave it for so much. He prevails with her, she sends ano­ther; he measures it, knowing as little of any mans measuring, as I did of Balls. Upon his account we two differed but one rood in the whole thing, which he had made it lesse then I did, by reason I measured half Shefford-brook more then he did. So I sav'd him 19 pounds ten shillings per annum; which if it had been yearly payment, at ten in the hundred, as money was then, compound interest came to above 1200. pounds, but being half yearly payments, nine pounds 15 shillings, half yearely, 42 payments at five in the 100, which was the com­mon reckoning both then and how still for half a year, comes [Page 5] to above 1300 pounds, a good Farmers estate. Therefore it behoves every man that hath, or may for himself or friend have occasion to let or hire, buy or sell land or timber, not to go on other mens legs, nor to see with another mans eyes, that have such easie means to attain the skill of it themselves. I make no doubt but that there are many Gentlemen, who have spent much time in the Universitie in Musick, yea, and other studies too, do wish at this day, (and more would wish, if they could see it) they had at least spent some of that time in the Mathematicks; whereby they might have benefited both them­selves and their Countrey: which in commendations of it, Pi­tiscus in his Preface to his book Geodaeticorum saith, Socrates hunc principalem Geometriae finem esse statuebat, ut agrum pla­num metiri, divideréque possit. I have seen some spend eight years in learning Musick; if they would bestow but two years in the Mathematicks, it would have done them more good, and they might have done the Common-wealth good. Of all the seven liberal Sciences that may best be spared, as least bene­ficial to a Common-wealth; and for my part, I had rather (if you will believe me) that my feet could pace 1000 acres of land of mine own, then my fingers to play 1000 lessons on the best Lute in the town, though I might have it for my labour; and he that is not of my minde, it's pitie, if ever he have 1000 acres, but he should change them for a fiddle. Recreation, I con­fesse, is good; but I would not have it made an occupation. They will account it small recreation hereafter to be able to say, ‘Post habui tamen illorum mea seria ludo.’

Divers such falsities I have seen; but I am loth to digresse too much. Divers other false ways there are; but I had ra­ther I were come to lay down true ways, then to discover er­rours. Therefore that we take not a false way to our purposed end, we will ride streight on to the next town; viz. the un­certain ways: where we must stay a little, and give our pen drink too, that so we may the easier finde the true way in such uncertain ways.

First, it is no certain way to lay a great deal of land upon a [Page 6] little paper, as to work by the scale of 32 as many do, where­by upon each inch of paper they lay six acres, one rood, 24 pole; and it is an easie matter for a good Artist with good in­struments to fail an acre in an hundred, much more with so small a scale, and blunt compasses: neither is there any that ever I knew use so small a scale, that can or dare say, that he is able to distinguish a quarter of a pole, whereby oft-times there is six in the hundred got and lost, not in a year, but in a day.

Secondly, To trust onely to the needle in any graduated in­strument, as Circumferentor, Theodelete: and partly for fear of a loadstone near; and also it is a hard matter by an ordi­nary needle, though of four or five inches long, to distinguish a degree, much lesse five or six minutes.

Thirdly, For over-curious ways, such as if I shall spend so much more time then ordinary, that the gain or losse will not countervail the time bestowed on it: therefore as upon buying and selling there is some land of 20 or 40 pound the acre: some I have measured where every man in the town hath hired the tythe communibus annis, for two shillings per acre; others have undertook plowing for 2 shillings six pence, others have let for five shillings, as the Lady M [...]rrison aforesaid. Now I will not stand so curiously upon that of five shillings per acre, nor work by so large a scale, as for that of 30 or 40 pounds the acre. This comes to five shillings the pole, the other very little above half a farthing a pole. Two pole got or lost in the first is the Surveyour's ordinary dayes wages; whereas five acres of the other will but do it. Again, as there may be curi­osity in measuring, so there may be in casting: but let the same rule be the guide in both: and although Pitiscus hath done exceeding learnedly through all his book, as like a Ma­thematick-Professour, and well skilled in the doctrine of trian­gles; yet he that shall seek out his sides, bases, and perpendi­culars by Sines, Tangents, or Logarithmes; or cast them up by Logarithmes, as some others haue taught of late: yet neither Pitiscus nor his followers have shewn themselves practitioners; neither of them ever measured, plotted, and cast 900 acres in [Page 7] three days, whereof for a mile together the side was as streight as Hockley-brook, as the Proverb is: (for it was Hock­ley-brook it self,) yet platted and cast every crook; and so did I Shefford brook also: and M ^r. Wingate hath measured 1000 on a day near Biggleswade in Bedfordshire. I denie not but these men may and have good skill in the Theorie, but as little in the Practick as the Londoner, that asked the countrey-Malt­ster if malt did not grow upon trees. Such a London Mathema­tician (perhaps) was Balls aforesaid, a perfect Surveyour, but never saw acre of land measured; so that he missed but 78 acres in 322.

§. 1. IF you intend to practise Surveying, make you a book of a quire of good strong paper, so folded, that the breadth of the leaves may be in octavo, and the length thereof may be the length of two quarters, well bound with vellum, that you may lay it on your left arm to write: and if it be your first book that you have filled, write on the cover a great (A). If the second (B). On the third (C), &c. Then page your first part of your book (A), all but some 12 leaves at the lat­ter end, on each severall page whereof you shall write a seve­rall letter of the Cross-row in Alphabetical order, and so your book is ready to go to work.

HAving made choise of your first station, before you be­gin to measure, take your field-book, & on the top of the first page write the name of the Parish first the ground lies in. Secondly, the year and day. Thirdly, the name of the close. Fourthly, measured by me, and for I. R. contra W. R. or if you are indifferently hired on both sides, write inter I. D. & D. I. Fifthly, your directour. Sixthly, your helper. And Seventhly, which way you went forward, whether cum Sole, or contra Solem: Cum Sole in a pasture is, when the hedge is on your left hand; contra Solem, when on the right.

Then in your field-book about two inches from the left side of the leaf, draw a line with your pen streight down to the bot­tom of the leaf, and on the left side about an inch from the line write A, signifying the first station, or the mark you stand on, and close to it on the same side, write O, signifying the begin­ning of the line; then if you intend to go contra Solem, mea­sure how many links are to the hedge or ditch on your right hand, and set them down right against A on the right side of the line; so all your lengths, as you go in the station-line, must be set down on the left side of that down-right line, and all the breadths on the right side. Yet before you go forward, you must know these several things.

Prolegomena. First, That always a ditch must be measured with that ground on which the hedge standeth.

Secondly, That you never need set up your Table at A, un­lesse there be another close adjoyning, which you are also to measure; nor yet at the last angle: so that if the ground have four angles, you need set up your instrument but at the second and third; neither is there necessitie of setting it up at the third, if you be sure you have measured all the station-lines right, calling your Angles BCDE in order, &c. by reason you may set out the two last station-lines of any ground what­soever by the scale and compasses, by tranning the first of [Page 10] them, and pricking the last, as shall be shown more at large, when we come to speak of measuring by the chain onely.

Thirdly, If one of your sides be bushy, woody, watery, &c. that you cannot come at the hedge for such things, leave that for the last, so that it be a streight side; for your plot will give you that side: so that, if you have done all right thitherto, you cannot fail in that, neither need you measure it, save for triall sake.

Fourthly, You must know, that wheresoever you have two closes to be measured joyning together, the station-line in one close serves also for the other, and the additions in one close are the subtractions from the other.

Fifthly, If a fair plot in colours be required, you must still, as you go in your station-lines, take notice and set down in your field-book all Churches, houses, rivers, ponds, gates, ways, paths, stiles, arbors, wind-mills, great single trees, woods &c. which fall within compasse of your plot or square, and set them down in your distance from the station-lines. If they be not on the same side of the station-line that the hedge is on, mark them with a crosse, and draw them all in your fair plot in prospective in their proper colours, with their manner of situation, East or West, North or South, and your needle in any of your instruments will help you always, making the North-side of your plot the over end, as you may see in plots of countreys; and at the bottom setting a scale of poles beau­tified with compartiments, and a pair of compasses: but your scale for this plot may (if the ground be very large) be smaller then that you measure by.

Sixthly, Before you begin you must make choise of your scale, wherein you are to consider the bignesse of the ground, the bignesse of your paper, and the price or value of the ground, and whether on purchase, or hiring, and that for a longer or shorter time; yet howsoever it is good, though it be upon letting, not to be too carelesse in it: for I have been im­ployed upon letting between Sir John Crofts and Sir William Bryars, yet before they concluded, they agreed on a purchase [Page 11] by the acre upon the same measure; therefore I seldome mea­sure upon purchase with a scale more then 8, never above 10 in the inch; nor upon hiring seldome above 10, never above 12.

Seventhly, Before you begin, you must consider wherea­bouts of your ground you begin, that so turning the length of the Table to the longest way of the ground, and beginning at the like place of the paper as you do on the ground, you may (not taking too small a scale) lay all that ground upon that sheet of paper, or (at least) all that you can measure that day; for it is somewhat troublesome to shift your paper in the field, or to fall beside it for a piece of a close; for which, if you do, we will give you these five remedies.

1. If it be but a small matter, and presently comes on a­gain, you may lift up the rulers, and that paper which they hold down cut it so, that so much as you need may lie upon the rulers.

2. If that will not be enough, you may make your station-line that you came, or else do come on, shorter then in­deed it should be by 10 or 20 pole, taking the next 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 [Page 12] 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-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.

[Page 13]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, How to set them­selves right in a line. 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-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 [Page 14] 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-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-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-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 [Page 15] 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 [Page 16] 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.

Now having set up your Table at B, lay your ruler with sights upon the line AB, directly placing your self between the Table and the end of the line, and your face toward A, in such a posture as if you were discharging a musket, and winking with one eye, having both your hands on the two corners of the Table next you, turn the Table till through the sights you see the mark at A: then scrue the Table fast, that it turn no more, and turning your back to the hedge you came by, having propounded to your self another mark to go to at the further side of the ground, by the next hedge-side, as you did at A, lay your ruler close to the prick B, with that end next you, and keeping one point of your compasses, or needle, or scriver, in that prick with your right hand, and the ruler close to it, lay your left hand, being spread, upon it, and turn the further end of it, till through both the sights you see that mark at C, and then holding it stedfast with your left hand draw that station-line BC also. Now if when you were at A, you had set up a mark at C, and another at D, and stroke AC and AD: and thus now also you had here at B struck BD, as well as BC, being the close hath but four angles; you need not have set up your Table any more, no, though you had but struck AD, nor yet have measured any more of it, if you be sure the hedges be all streight, (which is seldome seen in antient inclosure) and that the marks at C [Page 17] and D be set just in the angles. This way, I confesse, is some­thing quicker then to go round about, but not so exact: yet this way one M ^r. Sheppard of Maldon in Bedfordshire used, who formerly was my Scholar, and who ought Redburn-Parsonage in Hartfordshire, letting every man his tythes at two shillings per acre communibus annis. He took me along with him, and each of us a plain-Table, and finding almost all, four-corner'd closes, and streight hedges, we measured but one line in each ground. And indeed, where breadth and lengths are near equal, there will be no great danger; but where there is much odds, they will make such acute angles, that there will be no trust to them, the lines running so one in another, as it i [...] hard to say where they cut; and there fore such as have stufft their books with such whim­sies,

shall give me leave to laugh at them. Some shew how to measure the depth of a Well (but that is not well) by the plain-table; others teach to measure a piece of ground at two stations, 9 or 10 pole asunder, in the middle of the ground; but there is no trust to any of those ways, that give such a­cute angles. Let thē talk of never so many ways, this one way of going round is instar omnium. Whether they take the line AB or CD in this first figure for their sta­tion-line, they shall ne­ver make good work of it. And what will they do in such a figure as the second?

[Page 18]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 field­book 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 field­book, 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 [Page 19] 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-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 [Page 20] in Luton-Parish for Judge Crawley, where one Master Lawrence was my Antagonist for S ^r. 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.

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 foot­loose.

[Page 24]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 right­side 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, [Page 25] 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.

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-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 [Page 26] 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, [Page 27] 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 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 [...]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 [Page 28] 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.

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.

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 [...]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 ⅓, 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 plo [...], 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 [Page 30] 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-line, then 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 S ^r. Thomas Hillersden and S ^r. Oliver Luke; and ano­ther time in a wood at Hytchin. But not to detein you. If you [Page 31] 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.

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.

‘ Chest [...]rton. East-field in Broad-oake-furlong. Begin on the East-side of the furlong three lands per estimate three [Page 30] [...] [Page 31] [...] [Page 32] 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 [...]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.

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 [Page 33] 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 M ^r. 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 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.

[Page 34]Suppose this trian­gulated

figure ABEHGF to be one half of the fore-said wood, & that standing at A, I set up my Table with the fore-said Qua­drant upon it, and looking up to CI finde it to ascend 34 degr. measuring from A to C, I finde it 35 pole: so then keeping the standard at 34 of the limbe, 35 of the standard gives you both 29⅓ for your line of level, and 19⅔ both upon the plate at once: viz. AD, the line of level, and CD the perpendicular; now if you add AD, and FG, to­gether, being right angled at GD, and multiply the half thereof by DG, you shall fall so much too short, by how much the multiplication by your DG, is shorter then it ought to be: for in as much as FH is level, and AD so much rising as DC, it must needs follow, that GD riseth up to C, as ap­pears in the other figure. For it is the Hypotenuse to GD, a line of level, and CD a perpendicular. For suppose GD and AC in the first figure to be both of one length, viz. 35 pole a piece, and GD in the first figure, and AD in the second be all one, as if it were the line of level; but now if you lift up AD to AB, it will not reach to C, by the distance of BC in the second, viz. 5⅔; for if you subtract 29⅓ out of 35 which is AB, there rests BC, viz. 5⅔: so that your triangle GAD in the first is less then the triangle ADC in the se­cond, [Page 35] by the triangle BCD in the second, which comes to near 50 pole in that triangle. But hereby you see, that having this level plot, and your degrees ascending, and lengths of your lines ascended, you may finde out your perpendiculars: and by them, and the lengths of such lines as shoot upon them, I mean, having the height at both ends, which you shall al­ways take in going round▪ you may both finde the ascents of those cross lines, and lengths of them also by your Quadrant, without measuring them by the chain. For this instrument ha­ving the angle of ascent (whose complement is the angle of descent) and any one of the three sides of a rectangle tri­angle doth give you both the other, always making the stan­dard the Hypotenuse, and having any two of the sides, it gives both the angles of ascent, and descent.

Secondly, To work this by the limbe of any common Qua­drant. Take the angle of ascent as before, and measure the ascending line AC, let the angle be 34, and the line 35, as be­fore; and I desire first the line of level AD: secondly the per­pendicular DC. First, draw the line AC upon the centre A, making the angle A 34 degr. which is done after this manner.

Take 60 from the scale of chords, with that wideness set one foot in A, and with he other tran the arch DB, and take off [Page 36] 34. d. from the same scale of chords, and set it in the said tran from B to D, then draw the line AD, then take 17½ being the half of 35, and set from A to E, and again from E to D, making pricks in E and D. Keep one foot of the com­passes at E, and with the same wideness make a prick at D, and another at C so shall AD be your line of level, and DC the perpendicular; both which if you take with your compas­ses, and apply to your scale of equal parts, you shall finde AD the line of level, to be 29½, and CD 19 [...]/3, as afore.

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 [Page 37] 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 d [...]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.

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.

First, begining at any one angle, as at A, and so go round in order from angle to line, and from line to angle: Suppose the plot (A) to make another, viz. B but a quarter so big: yet like it both in form and content, onely it is drawn with a scale of half that bigness▪ for ½ the bigness gives but ¼, because ½ of ½ is but ¼ and so ⅓ make but 1/9 part so big, because ⅓ of ⅓ is 1/9.

First draw the line AB of the figure B, representing the line AB of the figure A, regard not though it be as long as it or longer: at the end thereof make a prick for a center, and write, [Page 38] or suppose (A) to be there written, then open your compasses to any wideness, as to F in the figure (A) and tran FG; with the same wideness do the like in the figure B, take FG in the figure A, and set it in the figure B, then take either [...]/2 the line AB of the figure A, and set it the same way in the line AB in the figure B: or else take half the length thereof from the same scale the figure A was

drawn by; do the like by the angle B, as you did by the an­gle A, and likewise by the line BC and so angle after angle, and line after line, till you have done. And thus may you make a plot bigger or lesser, as you please, onely by changing the scale, yet the area, or content, will be the same, as before. But if the borders of your-plot be very crooked, it wil be need­full to draw streight lines, either within or without both the plots, like station-lines in both the old plot and new, and to take the crooks from those, just as you did in the field, if you will have it equall in bigness to the other, and that your streight lines be of like length in both; then set the same wideness in your new plot from your station lines, each a­gainst its proper length: but if your new be bigger or lesser, then apply those distances to your scale, and take ½ or ⅓ or more or less, according to the proportion of your two plots.

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. [Page 39] 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.

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 3 ^d pag. 2 [...]) 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 subtende [...]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 [Page 40] line AXB, making a mark at X, and another at B: second­ly you must either take the sub [...]endent XC, setting one foot of the compasses in X, & tranning where you think C will fal [...]; 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 [Page 41] 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 [Page 42] 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 [Page 43] 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.

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.

Now because the meeting of the station-lines gives but one angle, which is the wood corner, or at least so near to it, that no subtendent can be taken from any part of one of those lines to the like, or any other part of the other, yet if you cross or lengthen them out beyond their meeting one or two chains length a piece, you shall then have three angles more, where­of the opposite angle to the wood angle will be the same with the wood angle, and either of the other will be the comple­ment of it to 180 degrees; so that if you can but take one short [Page 44] line in any of those three angles, you are well enough: as sup­pose A to be a wood, and at the angle C, I had two station-lines met, viz. AC, and CG, I continue AC forward to D one chaines length, or else set CG backwards to F a chains length, and likewise set back AC to B one chain of 100 links: now suppose I find FB or DE to be 60. now for that CB and CF are each of them 100 and FB 60. I first plot them, first striking a line, then I take 100 from some scale of equal parts, as CB in the figure B. And be­cause

CB and CF are equall, therefore I set one foot in C, and tran FB, also from B to FI set 60 of the same equall parts, then draw the line FC through C, and it gives the station-line CG; Or more easilie, if you draw out the line AC unto D, and make CD and CE 100. a piece, finding DE to be 60 then may you take 100 of any scale of equal parts & tran DE then set 60 of the same parts in the said tran from D toward E, make there a prick & draw the line CG through

E. But if by reason of impediments you can neither measure DE nor FB at 100 a piece, you may tran CB 200, and FC 100, or either of them what you will, so that you plot them accordingly; as if CE be 130, CD 100 and DE 50: then first set out CD [...]00 in the line CD, secondly take CE 130, set one foot in C and tran with the other, and thirdly take DE 50, set one foot in D, and with the other make a prick in the tran and draw the line from C through E as afore. Now if through impediments by none of the foresaid ways you can measure neither of the foresaid angles, then see what you can do to [Page 45] the angle FCD, or the angle opposite to the angle of the wood: for this therefore you must both lengthen AC to D forward; & CG to F backward, each of them 100 or more from C; then measure the distance DF, and apply it to your scale of equal parts, and what it gives set down in your note-book, as likewise you must do all the other lengths. Then supposing CD, and CF to be 100 a piece, I take 100 and set one foot in C, and tran from E▪ then suppose I had found DF 160. I take therefore 160, and set from D in the said tran, and it reacheth to F; therefore draw F ad infinitum, and it gives the next station-line CG.

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-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.

[Page 46]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 M ^r. Allen and M ^r. 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.

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 [Page 47] 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

[Page 48] 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.

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 [Page 49] 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 [...]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 f [...]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 [Page 50] 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.

Now having gotten this meridian-line: to finde the acute angle that this meridian makes with the wall; first, measure with your chain one chain, or half a chain in this meridian, and as much by the wall-side, and their distance for a third side, and plot it; then finde the quantitie of the angle of int [...] section of the meridian and wall-line by the scale of chord [...] ▪ the complement thereof is the decli­nation

of the wall. Suppose the line AB to be a meridian-line, and AC to be the wall-line, in either of which I measure from A to C, and from A to B 50 links, and I finde the distance of CB to be 24½, this I plot as afore is shown. Then to finde how many de­grees the angle CAB makes, take 60 from some scale of chords, and set one foot in A, and tran DE: then take DE with your compasses, and apply to your scale of chords, and it gives the angle of the wall, and meridian DAE, or CAB, which is all one, to be 30 degrees, and the comple­ment thereof 60 is the declination of the wall; which if it were taken in the morning, it is a South-west diall, declining West-ward 60 degrees: (for always the distance of the wall-line [Page 51] to the East or West-line is the declination of the wall:) if the Sun shine on it at noon, it is a South diall; if it shine

longer on it in the after-noon, then in the fore-noon, it is a South-west, & è contra.

Having a meridian in some open and plain place, to finde the Azu­meth, set up a stick at the South-end of your 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.

IN beautifying of plots, it is necessary that you draw a square round about the plot, the 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 [Page 53] 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 be shown with indico and azure, or black-lead: for seas, a greenish sky-colour of indico, azure, smalts, white-lead, and verdigrease.

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 [Page 54] 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-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 [Page 55] pleased M ^r. 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.

First, For taking of the angles, you need not set up your Quadrant oftner then you did the plain-Table; there­fore suppose this figure

ABCDE to be a plot of ground to be measu­red on the inside: I be­gin at A, not setting up the Instrument, but finde AB to be 20 pole, that I set down in my note-book, besides the breadths from the stati­on lines, which I omit here as sufficiently spo­ken of before Then be­ing come to B, there I set up the Quadrant, and finde it just 90 degrees, I set down B 90 degrees, so that all the lengths are measured by poles or links, and all the angles by degrees: then I measure BC, and finde it 28, and set it down: now I come to C, I lay the sharp edge of the rule to the line of the Quadrant, where the degrees begin, and then screw down [Page 56] the sights for stirring▪ AB. 20. p. B 90. d. BC. 28. p. C. 106. d. CD. 36. p. D. 108. d. DE. 22. p. E. 101. d. EA. 27. ½. p but turn the Quadrant till through the sights you see a mark at B, (as when you were at B you saw at A.) Now seeing that mark at B screw the socket pin, that the Quadrant turns not, but turn your sights to D: but I can­not, for they fall besides the board; but I have espied a mark at ☉ near the middle of the ground, viz. a tree, I turn my sights to that, and see the sharp edge of the rule cut 60 de­grees, that I keep in minde, then I lay the sharp edge of the rule again on the beginning of degrees, and turn the Qu [...] ­drant till I see the same tree again through the sights; then stir not the Table, but stir the sights till you see D through them: then looking by the edge of the ruler, I finde it cuts at 46, which added to 60 gives the whole angle C 106: and so of the rest.

To plot a plot taken by gra­du [...]ed In­struments.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 [...]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.

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.

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 [...]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.

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 [Page 59] 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, [Page 60]

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

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.

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 eit [...]er of which we will lay down some Problemes, and first as it is a Qua­drant.

THe sides of the

Quadrat SK, & K [...] (of which SK is called of Pitiscus the right shadow, & KL the contrary) are nothing else but the natural tangents of arches less then a Quadrant, which if each of these sides be divided by decimal division, they will agree with the Tables of natural tangents, either of Blunde­vil, or Pitiscus, which holds in the contrary shadow, but be­cause the contrary shadow is not continued streight on, but is turned again at 1000; therefore there it begins to be reckoned back again to 0, as M ^r. Wingates, or M ^r. Gunthers rule is. So that now if you turn AS down-ward, then KL will be the right shadow.

But to distinguish the right and contrary shadow, you must first consider whether your Quadrant goeth with a moveable rule and sight upon it, as Pitiscus hath it; if so, then one edge is always plumb'd, then the right shadow is the horizontal above, and the left shadow is perpendicular; which if the ruler falls on it, the thing seen is lower then 1000 parts by his account. But by Gunthers Quadrat, which is with a plummet onely, and the centre upward, the plummet falls in the right shadow, when the thing is seen lower then 45 degr. of the Quadrant, or a 1000 of the Quadrat. But M ^r. Gun­ther hath (in my judgement) expressed himself in doubtfull terms, in defining right and contrary shadow, where he saith that the right shadow of a Quadrat is that which is nearest [Page 69] to the horizontal. May I not well ask what horizontal line he doth mean? or where is there an horizontal line in that kinde of Quadrat? Certainly there is none at all; what doth he then mean? he meaneth that that is the right shadow, that in taking any height lieth most level; and so it agreeth with Pitiscus: and although Gunthers rules are fully sufficient for his Quadrant, yet will they not serve to Pitiscus without some alteration. We will therefore beg leave of M ^r. Gunther to borrow his rules, and to fit them to both.

APply one edge of your Pandoron to the plain, and the plummet to the edge next you; if that edge be upright, the plain is upright: if it rec [...]ine, take off the ruler, and ap­ply o [...]e of the edges next the centre that are not divided to the plain, so the degree cut by the thread gives the inclination. But if it recline, then turn the centre downward, and holding that thread in your hand, moving it to and fro with your thumb upon it a little above the limb, till the thread fall on the centre: so the degree cutting the line, shall be the reclination. Or you may put on the rule, taking out the sights, turn the centre downward, and one of the sides next it to the plain, turning the rule till the thread fall in the middle of it, then the siducial edge thereof will give the degree of reclination.

But for the declination: Although you may go some­what near by help of your needle and card, if there be no [Page 72] iron near you; yet work as exactly as you can, I will be [...]oth to trust it, but rather I will go further about, and finde it by the Azumeth; which to do, I must first by my Pandoron take the angle of the wall and Sun, thus▪ Apply one of the edges thereof next the centre to the plain, and turn the ruler till the Sun shews the shadow of the thread of the sight next the Sun, along the midst of the rule, then shall the fiduciall edge of t [...] ruler give the degree of declination. But you must mark whether it be taken in the fore-noon or after-noon, and likewise the moneth and day of the moneth: likewise you must at the same moment take the Suns altitude, thus; Either hang the Pandoron on the pin of the neck, or rather [...]et one of the undivided edges on a stool, and plumb the other; then turn the edge of the Table to the Sun, moving the ruler up and down, till the shadow of the thread in the sight next the Sun shine streight along the middle of the rule, so the fiducial edge gives the Suns altitude in the degree of the limb. Now knowing these things, you may finde the Azumeth either by calculation, or by your Pandoron, if you have Gunthers Quadrant drawn on it. First, by calculation having the moneth and day, you know the Suns place by this rule:

2 tens, 2 elevens, 4 thirteens, 12, 11, 10, 9. These are the days of each moneth the Sun changeth his signe, beginning with March. If the day you seek the Suns place be after the change day in any moneth, subtract the change day out of the day you seek, and you have the degree of the signe of that moneth. Example. I desire the Suns place April the 25.16 6. I finde by this rule April 10, the Sun entred ♉, take 10 out of 25, rests 15: so I conclude, the Sun is in the 15 degree of ♉ that day.

But if the day you seek be before the change day in any moneth, then first you must subtract that day from the change day, and then the remain always from 30. So April the fifth [Page 73] take five out of ten, there remaineth five; and that taken from 30, there rests 25 degr. which being it is Leap-yeare, you may make it 26 of ♈, of the moneth preceding.

Then you must seek the Suns declination either out of some Table for that purpose, or by this analogy: as the Radius to the sine of the Suns greatest declination 23 degr. 30 min. so is the distance from the nearest Equinoctial to the declination desi­red. Suppose April 5. the Sun in 26 degr. of ♈, that is 26 degr. from the nearest Equinoctial; say, As the Rad. to the sine of the Suns greatest declination 23 degr. 30 min.

23 degr. 30 min.

960070

26

064184

so is the distance from the nearest Equinoctial to the declination desired 10 degr. 4 m.

924254

which because it is in a Northern signe, as ♈ ♉ ♊ ♋ ♌ ♍, therefore it is North declination, and is so much nearer then 90 degr. to the North-pole, as the Suns declination is, viz. 79 degr. 56 min. Now add this distance, the complement of the altitude, and the complement of the latitude, all three to­gether, and from the half summ subtract the distance from the pole, and note the difference. Let us suppose the Suns altitude taken about nine of the clock in the morning for the latitude of 5 [...] degr. 15 min. took by the Quadrant as you are direct­ed in Chap. [...]0, to be 32 degr. then proceed thus; The Suns North declin. 10 deg 4 m. distance from the pole 79 d 56 m.

As this fourth sine 21 d. 17 m. Comp. Ar.

028467

to the S. of the half summ 87 d 50 m.

599969

so is the S. of the difference 7 d. 54 m.

913813

to a seventh sine 15 d. 20 m.

1942249

Add to it the Radius, the half (971124 30 d. 58 m.) thereof is the mean proportional, being the sine of 30 d. 58 m. whose comp. is 59 d. 2 m. that doubled is 118 d. 4 m. the Azumeth from the North.

Now suppose you had taken the wall and Sun 40 deg. that must always be set backward in the course of the Sun from the Sun or Azumeth: viz. from West to South, from South to East, &c. so then our angle of wall and Sun being taken in the morning, the Sun must needs be on the East-side of the Me­ridian line, and being found 118 deg. 4 min. from the North, that is 28 deg. 4 min. beyond the East, now if I set back 40, that is take 28 deg. 4 min. out of 40. there rests 11 deg. 56 min. from the East toward the North; and there

was the Sun when first it shone on the wall thence draw your wall-line through the centre, and always the distance between the East or West-line and the wall-line is the declination desired 11 deg. 56 min. as afore in Chap. 14. Now because the Sun shines on it at noon: therefore it is a South diall; and because the Sun shines on it longer in the fore-noon then in the after-noon, therefore it is a South declining East-ward 11 deg. 56 m. But if having the day of the moneth April 5, you take it in the morning and the Suns altitude 32 deg. and the angle of the wall and Sun 40 deg. as afore, and you have Gunthers Qua­drant drawn on your Quadrant for your own latitude, and that you have your line of the Suns declination drawn on the ruler as well as on the left-side of the Quadrant. And thus you desire to know all things by it without any calculation; First lay your ruler on the day of the moneth; see what degree of declination is cut by that 12 of clock hour which is proper to the time, whether it be summer or winter, carrie that de­gree [Page 75] to the Ecliptique and you have the Suns place. Also carrie it or take the same degree in the declinations on the left side▪ it gives the time of Sun-rising in the fore-noon-hours and the setting in the after-noon. Lay the ruler on the deg. of the Suns altitude in the limb reckond from the left-hand, and your deg. of declination gives the hour of the day: carrie it to the right-side and reckon the altitude from thence, and the same deg. of declination gives the Azumeth either for summer or winter: but not from the North, but from the South. Then may you cast up your declination of the wall, having your A­zumeth as you did before, or else finde it by help of a scale of chords drawn toward the top of the Quadrant on the right hand with a circle of the Suns Radius divided with two cross Diameters, and marked with East, South, West, North, and thereby with your compasses take your distances from your scale and set [...]hem out upon your circle. Further if you bring your deg. of declination upon your ruler to the Horizon, you have the Suns Amplitude in the Horizon also lay your rule on the place of the Sun in the Ecliptique it gives its right ascenti­on. If you bring your deg of declination to the Horizon, the edge of the rule shewes in the limb the Ascentionall difference; which known, turn this Ascentionall difference into time, al­lowing an hour for each 15 deg. and 4 min. of an hour for each deg. it shews how long the Sun riseth before six of the clock in summer, and after six in winter. If you bring the de­gree of the Suns declination in summer to any of the winter hours, and for morning hours of the one take the afternoon hours of the other, it gives in the limb the depression of the Sun below the Horizon. Bring the ruler to 18 deg. of the limb, and see where in summer the deg. of declination cuts the winter after-noon hours, and that hour is the break of the day▪ but in the fore-noon hours for day-light shutting in and the contrary; lay your ruler on the day of the moneth, make a mark upon the rule, where it cuts the sixth hour in Faels Quadrant, then lay your ruler on the Suns altitude in the limb and your mark, which give you the planetary hour. But it was [Page 76] not my purpose to shew all that may be wrought by the Pan­doron, so I may have work enough for a good while; but onely to shew the use of it in measuring of land, taking of altitudes, & conveying of water. They that desire more of the making & use of it in these things, let them see Gunthers book it self, or for the use of it let them see a little book thereof by it self sold by M ^r. Moxon at the signe of the Atlas in Corn-hil, together with printed papers of the said Quadrant for London-latitude one­ly. But if any desire the making of it for other latitudes, let them peruse my Fale redivivus or Sun-shine of shadows where­in they shall finde Gunthers first chapter touching the making of this Quad [...]ant explained, with Tables to make it for all la­titudes throughout all England, and also Tables for all Hori­zontall dials, and for all erect South and North, East and West, and all decliners from one deg. to 90 for each whole deg. as also for all Polars, and all these for nine severall lati­tudes from 50 to 56, as also divers others curious dials Qua­drants and Nocturnals.

I Find great difference among our best Authours concern­ing the odds or difference between the true and water-le­vell. M ^r Hopton in his 24 ^th chapter of his Topographical-glass saith, that after the ordinarie manner to bring it in pipes, the ground must be lower by 4½ inches for each mile, then at the spring-head: so that I suppose his meaning is, if it be 10 miles, it must be each mile alike, viz. ten times 4 and ½ that is 45 in­ches, or three feet nine inches; but neither demonstrates it nor gives any reason for it. Again M ^r. Diggs in his Pantometria ( lib. 1. chap. 3.) saith that in ten miles distance, the water-level is below the true nine paces, four foot eleven inches: which if every mile give a like we have five foot in a mile. And because there is such a vast difference, I will lay down both Diggs his rule to finde it, and his example, as he calculated it in his own [Page 77] words: his rule is thus. First it behoveth you to get the di­stance of the fountain from the place whither you will con­vey the water, which distance you shall multiply by it self, adding the off come to the square of the earths semidimetient, and from the summ extract the square-root, and out of which root subtract the earths semi-diameter, the remain is the diffe­rence desired. His example is this. Admit the distance BE

10 miles. The semi-diameter of the earth EB 5011 Itali­an miles. But how the semi-diameter can be 5011 Italian miles, I cannot imagine: for if the semi-diameter be 5011, the whole diameter must be 10022, which multiplied by 22 gives 220484: that divided by 7 gives 31498 the circumference; which divided by 360 deg. gives 87½ Italian miles to a de­gree.

Now because an Italian mile is 1000 pases, and an En­glish mile 1056, say, As 1056 . 1000 : 87½ . 82. So that by this account there should be 82 English miles to a degree, which was never heard of; our common account is but 60. our mo­dern Artists hold 66, the most that ever was reckoned of is less then 69, but this is 13 more.

But suppose the semi-diameter to be, as he saith, 5011 and [Page 78] the distance 10 miles, each mile 1000 pases, each pase five foot; the square of 10000 pases, that is 10 miles, the distance is 100000000, and the semi-diameter in pases is 5011000, the square thereof is 25, 1101, 2100, 0000, add both these squares together, they make 25110221000000 hence extract the square-root, it is 5011009 9801919/10022019 If hence you subtract the semi-diameter in pases 5011000, there rests 9 9801919/10022019 or 10 pases ferè, that is 50 foot, whereas Hopton hath 10 lines 4½, that is 45 inches, or 3 foot 9 inches, so 40 miles distance requires 48½ poles. Now whe­ther we reckon the semi-diameter 5011 Italian miles, or 3436 English miles, 60 miles to a degree, or 3780 English miles, 66 to a degree, that decides not the controversie, whether of these either Hopton or Diggs is right, or either of them both, or neither of them both.

First for Hopton I cannot think him to be true; for that he sheweth no reason, nor demonstration of it: and although 4½ inches may serve the first mile, yet I cannot think every mile is alike, for this water-level must of necessitie be supposed to be a right line drawn or running from the top of the earths hemisphear, there making an acute angle with the tangent, and running between the said tangent and the earths Perimeter, such as the tangent-line BG in the last diagram. Now there may be infinite such lines supposed between the said tangent and the earths circumference, and is there not as good reason for all, as for any, for one as for another; there must be a terminus ad quem given, as well as a terminus à quo.

Besides all this, all these lines will be in the aire above the earth; but the water must not run above the earth (that is Gods decree) but in the earths Perimeter.

Therefore this difference of levels must needs be a line fal­ling from the tangent-line, that runneth from the top of the earth to any distance desired, which (according to Digs) is the excess▪ of an Hypotenusal above the Radius, or earths semi-dia­meter, running from the centre of the earth to any distance of [Page 79] miles, poles, pases, or feet desired; or it is the natural secant of the arch which it cutteth in meeting with any distance of the said tangent assigned.

In the former diagram, let ABCD represent the upper he­misphear of the earth, E the centre, EB or ED, or any of the pricked parallels falling on ED, conceive them all to be semi-diameters of the earth, B the top of the earth, BG the tan­gent line, BN a line in the aire between the tangent and the circumference of the earth: now for that it is impossible to make his example to appear to the eye out of the said dia­gram, both by reason the said secant falls so near the semi-dia­meter EB; and that there is no apparent difference between the said tangent and the earths Perimeter, let us suppose the semi-diameter of the earth both EB and BG, to be either of them 100 miles, and let the distance BF be 40 miles, then the secant or Hypotenuse is EF, which for that it is longer by FO. then EB; therefore FO. is the difference of the levels found, as is before declared.

And although Digs neither doth set down the reason of his finding it after this manner; yet it is easily perceived of every one that hath any understanding in triangles: for it is but the finding out of the Hypotenuse of a rectangle right-line tri­angle, having the two leggs given, and it may also be wrought by the Logarithmes; but with little less labour.

Some think also that the line FP is the difference of the levels: but since the difference in 100 miles is almost insensi­ble between those two, we will onely demonstrate it to you, and then let every man use his own discretion.

[Page 80]

Let us suppose in this diagram ABFD the upper hemi­sphear of the earth, whose semi-diameter EB is 3780 English miles, 66 to a degree, to which is equal both BG, and FM, and ED: for ED is equal to EB, Element. 1▪ Defin. 15. and BG and ED. Element. 1 Prop. 36. therefore it is equal to EB, Axiom. 1. Element. 1. and FM is equal to EB, Elem. 1. Def 15. and BG, and ED Elem. 1. Prop. 36. therefore equal to EB, Axiom. 1. Elem. 1 and ME is equal to FB▪ Elem 1. Prop. 36. And because in the other example we could not distinguish one thing from another, because of the near­ness of things one to another; therefore we will take the di­stance BF, which suppose 1500 miles, which (to save labour) we will keep still in miles.

First therefore, to find EO, EF, and OF, first EO is = to EB, Elem. 1. Def. 15.

for EF square EB, 3780. it is

14288400.

also square BF, 1500, it makes

2 [...]91000.

these added make

16538400.

whose square root EF is English miles

4066¾.

Whence take EB, equal to EO. Elem. 1. Def. 15.

3780.

resteth OF, English miles

286 [...]/4.

[Page 81]Then to finde BEF.

As 3780 Comp. Ar.

642250

is to Radius:

 

so is 1500

317609.

to tangent 21 d. 39 m. of BEF,

959859.

whose arch is BO, whose natural tangent BF is 39694 parts, and that is equal to LP. Elem. 1. Prop. 36. which is sine of 23 d. 24 m.

for as 3780

3,577492.

to Rad. So 1500

13,176091.

to S. 29 d. 24. m.

9,598599.

whose complement is 66 degr. 36 m. and the sine thereof MP 91775, and the versed sine thereof FP is equal to LB 8225 parts.

And to reduce them into miles, say, 100000. 9225 ∷ 3780. 311. FP. whence take [...]F 286 [...]/4, the difference is 24¼ miles difference in 1500.

But how can we do so? since M ^r. Frost (then Manciple of Emmanuel Colledge in Cambridge, since Sword-bearer to the Lord Maior, and since that a Secretary to the Councel of State, a man beyond all exception for integrity of life, an excellent Mathematician, one that brought the water from the Spittle-house to Emmanuel, and thence to Christs Colledge,) told me, that he came upon a time (by mere accident) in the Fenns to a place where an old river had run down some four miles, and was brought four miles back again in a new cut; and when they met, the water in the old was but four inches above the water in the new. Now the question is this, Doth not this confirm, or rather out-vie Hoptons tenent of four inches and an half to a mile, seeing here is but four inches in eight miles, which is half an inch for a mile? Truly I think not, for wheresoever you conceive your self to be, there is the true top of the earth: if there you are withall neither above nor be­low the true circumference of the earth, such as I conceive the Fenns for the most part to be▪ having formerly been made le­vel, as being part of the sea, I see not but that the water may [Page 82] run both ways as well as in the sea, if not all four ways, as well as the four rivers in the garden of Eden. And by this means if the meeting place was not some bowing of the earth of four inches thick, why might not they have met of equal height.

Every one (I suppose) will confess with me, that I being at B, the water will run to C, and to o; and if you turn C upper­most, will it not run from C to B as well? are no places up­permost but B, because I am not there: certainly I am some wonderfull vertuous fellow: well, I will get thither, and then it will run thither. If any dislike this answer, let him give us a better.

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.

[Page 83]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 [Page 84] 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 [Page 85] 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. For find­ing how high you may set your cock in a house, see the last page of this Book.

But for long distances, although I have fully shewn the use of it already in the Pandoron, yet because of the shortness of the lines, there is as little reason for to use that in doubtfull cases, as for one to shoot at wild-geese a furlong off with a pistol, or to take on observation with a Quadrant of 3 inches Radius. I will therefore here give the making of a most ex­cellent Instrument, soon made, and cheap enough. First, let

AB be a piece of deal, or some light and soft wood, about two inches square, or inch and half, and seven or eight foot long: in the upper-side thereof let there be a groove or chanel made with a round plane, like the chanel for a bed-cord, about an inch wide, and of like depth: likewise let ED and FD be two pieces of an inch broad a­piece, and a foot long, and half an inch thick a piece; to make brackets to be lapp'd one over the other at D, and likewise the beam with screw-pins made of pieces of old keys, to screw onely into the wood, without any forills at all, and likewise an other piece DG of six foot long, a quarter of an inch thick, [Page 86] and an inch broad, with a jage-stroke down something toward one side of it, that you make the screw-holes beside it: this must be screwed together with the two brackets, within an inch of the end, all three with one pin. Also you must screw it to the beam at C, that the jage-stroke may be exact­ly perpendicular to the beam: this hole must be bored close to the bottom of the groove, and in the bottom of the beam you may glew on a piece of some eighteen inches long, in the middle, of two inches broad and an inch thick, to thicken it; because just in the middle you must make an hole so big and so deep, that it may fit to go on the top of the three-foot staff, or foot of the Pandoron, when both it and the neck are took off; yet you must take heed you bore it not quite to the groove, and let it go on as stiff as you can possi­bly. Also at either end glew on a piece of an inch thick, eight inches long, and of the breadth of the beam, or nayl them on to the beam, and cut the bases true and square: then get two thin sights made after the manner of this figure, eight inches long, and nayl them on to the ends at AB, so

that the sight-hole of the one may look over the flat of the other, and when you will use it put it on the staff, and put on a plummet and thread of the length of the jage-stroke; then set it up and move it by the feet till the plummet hangs right with the jage-stroke, then fill the groove with water: if it be truly plumb'd and that set perpendicular to the beam, then may you fill the groove so full of water, that it will rise so high above the wood at both ends, that you may thrust a needle through it close to the beam, and yet the water will be above the needle.

MIne intent is not here to describe the manner of making engines, sluces, Cochleas, mills, &c. to mount the wa­ter [Page 87] 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 opus [...] 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,

And in another place,

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 [Page 88] 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.

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 [Page 89] 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 M ^r. 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.

[Page 90]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 wood, he makes a plow, whose neck and handle were both one piece: with this plow he plows this ground, and never digged at all, onely he had two following him with mattocks, that if the plow was hanged in the middle of a great root, that the horse could not break it, then they cut it in sunder.

And lastly, one exploit more was by a plow done by M ^r. Taverner of Hexton in Hartfordshire Esquire, Lord of the Town, who (because their high-way to Luton-market was up an extream steep hill for two or three furlongs space, and of­ten-times both in frost and rain so exceeding slippery an horse could scarce stand, being all a rock of hurlock;) gets a plow, and the neighbours willingly bear him company: they plow about in a spiral line, and so plowed furrow after furrow, all one way, turning all the moulds down the hill; and so when they had plowed it broad enough once over, then they begin and plow two or three furrows of the moulds twice over, and the highest side deeper: thus doing, till they had made the highest side lowest onely by plowing; so that they can now draw five quarters of wheat more easily up that hill with three horses, then up the other with five.

And thus have we the way to drain such grounds, wherein you may have the help of the plow. It follows now to speak [Page 91] of those that must be done either chiefly by the spade, or one-by the spade. Chiefly by the spade, called water-furrowing, that is, when you have new sown any grain whatsoever, then presently water-furrow it, either with plow, or spade, or both.

But if it fall out that in a floud the water goes not away so fast as it comes, though within two or three days after it will be clean gone; yet you are never the near, it hath done alrea­dy what hurt it can do, your grain is drown'd, and the fault is in the main drains; yet not in their depth, because they will be dry within two or three days after, but in their breadth.

Now, if this had been a new drain, you might have made it with the plow, as was said before: or if you will deepen this old one with the plow, it may be you may; but to make it broader you cannot, if it be either very deep, or very nar­row in the bottom; therefore you must widen with the spade onely.

And for that where cattel go over such drains, they com­monly tread in the earth, and stop up the water, therefore to prevent it, get good oaken timber, hew two sides of each piece, which let it be eleven or twelve inches Diameter, slit these in the middle, let them be two or three foot longer then the breadth of the ditch, lay them edge to edge, the sawn side upward, nayl ledges on the out-sides, and lay gravel or earth on the top, and stop up with bushes, or ditch up, or both, the old going over.

IF it be full of weeds, get a drag or dung-rake with three teeth, and drag out the weeds: likewise for the mud get a mud-pan, which is made of the back of an armour, make a socket, and slit the little end forked, and flat it, and spread it four or six inches, and rivet it on the plate, then rivet another round piece, both close by the socket, and also into the bottom of the plate to strengthen the forks, setting it coming toward you as your drag [...]rake doth. Then, if there be much mud, draw out some of it first all along the ditch, and when that is hard, so that you can go upon it, then draw out more. Thus may you go to it when you will, and leave when you will, without dressing you, or damming the water. And thus one man will draw out as much in an hour, as three men will throw out with scopets.

YOu shall for this purpose get a boat and a haling-line, good store of drags, cutting-knives of both sorts, such 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 [Page 94] 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-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.

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 [Page 95] 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.

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 [Page 96] 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 coals, and then took the buck-cloth by all the four corners, and threw up the ashes into the chimney, and finding a pail, I ran and fetcht turf-ashes and water together, and quenched all quite in a quarter of an [Page 97] hour. All this while not one body came; so I was going thence, and as I was going out at the gate, there came near half a score, which she brought out of the field from haying: with these I went back again, fearing lest they should do hurt; so presently some of them get ladders, and to pulling off the thatch; but I prevailed with them with much ado to let it a­lone, and willed them by all means to keep it into the chimney: if they found any holes that it could come out at, to stop them up with dirt or cow-dung, and throw dirt or cow-dung on the thatch if they would, and if they saw any more fire in the chimney to cover it with a wet blanket.

If it be within a dwelling-house, on any ground-sels, or studs, it is easily quenched, doing as afore.

If it be between parget and loft-boards, wheresoever it breaks forth, lay on wet woollen-cloths, hair-cloths, cow-dung, or hors-dung, with water, ashes, or sand.

If it be on the inside of an house either thatched or tiled, between the parget and the roof, cover the out-side with wet blankets, hair-cloths, &c. that neither the flame get out, nor air get in. And on the inside be sure there be no vent in the parget, but stop it with cow-dung, &c.

If it be on the out-side of a roof, cover it with wet wool­len; or on the top of a mow: and throw no water, but ashes, sand, hors-dung, &c.

If it be on the inside of the roof of a thatcht house, cover the out-side with wet cloths as afore. If there be no parget, your onely Instrument is a scovel, or mawkin, or mop often wetted, and with them sweep down the fire. And thus I and a boy with a scopet, throwing in mault instead of ashes, did at Tame que [...]ch a thatcht-house adjoyning to another in the market-place, which was on fire in eight places at once on the inside, hard by the eavs; yet being new thatch and hard, it glaunced up to the roof▪ and broke not out, till it came at the ridge, where were on the out side as many people as could stand on ladders, ready with water, that no sooner could a flake of fire peek out of the ridge, but streight they saluted [...]t [Page 98] with a bucket of water: but for all that, so soon as the fire had broke out at the eavs, (which had been, had not we two asswaged it,) they must all have sought a new way down, or else have gone through the fire.

If it begin likewise upon hemp, or flax, cover it with co­verlets, blankets, hair-cloths, &c. and throw on ashes. If it be on the side of a mow, hang wet hair-cloths, or woollen-cloths before it, and cover it at the top, that no flame get out, holding the fore-side-cloths as close to it, as possibly you can. Thus have we shewed the ways, how to quench fire in any house, where or howsoever it shall begin, without pulling down. Now to prevent fire coming from another house, co­ver it with hair-cloths, coverlets, &c. and throw on them wa­ter'd ashes, dirt, dung, &c. Also if an house be pulled down, by no means let it lie there; but, be it what it will, timber, or grain; hay, or straw; quench it throughly, and get carts and away with it into the field, and there spread it. I saw one at Burton in Bedfordshire at one Francis Woodward's, who had his barn burnt down, that it kindled again in the carts before they got a furlong from home. And I have heard my Father speak of it often, that there was a Parsonage-barn, with much corn in it, burnt down at Leighton-Buzzard, where he was born, and they did not carry it away, but watched it continual­ly; but for eight nights together still about mid-night it broke out again, that they were forced to ring the bells, and to carry all away at last, when they had wearied them with watching.

If any shall doubt of the efficacie of these things, I desire him to consider of these five things.

First, He seeth dayly, that an extinguisher puts out a can­dle; yea a candle puts out it self by turning the flame down­ward: then a blanket on a chimney, or any where else, much more.

Secondly, If any doubt the blanket will burn; it may be so, if it have holes in it: but they are easily stopt with throwing on horse-dung, or dirt. And for both these let him try this conclusion: Let him take a woollen rag, and a burning coal [Page 99] either of wood, sea-coal, or turf, (which of all other is hard­est to be extinguished, and therefore we use to take a piece of turf and wet it, and rake it up in the ashes to keep fire, yet) let him wrap this coal in his cloth, or lay it on the hearth, and cover it close that no air can get in, and your coal quick­ly dieth.

Thirdly, Ask any souldier, and he will tell you, that the best way to put out his match is to put it into the mouth of his piece with the coal down-ward.

Fourthly, You may easily see the effect of dust, sand, hors-dung, or such like, if ever you saw an hearth of char-coal burnt, and quenched.

Fifthly, If a mow should be covered at the top, and not at the end, you will say it will burn underneath like an oven: I answer, put a whole sedge-sheaf into an oven at once, let it be at full fire; stop up the oven, and presently the fire goeth out.

I Have before, in the last chapter, shewed you how to put out fire: now in this I will shew you how to keep fire a long while light with a little charge. Suppose you dwell in a lone-countrey-house, where one is sick, and you have but one farthing-candle in the house, and borrow you cannot, and you would fain have it last burning a whole long-winters-night; then do thus. Cut your candle in two pieces, light one of them; and heat a great pin, and thrust it into the great end of the candle long-wise half the pins length, then fill a pail with water so deep that the length of the candle, pin and all, will not reach the bottom, then holding the candle by the light, let it down gently into the water with your fore-fin­ger and thumb, till it comes to the flame, there staying it a while till the water be still, and then take away your hand; so still, as the candle burns the flame will raise it: and which an­swers [Page 100] the whole business, that the fire will go no otherways, save upward to his own element.

OF all ground the best to lay for sward is the black-mould, o [...] strong clay. And although the black-mould be excel­lent both for Wheat, Barley, and Beanes; yet in the low le­vel ground it is infinitely more commodious for pasture in sum­mer; that the three years crop of grass without any charge at all is more worth then your two crops of grain with all your two years seed, your dung, and carriage, and five or six plowings, harrowings, rowlings, and weedings. But you will say, ground is long in grassing, and I am but a Tenant, and have but a short time in my lease; when I have made it fit for another, my Land-lord will turn me out, or make me pay more rent. This, I confess, is something, and in some cases may serve for an answer: but yet upon this condition thy Land-lord will renew thy lease for one and twenty years, (if he be wise) and then you are well enough: for whereas you say it it long in grassing, that is remedied with one years charge of arable; for if thou first plow it, and lay it flat, and with as few furrows as may be, about November, and then dung it, then plow it again, about the beginning of March, still laying it flat, and filling up the furrows; then sow it with hay-dust, or chaff-dust, which every hors-keeper, if they are spoken to about Michaelmas before, will (for a trifle) save for you on purpose. If you harrow in this, you shall have a crop of grass at Mid-summer, will be worth 30 or 40 shillings an acre, and still be better and better. But by all means plow in your dung. I have laid some in that manner, and some I have dung'd above ground three times, yet this will not be comparable to the other; yet but a furrow of a plow between, and both laid down 40 years ago.

And by no means lay down any ground, that is worn out [Page 101] of heart; for by that means if ever thou get good grass of it in 40 years, I'le never be trusted, unless thou dung it extraor­dinarily; and yet it will not do. Rather this do; if it be inclo­sure, take nothing but the mowing crop for divers years toge­ther, and so doing that crop will be more worth then two whole years crops taken as ordinarily. I speak all this of mine own experience upon my own grounds.

But I have often heard of, and in part seen another sort of speedy grassing, which is this. They sow their ground with seed of claver-grass, a very small quantitie on an acre, and in some places they mow it twice in a year, yet never sow it but once. Whether they plow it or not, I cannot justly tell: I think not. Thus I have seen at Maddingley three miles from Cambridge, they save their common fallow fields till Midsummer; and then have an exceeding crop of claver, and then fallow. But whe­ther they sow for each crop, or whether it be of the nature of Mustard-seed, that need never be sown▪ but once, though the ground hath lien sward 40 years before, I know not.

But you will say, yours perhaps is common-field, if you should lay it sward, you should lay it for other folks. And what of that? If you have more benefit that way, then you had before, never grudge at it, though others take a part. 2 ^ly, Thou shalt take part with others of it, as they do with thee. And in most places one acre of sward hath as good right of common as three, or in some places five acres of arable hath. 3 ^ly, There is no doubt but others seeing thy good and speedy success will soon second thee, and then thou shalt have as good benefit of his, as he hath of thine.

Ob. But if every one should lay sward that would, how shall we do for bread? I answer, I do not say I would have every one that list should lay down for sward; but this I say, I would have all ground turn'd to the most advantage, first of the Common-wealth, then of the owner: I would not have such ground, as will bear two or three load of as good hay as ever beast eat, turn'd to arable, when the next acre to it be­ing sown some years hath scarce yeelded the seed again. Where [Page 102] an ordinarie acre of pasture is worth 50 shillings per annum, and the best arable not above 8 shillings, for as for an acre of sward, though it be worth but 20 shillings to the owner, yet to the Common-wealth it is worth 30 shillings the after-pasture, where it is reckoned at a third part of the rent; with us at Cambridge far more: and that is not lost, it doth not vanish into air; and though the Master get it not, the Common-wealth doth: and how would Luton and Hitching do for hay, were it not for Harlington, Pullox-hill, Gravenhurst. Or how would Cambridge do, were it not for the Fenns? Yea, I have known that hay hath been carried out of Bedfordshire to London, thirty five miles. And I am sure, that it is an easier matter to drive fat cattel an hundred miles, then to carry corn fourty by land. Neither would I have Chiltern-ground turned to pa­sture, because there an acre of arable is more worth then an acre of pasture. Yet certainly it plainly appears by this, that generally there is more want of pasture in England then of arable; for that we have daily fat cattel brought out of Ire­land and Scotland, but never any go out; but where grain comes in once, it goes out ten times.

FOr a generall fat soil, and such as is good for all things, or at least most things, both grass and grain, (for indeed no ground is fit for all things, Non omnis fert omnia tellus) the black ground of a good deep staple, with a mixture of gra­vel or sand, is not unworthily commended of the Poet, Lib. 3. Georgic.

[Page 103] For this we commend Ailes-bury.

And some extoll as highly earth that is of a reddish colour; as the ground about Armagh in Ireland, which (some report) hath had no manner of manuring since the memory of man. I know some such black ground in Pullox-hill afore-said, but I know no such red. Virgil also saith, That if you dig a deep hole in the ground, and fill it up again, if you cannot tread in the earth again, then it is rich arable ground, 2. Georgi [...].

Also a sweet smell after the first rain, or a drought, or after new plowing, is a token of a rich soil. Also where thistles, nettles, or other weeds grow rank. Also where trees grow long and upright. Also where fruit, especially pears, are more pleasant in tast then in other places: for if a young pear-tree bears pleasant pears in a good ground, and you remove it into a bad ground, you will think the fruit not to be of the same kinde; yet all grounds are not alike for all things: ‘—Non omnis fert omnia tellus.’ And for the most part, those grounds that are most barren above, are richest within, as stone-pits, fullers-earth, lead, coal, tin, silver and gold-mines.

Some grounds are fitter for wood, then either for corn or grass. I have seen a ground in Hartford-shire, that hath been laid two years, where were grown naturally black and rank sallows all over the ground in tussocks, some six, some seven foot high, so that the crop of wood was more worth then the crop of grass.

LEan grounds are either inriched with rest, or with dung­ing. As for pasture, if you neither eat nor mow it two or three years, or onely mow it once a year; or if you will eat it, by no means eat it too low, and you will greatly thereby both better the ground, and get a speedier increase of the crop; for after it once covers the ground, it grows more in a week, then in six weeks before, by reason it keeps the ground both hot and moist, yet not so hot as to be scorched with the Sun: therefore be sure to spare such barren grounds by Candle-mass at the furthest. As for lean arable, though common-field ground, it is a common thing in divers places, where they have a great deal of lean land that lies far from any Town, to let some thereof lie lea six or seven years; and the longer it lies, the more heart it gets.

As for dunging, the benefit of hors-dung and cow-dung is every where known in part, yet not to all alike; some will not lay it on their land till it is rotten, but will carry it out of their yards, and lay it on dung-hills in the field, either at the lands end, or some place near to it, though the land be not then sown: whereby they make a double labour, and lose a double benefit of their dung, which they may easily finde by this, that a great part of the strength of it goes into the ground it lies upon, as appeareth in this; for if they lay it in small heaps on the land where it should be spread, if it lieth long unspread, let them spread it as clean as they can, yet those places will be ranker corn then the rest. A second benefit which they lose is the stiving upward, which in dry weather should be the onely nourishment to the corn. If you please to try two acres of like land lying together, and carry out twenty loads of hors-dung about Mid-summer, that is new-made, as such you may have at an Inn, and lay that on a heap in the field by it self till February or March, and then fetch twenty loads more of the like; lay these twenty on one of the acres, and the heap [Page 105] on the other, but let your loads from the Inn be alike, and then tell me which acre is the best barley. But though you finde but little difference in the barley-crop, you shall finde a vast difference in the peas-crop. And if you will sow them three years together, there will be no small odds; for the stiving of the dung will be over in two or three years. And this also will appear, if you take a load of straw, and lay it in some Orchard, where no cattel come, upon planks, boards, or stones, and spread it so that the [...]ain may get into it, and turn it three or four times in a year; and by three years end you will hardly have a quarter of a load of dung left, and that which is left will be turned to earth also: yet I deny not but that earth may be better then ordinary.

Also street-earth, especially in Market-towns, Street-earth. where goes store of sinks from stables, kitchens, dairy-houses, but especial­ly cisterns for malting. I have known them that have got up all the piss they could get in a Market-town, and carried it to their land in a tun, and there strewed with good success. But if they, that have such convenience for carriage, would but make triall of the water of the sink of a Chees-press, or of cistern-water, I doubt not but in short time there would be little of it lost.

And we see now how much soot is set by, Soot. which within these fifty years men would not suffer to be thrown upon the dung-hill, but into the midst of the street.

And although, by Moses Law, Salt. some great offenders were to have their land sown with salt; and likewise in Judges ix.45. Abimelech, when he took Sichem, destroyed it, and sowed it with salt; the reason was, that it should never bear grass nor grain. And indeed it is an easie matter, either with soot, salt, pigeon-dung, or piss, to over-dung and spoil all. I have known some carry out pigeon-dung in sacks in May, and lay a sack-full on a heap upon the corn; but they could not gather it up so clean, but they kill'd all the corn as far as the heap lay.

I have sown pigeon-dung in an extream hot and dry year Pigeon-dung. [Page 106] upon barley, on an hot and dry land, when at harvest the bar­ley hath scarce peeked out of the hose, yet it hath been the best in the furlong. Again, I have in a wet year sown pigeon­dung on sand, when my crop hath been more worth then the fee-simple, or value of the ground.

Folding of land. [...]and that is folded a little before, or presently after the sowing, doth far better then otherwise. But herein many men wrong themselves in surfeiting their sheep in Summer-time, when their fold goes on single-lands as on roods or half-acres, in laying them so thick, that they over-heat one another; thinking that if they have as many hurdles as they had before, that then they lie as thin as they did before, but this I have spoken of before in the first Chapter; where also I have shew­ed the disproportion, and therefore to it I refer you. Yet be­fore I leave this, I must add further, that I see no reason why other countreys may not fold in Winter as well, or rather, then Oxfordshire, or Buckinghamshire: nay, far rather, either upon sward or arable, especially Hartfordshire, or Middlesex, if they will do as they do, that is, winde their hurdles on two sides with broom, and remove their hay-rack and cratches with their folds. Hartfordshire hath far drier laire, their sheep more hardy and sound, and never rotting, more hedges to shelter them, and dung infinitely dearer. And if they broom their hurdles to keep them warm, then why not to keep them warm by keeping them together? I never knew sheep take hurt by lying warm in Winter. If you will not fold your ara­ble, yet fold your sward, if not your sward remote from the hedges, yet at lest your hedg-rows. It is the office of a land-meter, to give the quantity or mensuration; but the office of a Surveyour, to acquint you with all means of melioration.

Rags and Horn-shavings.Now we are come to rags and horn-shavings. It is almost incredible the odds of an acre of the best barley in Hitching-parish fifty years ago, and twenty years ago, and all by buying rags and horn-shavings at London, carrying up malt, and bring­ing them down all the year long. As for their rags, they carry them to the land, and lay them on heaps like dung heaps, but [Page 107] not so big; then chop them in pieces on a stick with a hand-bill, and then plow them in, and these and horn-shavings en­dure a long-while, and have so mended their soil thereby, that whereas about fifty years ago, an acre of their barley was not above three pounds ten, or four pounds the best; now about twenty years ago, I was requested to measure two acres of barley in a field called Kings-field in Hitching-parish that the very crop of them was sold for nine pounds an acre by the Statute-pole.

Malt-dust also is little inferiour to Pigeon-dung. Also lime, Malt-dust, Lime, Ashes, Chalk, &c five or six quarters to an acre. Ashes of all sorts. Chalk for all red grounds, both arable and sward. Scowring of old ditches, good for all white grounds and clay. Also marl of ponds, where sinks of yards run into them; but in a spring or running water, though the mud look never so black, there is no heart in it, except holpen by land-flouds, because there is no salt in it; for salt is the strength of all dung: therefore let it alone, unless to lay on a white ground, for mixing of earths; for if you lay an hungry gravel on an hungry clunch, & con­trà, they fertilize each other.

Also any sward plowed up, and thrown on the land, or laid on heaps till it be rotten: or making a dung-hill, and laying stratum super stratum, a laying of street-earth, and a laying of these turves, laying upon laying, till they be rotten, makes an excellent compost for many years.

The burning of hawm upon the ground, commonly called Devonshiring (because much used in Devonshire) is not un­worthily a little extolled of the Poet: Georgic. lib. 1.

To this give me leave to add a little of mine own experi­ence. About the year 1607/8, was such a frost, without snow, that it killed all our wheat: one M ^r. How of North-Myms had but two bushels growing of thirty acres sown. I sowed most part of mine again with barley in March, onely I had one head-land that looked most gloriously, covered green all over, as thick as grass in a meadow. I thought this might do well enough, I let it alone till mid- May, then I began to mis­trust by the blade, that all were but wild-oats. I digged up a turf as broad as my hand, wherein I found two wheat-corns, but 200 wild-oats, grown to that height all of one depth per­fectly upright, as thick as they could stand one by another, just as letters are set in a frame to print a book. How they should come there at all, the Lord knows, much more in that manner. Well then, I saw there was no hope of a crop of wheat, and thought it too late to sow barley, neither had I any left, save a little tary-head-corn, that I took & steep'd it a day and a night in water of an hors-dunghill. I sowed all that head-land; but one quarter of it, which had been troden with horses turning upon it in wet weather after it was sown. This barley, when harvest came, was the first I had ripe, clean without tares, or any other soil, as thick as it could stand, and every way the best that ever I had growing: but the wheat not worth the reaping; wherefore I let it stand till harvest was home; but had I mowed it green, it had been the best hors-meat of all other, as afterward I found in wild-oats and beans. When harvest was home, on a fair day, the winde sit­ting right, I set fire on it: but he that had seen that fire, and heard the noise, and had not read Virgil before, would have said certainly Virgil was at that fire before he made his book, and that there he learnt it, or else he could never have found out such an Epithete, as — Crepitantibus urere flammis: for whether it was by reason of the wild-oats, in every hors-footing made by turning on in wet weather, or otherwise, [Page 109] there was such a noise as if twenty muskets had gone off at once, insomuch that an herd of cattel being a quarter of a mile off, seeing the fire, and hearing the noise, as if they had been out of their wits, or rather stark mad, set up also such a running, roaring, bellowing, and howling, that it made me to run as fast as they, to hear such an hideous noise, and the fire so violent, the weather being dry, and the whole crop being still there which was very great, and the winde full in one end, and whistling, insomuch that all the ground for two or three and twenty pole long, and a pole and half broad, was all on fire at once: this past my skill to quench, neither would all the blankets in the Town have served the turn, if I had had them there. But that this was soon out, I think neither the Sicilian Aetna, that throweth stones sixty miles▪ nor Hecla in Ise­land, nor Vesuvius in Campania, that sends his ashes more then two hundred miles off; (or, if you will believe Cassiodorus, in the time of Titus and Vespasian, they flew into Asia, Syria, and Egypt: and lastly, breaking out again in the year 1632, Crepitus miliaria centum auditus: & did you not hear this cre­pitus? certainly it was because either you were deaf, or not near enough) could present a greater terrour. But notwithstanding all this, my wild-oats were not yet killed; and then I was vexed with my self, that I had not mowed them green for hors-meat: for out of every hors-footing, contrary to my hopes, I could takeup whole-yea psonds, that were never the worse for the fire, save onely their smell. Then I filled my hand-kerchief and both my pockets with them, to carry home to my hoggs, hens, pi­geons; but not a corn any of them would touch. All this was still worse and worse. About All-Saints-day following, there came a frost and a little snow, upon that there was so many flesh-crows, that you would have thought that there had been proclamations set up in all woods, groves, fields, and yards through the whole land to summon them thither; or whether that was their beacon when I burnt it, or no, I know not. These for a fortnight together so covered the ground, that you could not choose but say, it was far blacker then ink: for [Page 110] this was of a double die, one of black crows, and another of black ashes. The frost breaking, those that they had not eaten they trod into the ground with their feet, so that by the later end of the moneth, no meadow could be thicker of green grass, then that was of green-oats. I plowed them in, and by Candle-mass it was green again; I plowed it again, then it lay till the later end of April, and was green again; then I steep­ed my seed as I did the year before, and sowed it with barley, and had a very good crop, and so killed the wild-oats.

Burning of queach, &c.The burning of queach also, in some ground, is exceeding profitable. And not onely the steeping seed in dung-hill water helpeth greatly, but also in lime and water, by reason that which gives it heart lies close to the root. Some also wash seed-wheat and rie in lime and water in the seed-leap in the field, and then sow it, and so no crows nor pigeons will ever touch it.

INstead of beetle and stake, or crow of iron, make you an augre like a pump-augre, make it after this manner: Make a plate like a peel of a foot or fourteen inches square, well steeled, and turn it as an augre is turned; let it have a socket like a peel, but four-square, into which put a stake of good tough ash two foot long, and four-square, as the socket is, with a bar or hoop of iron about it at the top, to keep it from cleaving: let it be two inches square at the least upward, in which near to the top bore an hole, or else make a mortes to put in a cross piece to turn it by, and to take it out by, then enter it a little with your spade, as you do a carpenters wimble with a gouch, and then bore your holes; which in strong clay is an exceeding speedy way. Besides that, if the sets be not very great, you will have room enough to ram the moulds down to the bottom.

I Have severall times measured ground by statute, which should have been done by the eighteen-foot pole; but ne­ver the contrary. One amongst the rest was a close in Hexton in Hartfordshire, where three Copy-holders had each of them apart expressed in their severall copies, how much by measure; but not by what measure: thereupon it was taken for granted, that it must be statute-measure. One of the three had held all in his occupation divers years together, and lying in stitches, & no banks between had plowed one amongst another. A and B would have theirs again. A must have so much on the East-side, B so much on the middle, and C the rest; for C would neither shew his copie, nor yet make known how much he should have. So I laid out each man his share accordingly, and took a plot of the whole. Still it runs in B his minde, that his part was not so good as it had been formerly, mistrusting that I had done him wrong in laying it forth; so that he ac­quainted the Lord of the Mannour with it, who demanded of him by what measure he had measured it: he answered by the statute-pole; Then, quoth the Lord, there is the errour, the custome is eighteen foot, and was the measure taken in Henry the eight his time. This being known and reduced, C shewed his copie, and there was not a pole difference in the whole thing: so I gave them direction to alter it without going to the ground. To do this there are severall ways. First a statute-pole is sixteen feet and an half, or 33 half foot long, there­fore 33 half-feet square is 1089 square half-feet in a statute-pole: but in an eighteen-foot pole, which is 36 half-feet square, are 1296: so then if you multiply your statute-poles by 1089, and divide the product by 1296, you have the num­ber of eighteen-foot poles, which divided by 40 gives you the roods, and vice versâ. And thus six acres of statute, which [Page 112] is 960 poles, multiply'd by 1089 makes 1045440, and that divided by 1296 gives 806 864/1 [...]96 or ⅔ which is five acres six pole ⅔ of the 18 foot.

Likewise five acres of 18 foot is 800 pole; that multiply'd by 1296 produceth 1036800, which divided by 1089, quotient 952 72/1089 pole, that is 5 acres, 3 rood, 32 pole. And this is the best way. So that the analogy is thus.

As 1089 . 1296 ∷ 800 . 18 foot pole to 956.1089, id est, 5 acres, 3 roods, 32 pole 72/1089. And as 1296 . 1089 ∷ 800 statute, to 672 2/9, id est, 4 acres, 3 roods, 32 poles 2/9. And this is your best way: and thus may you do with all other poles.

Another way is; if upon your scale you have two scales, one of 11 in the inch and another of 12: if you lay down sta [...]e-measure by the scale of 12, and then measure the same plot by the scale of 11, it gives you the wood-land measure, and like­wise on the contrary.

SUppose any scale, as 10, and measure it by that; now if by measuring it by the scale of 10, it comes to but 23 acres 82 parts: but it is truely 34 acres, 31 parts; therefore finde a mean proportional between these two; which, because the work is somewhat difficult, I will therefore shew you the man­ner of it.

First multiply 32.82. by 34 31. as here it is set down: so you see it produceth 817⌊264 [...]. And be­cause [...] there are four figures in the Fracti­ons of the two Factours; therfore there [Page 113] are also four in the product; so the whole [...] number is 817 and 2642, the Fraction, the square-root is 28⌊59. which is the mean proportional desired; then say, As the lesser of the two numbers, viz. 23,82. is to your mean proportional 28 . 59 : so is your supposed scale to 12. the true scale, as 23 . 82. 28 . 59 ∷ 10 . 12. See the work.

But because there is too much difficultie to finde it this way, and so little by the line of numbers, and so soon done, and is exact enough; therefore by it divide the distance be­tween 23,82, and 34,31. into two equall parts, and the compasses will fall at 28,59. then because 28,59. is more then 23,82. therefore set one foot in 10, and turn the other upward; it will fall at 12, the scale desired.

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 [Page 114] them all; writing at the top of each page the name of the Pa­rishes, or Parish, wherein the land [...]th cont [...]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 par [...]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 [...]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:

• 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.