the Roots begin to rot they then come up best then stock them all up the other Wood will grow the better and they will pay you well for your Charge they will cost you about 6 s. a Stack and here they will be worth 12 s. or more when stocked up When you fell your Woods or Coppices cut them smooth and close to the Stub and a little slanting upwards as I advised you about Lopping Pollards the oftner you fell your Woods Coppices or Hedges the thicker they will grow for every felling gives way to the young Seedlings to get up and makes the weak Plants shoot strong Those Woods which increase by running Roots as Elm Cherry Popler Maple Sarvice c. which thicken your wood much And Felling makes the Roots of a tree to swell as Lopping doth the Body and so it produceth the greater shoots and comes sooner to perfection Whereas great wood and old and ill taken off from the Stub many times kills all When you fell your Woods leave young Trees enough you may take down the worst that stand next fall especially neer a great tree that you judge may go down next fall for by its fall it may spoyl some The Statute saith you are to leave twelve score Oaks at every Fall on an Acre for want of them so many Elms Ashes Beeches c. But leave according to the thinness of your wood and where underwood sells well there let your Timber-trees stand the thinner and in such Countreys where Coals are cheap and Timber sells well there let your Timber-trees stand thick and then they will need but little pruning up Endeavour to plant in your Woods such sorts of Wood as the Ground is most proper for if wet then Alder Sallow Willow Withy c. if shallow and dry Ash Cherry Beech Popler c. if shallow and wet Hornbeam Sallow Sarvice c. but remember that the Oak and Elm be entertained in all places If your Woods or Coppices be in Parks where you lye open to Deer then at every Fall plant in them such woods whose Barks the Deer do not much love such are the Hornbeam Hasel Sycamore c. When Trees are at their full growth there be several Signs of their Decay which give you warning to fell it before it be quite decayed As in an Oak when the top-boughs begin to die then it begins to decay In an Elm or Ash if their head dies or if you see they take wet at any great Knot which you may know by the side of the Tree being discolour'd below that place before it grows hollow or if hollow you may know by knocking it with the head of an Axe of which you may be the surer satisfied by boring into the middle of it with a small Auger or if you see the Nighills make holes in it these be certain Signs the Tree begins to decay but before it decayes much down with it and hinder not your self CHAP. XXXVII How to take the heighth of a Tree several wayes the better to judge the worth of them c. HAving shewed you how you may judge of Timber whether it be sound or not in the last Chapter I will now shew you how to take the heighth that you may the better know the worth of it for where you have a Rule to go by you may then the better ghess There be several wayes to take the Altitude of a Tree or Building that is perpendicular as by a two-foot Rule or two Sticks joyned in a right Angle that is square as the Figure A. B. C. having at A. a pin or hole to hang a Thred and Plummet on Suppose you were to take the height of X Y first then hold that end of your square marked with C. to your Eye then goe backward or forward till the Thred and Plummet hang just upon the middle of your Square perpendicular and your eye looking through two sights or two Pins at A. and C. or over the ends of the Square thus look to the very top of the Building at X. See Fig. 8 9. Which found with a Line and Plummet from your Eye at C let fall to the Ground at D measure the length of that Line and adde it to the height that Length to E then measure the distance from E. to the foot of the Altitude as at Y and that if your Ground be level is the height of of X. Y. Or take the Level from your Eye to the height and adde that which is below the Level to the Height c. as the Line C. F. sheweth To find the height of a Tree c. by a straight Staffe or by a Line and Plummet the Sun shining the Altitude perpendicular and the Ground Level if not you must make the end of both the shadows level to each foot which is soon done As if I should take the Level of B. at C. finding the very top of the shadow to End there I measure the Distance from C. to B. and find it 60 foot then at that very instant I set up a stick perpendicular as E. D. 12 foot long which I find to cast a shadow just 9 foot and then the Rule orders it self thus As 9 foot to 12 so 60 foot to 80 which you will find true if you work it by Logarithmes or by Rule and Compass thus Set one point on 9 extend the other to 12 that Extent will reach from 60 to 80 Or if you work it by Natural Arithmetick as 9 is to 12 so 60 to 80. See Fig. 10. The same may be done by Line and Plummet To take the Altitude or height by a Bole of Water or by a Lookingglass placed parallel to the Horizon Place on the Ground a Bole of Water or a Looking-glass at a convenient distance from the Building or Tree as far as you think the height is then go back till you espie in the middle of the Water or Glass the very top of the Altitude which done keep your standing and let a Plum-line fall from your Eye till it touch the Ground which gives the height of your Eye from the Ground 2. Measure the distance from your Plummet to the Middle of the water 3. The distance from the middle of the water to the foot of the Altitude Which Distances if you have measured exactly straight and level by Proportion you may find the Altitude required thus As the distance from the Plummet level to the Center of the Water or Glass Is to the height of your Eye from the Ground which is the Length of your Plum-line So is the distance from the Center of the Water to the Base or foot of the Altitude exact perpendicular to the very top of the height which gave the shadow to the Altitude for if your Object be not upright and you measure straight and level and just under the top that gave the shadow If you miss in any one of these you are quite out in taking the height
Figures and how they are to be measured TO speak of all sorts of Figures will be far beyond my intentions there being so very many irregular Figures which have many unequal sides and angles but they may all be brought into parts of some of the Figures following and Measured like them I shall shew you one Useful Prob. especially to make your Ovals by whether they be made from two Centres or four and then I shall touch at some Superficial Figures See Fig. 30. Suppose three pricks or points given so they be not in a strait line to find a Centre to bring them into a Circle This may be done several ways viz. either by Circles or by raising Perpendiculars as if the points at A. B. C. were to be brought into a Circle Draw a line from A. to B. and in the middle of that line raise a Perpendicular as the line D. E. which you may soon do for if you open your Compasses to any convenient distance and set one point in B. draw the Arch 1. and 2. then setting one point in 4. draw 3. and 4. where these cross draw the line E. D. Do the same with the points B. C. and where the two Perpendicular lines meet is the Centre as at F c. Superficial Figures that are irregular and right-lined are such whose Sides or Angles are un-equal of which some are triangles or triangular Figures and here Note that there are five sorts of triangles which are thus Named and known 1. Isocheles hath two of the sides unequal 2. Scalena hath the three sides unequal 3. Orthygone hath one Right and two Acute Angles 4. Ambligone hath one Obtuse and two Acute Angles 5. Oxygone hath three Acute Angles or Equilateral triangles See Fig. 31. Every triangle is half of a square whose Length and Breadth is equal to the Perpendicular and Side cut by the Perpendicular as is plain in the first Figure shewed by the pricked lines therefore to Measure any triangle raise a Perpendicular from the Base to the greatest Angle Then Multiply the whole Base by half the Perpendicular or the whole Perpendicular by half the Base and the Product is the Content Or thus take the whole Base and whole Perpendicular and Multiply one by the other the half of that Summe is the Content of the triangle c. Square or Quadrangular Figures are these following 1. A Geometrical square this hath Right Angle and sides equal 2. An Oblong-square which hath equal opposite sides and Rectang 3. A Rhombus hath equal Sides and unequal Angles 4. A Rhomboides having unequal Sides and Angles opposite equal 5. Trapezia Are all other four-sided Figures See Fig. 32. The first is Measured by Multiplying one of the Sides in its self In the Second the length Multiplyed by the breadth gives the Content The three last may be turned into two triangles each and so Measured as is before said Polygones are these Figures following as the end of a Tree hewed into five equal sides this is called a Pentagone of six sides Hexagone seven sides Heptagone eight sides Octagone nine sides Enneagone ten sides Decagone twelve sides Dodecagone To Measure any of these take half the perimeter that is half the Compass about and the perpendicular drawn from the Centre to the middle of any one of the sides Multiply the one by the other and it giveth the Content Circular Figures are these which be thus Named 1. The Circle is near Equal to a square made of ½ Diameter and ½ Circumference 2. The Semi-Circle to a square made of half the Arch line and ½ Semi-diameter 3. The Quadrant or fourth part of a Circle 4. The Segment Arch or part of a Circle The first is Measured by Multiplying the Semi-circumference by the Semi-diameter The second by Multiplying the Radius or Semi-diameter by ¼ of the Circumference of the whole Circle The third by Multiplying the Radius by ⅛ of the Circumference of the Circle that it was made of The fourth by Multiplying the Radius by ½ the length of that Arch-line thus have you the Content or Area of each To find the Diameter of any Circle or the Circumference by having one given the lowest Number is as 7 is to 22. so is the Diameter to the Circumference or as 22 is to 7. so is the Circumference to the Diameter To find the Length of an Arch-line Geometrically This Problem is Useful to be known for to Measure the Quadrand Segment of a Circle or Oval for the Oval is made of parts of the Circle First Divide the Chord-line of the part of the Circle into four equal parts then set one of these parts from one End of the Chord-line also set one of the four parts from the Angle in the Arch-line then from one point to the other draw a Line the length of this Line is half the length of the Arch-line See Fig. 33. Examp. A. B. the Chord-line Divided into 4 parts one of the 4 parts set from B. to C. and one part set from A. to D. then draw the Line C. D. which Line is half the length of the Arch-line A. D. B. which was to be found out Thus may you Measure this part of a Circle or the like but if the part of a Circle be greater than a Semi-circle then Divide the Arch-line into two Equal parts and find the length of one of these as is afore-said which doubled giveth the length of the whole Arch-line This Rule will assist you to Measure the Oval whether it be made from two Centres or four c. There is no regular Figure but may be Reduced into some of these Figures afore-said therefore I shall shew you the Use of some Geometrical Figures which are very Useful not Questioning but that you Understand the first Rules in Geometry as to draw a parallel Line to Raise a perpendicular-perpendicular-line from another c. for those things are out of my intended Discourse therefore if you be to seek in them consult with Euclid and others How to Raise a Perpendicular at the end of a Line by which you make a Square very Vseful also to set off a square-square-line from a strait-strait-line in any Garden Walk house-House-end or the like See Fig. 34. Examp. If you be desired to set off a square-square-line at B. from the Line A. B. take six Foot Yards or Rod and Measure from B. to C. in your strait-strait-line then take eight of the same Measure and set from B. to D. and ten of the same holding one end at C. bring the Line B. D. till it just touch the Line C. D. at D. so have you an Exact Square made by 6. 8. and 10. See Euclid first Book Prob. 47. and p. 35. Math. Recreations p. 93. See Fig. 35. This you may do in other Numbers that bear the like proportion for Euc. tells you that the square made of the side subtending the Right Angle is Equal to the squares made of both the sides containing the Right
three Inches and 078 1000 make one Foot take with your Compasses three Inches 078 from off a Scale and so many times as there is that Length in your Tree so many foot of Timber are there c. If any Tree be above 100 Inches Circumference then take half that Circumference and find the Number belonging thereto in the Table then take one fourth part of it and that makes one foot of Timber Suppose a Tree to be 146 Inches about the half of it is 73 against this in the Table is 4 Inches 075 parts one quarter thereof viz. one Inch 019 parts makes one foot of Timber at that Circumference These Tables with what hath been before said will be sufficient to measure any Cylinder by and how to measure a Cone I have shewed already A Cone is such a Figure as the Spire of a Church having a Circular Base and ending in a sharp point It is measured by the superficial Content of the Base multiplyed by one third part of the Altitude or Length A Pyramid or Pyramis is such a Figure as hath an angular Base and ends in a sharp point which is measured as the Cone is A Sphear or Globe is a solid Figure every where equally distant from the Centre it is measured by cubing the Diameter and multiplying that by 11 and dividing that product by 21 the Quotient sheweth the solid Content of the Sphere There be several other sorts of solid Figures as several parts of the Sphear but they all depend on the proportion of a Circle and its Diameter Also the Hexaedron which hath 6 Bases Octaedron 8 Bases Dodecaedron 12 Bases and several other which to name I shall forbear CHAP. XLIII Of the Oval how to make it and how to measure it with other Observations thereon HAving the Length and Breadth of the Oval given you you may take the whole Length and half the Breadth as is shewed before in bringing three Pricks into a Circle and from the Centre of these three poynts draw half the Oval and so likewise the other half as you see the Oval in the Figure drawn for the poynt F. is the Centre of the Arch A B C and the Arch A G C is made by the same Rule and where the Line F H. crosseth the Line A E C as at K there is the Centre of the breadth B G and the End A from the Centre K may you make the Ends of your Oval Round as you please so that from four Centres you may make the Ends of your Oval round as you please but if they be made from two Centres as that is then will the Ends be more Acute Or you may make your Oval thus Having resolved on the breadth draw the sides from Centres in the mid-Mid-line of the breadth as before then set up two sticks exactly in the mid-Mid-line of the Length at equal distance from each End then hold the Line at one and turn the Line to the side of the Oval and then on the other side the stick with the same length so may you make the Ends of your Oval as Round as you please for the nearer you place these sticks in the Centre of the length and breadth of the Oval the nearer Round your Oval is made even till you come to a Circle This way your Ingenious Work-men make their Ovals in small works as your Plaisterers Joyners c. and it is a good way and so common that I need not say more to teach how to make an Oval of any bigness but here I shall take occasion to shew the Figure of one at Cashiobury now made See Fig. 46. To measure this Oval which is 28 Rod long and 19 Rod broad as 't is now staked out at Cashiobury intended for a Kitchen-Garden This Oval being made of 2 Segments of a Circle whose Semi-diameter is 15 Rod as 't is found by making the Oval it being the Centrepoynt of each Arch-line of this Oval as the lines F A. F B. and F C. Now to find the length of one of these Arch-lines is shewed before which I find to be 18 Rod the half length of one which is shewed by the line D D. so the whole length of one Arch is 36 and both Arches round the Oval is 72 Rod. Now take the ½ of one of the Arch lines which is 18 and the Semi-diameter of that Arch which is 15 Rod Multiply the one by the other and it is 270 Rod which is the Figure A. B. C. F. that is half of the Oval and the Triangle A. F. C. which must be substracted out of the 270 then the Semi-Oval will be 192 Rod. For the Base A. C. is 28 Rod which is the length of the Oval and the Perpendicular of the Angle which is E F. is 5. 57. Now half the Base which is 14 Multiplied by the whole Perpendicular 5 57 100 gives 77 98 100 which is 78 Rod ferè this taken from 270 the Area of the Figure A. B. C. F. there then remains 192 Rod which is half of the Oval that doubled is 384 Rod which being Divided by 160 sheweth that the Content of this Oval will be 2 Acres and 64 Rod. But if your Oval be round at the end as your Ovals are that be made with 4 Centres then they be more difficult to be Measured however these Rules are sufficient An Oval is no ill Figure for a Garden for if the Garden-wall be an Oval and the length of the Oval point North and South as the afore-mentioned Oval doth A. being the South point C. the North then may such a Wall be Planted with Trees both in-side and out-side and have never a Tree stand to the North Aspect for it you make your going in at the South end of your Oval then will those 2 Trees or Tree that stood on the in-side or were to stand there be removed from the North aspect to the North-East and North-West according to the largeness of your Gate so will every 2 Trees on the in-side of your VVall tend nearer the South-point till they come to the point C. which is South and then the Trees on the out-side every 2 Trees will fall nearer the North-point at C. till you leave that point of the Oval between 2 Trees so will not one Tree stand to the North aspect and but few near the North aspect the like whereof no other Figure can do that I can think of An Oval with the ends pointing East and VVest is no ill Figure for a Garden for the walls in this as in the other are not so subject to oppose the winds as straight walls be therefore not so blasting as you may well conceive 2. Ovals on each side the Front of your House would be no ill Prospect but in many things very convenient these being at equal distance from the middle of your Front and poynting upon your Lawn c. CHAP. XLIV Suppose you have a Plat to draw on one or many Sheets of
top-heavy You may safely cut off small branches and prune small Trees at this Summer-season And for such Trees as have a great Pith as the Ash and Walnut I take it to be the best time for them And whereas some say to the contrary yet if the Reader will be Advised by me let him prune such in Summer But in the midst of Winter forbear to prune most Trees especially great Boughs or such Trees as have a great Pith or tender for then the wound lyeth exposed to the open Air and Wet and Frost coming upon the Wet and piercing so far into the wounded place as the wet hath gone kills the Wood and makes a hole in that place and that hole holding Water many times Kills many a good Tree especially where great Boughs are taken off for they be long a covering over and never will be covered if the Tree be Old Therefore if your Tree be Old forbear to cut off great Boughs but if for some Reasons you are forced to do it then cut off such Boughs two Foot or a Yard from the Body of your Timber-tree and let the place where you cut off such a Limb be perpendicular to the Horizon rather inclining to the Nadir than the Zenith by so doing the water will not lie on such a place and then the Tree will receive no harm But if your Tree be young and thriving then cut off the Boughs as close as you can keeping the wounded place perpendicular to the Horizon and be sure not to leave Elbows to receive the wet as too many of our Husband-men do for the closer you cut off a Bough to the Body the sooner the bark covereth that place therefore cut off the side-boughs of young Timber-trees close and smooth I wish I could perswade all Lovers of handsome Timber-trees at every Fall of their Woods to prune up all the Timber-trees but then the Wood must not stand too long before it be fell'd You may prune off boughs of ten years growth very well and so every ten years or oftner if it be in Hedg-rowes prune up your Trees till you have got them to such a height as you find most convenient viz. to fifty or sixty foot high For I have many times observed Trees of Oak Ash Elm and Beech to have leading shoots sixty foot high and more when they have had not above ten foot of good Timber for Boughs have broke out at that height and have so distributed the sap that they were little worth but for the Fire when if they had been pruned up as is before directed you might have had the same height of good Timber which how much more profitable it would be and also beautifull I leave to any mans Judgement The Ash and Beech cover the wounded place over soon and seldom break out many side-boughs The Elm very frequently breaks out side-boughs yet will arrive to a great height of good Timber the Oak is a little subject to break out side-boughs and though a slow grower yet by its own hardness of his Wood he preserves himself well till it hath over-grown the wounded place which it will in a few years doe if your Tree be young and thriving and the boughs not very great for if the boughs be great that place when they be cut off is such a Damm to the sap that it forceth it to break out with many small boughs there especially in such Trees as have a thick and rugged bark as the Elm and Oak have when old But if the Tree be young and thriving then is the Bark thin and loose and will more readily give way to the sap to ascend into the Head and not break out into side-boughs but if some few do break out often pruning them close off will prevent that But if you would be at a little more trouble note this which I have found to be true and your Timber shall pay you well for your pains At Midsommer after you have pruned up your Trees take off all the small shoots that are broke out on the side of your Trees close to the body of the Tree do thus two or three years together and you will find every year the side-boughs to be fewer and fewer till you have a clear body beautifull to behold and profitable for as good Timber thirty or forty foot or more which otherwise would not have been a quarter so high Thus may you make an Elm which is a Tree most subject to break out side-boughs as clear from boughs forty or fifty foot high as they be Your Oak that is young you may easily master and bring it to a clear body though it is some what troublesome in Woods yet in Hedg-Rowes it may be practised with ease or in Walks or on single Oaks But our Yeomen and Farmers are too much subject to spoyl such Trees as would make our best Oaks by heading them and making them Pollards I wish there were as strict a Law as could be made to punish those that do presume to head an Oak the King of Woods though it be on their own Land By this means we should have the Farmer that is scanted in Wood by often pruning off the side-boughs make many finer Trees than now there are for in such places there is great food to make him a great Tree and then in Coppices if you let a Tree stand to be very great it spoyls many a young one and also your under-wood But methinks I hear some opposing me saying that by so pruning up of Trees they do not prove so well for the Joyner Carpenter Wheeler c. for they say if the Tree doth over-grow the Knot when they come to cleave such a Tree that place proves faulty within and the Timber is not so good Secondly They say that cutting off the side-boughs makes Trees more knotty Thirdly they say that it makes a Tree decay sooner To these three Objections I shall answer and then hasten to conclude and so leave my beloved Oak I do grant that if the Knots be great though the Trees be young and thriving and have covered the place over well if you come to saw out such Trees for Plank Board or VVainscot that there may be some Defect there where great boughs were cut off but suppose there be you have still the same length clear Timber at the lower end as you would have had if these boughs had not been cut off and then by pruning up your Trees they grow straighter and your Tree carries a greater length of Timber usefull for Beams Summers Raising VVallplats Rafters Joyce c. and how much Timber these spend more than the other viz. Board and VVainscot c. I leave you to determine But my Advice is not to let your boughs be great but take them off from such Trees whilest young and then the boughs will be young and small and such Trees will cover such places in a little time and these small Knots will not
such up you spoyl their spearing by breaking it off or by letting in the drye Aire and so kill it therefore keep your Beds clean from weeds and about the middle or latter end of August they will be come up About the midst of September sift a little richer Mould all over the Bed but not so much as to cover them thus doe the next Summer and take off the side â— boughs though young and when they have stood two years on that Bed then plant them on beds in your Nursery keeping them with digging and pruning up yearly till you have got them to the stature you think convenient to plant abroad In setting this or any sort of Tree forget not to top the ends of the tap-root or other long ones and also not to leave a bruised End uncut off You may set them in streight lines in your Nursery about a yard one Row from another and about a foot and a half one Tree from another in the Rowes mind the Natural depth it first did grow at and set it so when you remove it have a care of setting any Tree too deep and also keep not this Tree nor a Walnut long out of the ground for their spongy Roots will in a little time grow Mouldy and be spoyled Therefore if you cannot set them let them be covered with Earth and then you shall find this Tree as patient in removing and as certain to grow as any Tree I know The ground they like best is a light Brick-earth or Loom as I said before that they dislike most is a rocky ground or a stiffe clay but if one have a mixture of Brick-earth c. and the other of small Gravel Drift-sand Sand c. then there they will do pretty well They naturally increase very much of themselves and the more where they meet with natural ground if you fell a thriving Tree and fence in the place you then may have a store to furnish your Woods and Hedge-rows with the worst and the straightest to nurse up in your Nurseries for to make VValks Avenues Glades c. with for there is no tree more proper for the certainty of its growing especially if you make good large and deep holes and where the ground is not natural there help it by some that is and then you may hope for a stately high growing Tree if you take care in pruning it up as is before shewed of the Oak You need not much fear its growing top-heavy for it having such a thick bark the sap is subject to lodge in it and break out many side-boughs and the Roots apt to break out with suckers the more when pruned therefore prune it up high and often but let the season be February for then its fine dark green-coloured Leaf and long hanging on it is the more ornamental and fit for walks As for the way to increase it from the Roots of another Tree I doe referre you to the seventh Chapter which will shew you fully how to perform the same observing but them Rules you may raise many fine young Trees from the Roots of another much better than naturally they will be produced from the Roots I advise you where you find your ground Natural in your Hedge-rowes there to plant some of this most usefull wood for it will run in the Banks and thicken your Hedges with wood and is very courteous to other sorts of wood growing by it Do not let ignorant Tradition possess you that it will grow of the Chips or of Truncheons set like Sallowes though the Author of the Commons Complaint saith it will for I assure you it neither doth nor will In Lopping of this be carefull to cut your boughs close and smooth off minding to keep them perpendicular to the Horizon the better to shoot off the wet It will grow well of Laying as is before noted and also directed in the Chapt. of Laying in which if you take but a little labour more than ordinary from one Tree you may have in a few years many in your Hedge-rowes or elsewhere therefore deferre not but put this in practice especially the great Kind My Lord Bacon adviseth to bud it to make the Leaves the larger but that is needless Part of these Rules I wrote some years agoe at the request and for the use of the truely ingenious Planter and Lover thereof Sir Henry Capell and I shall give you the same Conclusion now that I did then to him which take as followeth Since Gard'ning was the first and best Vocation And Adam whose all are by Procreation Was the first Gard'ner of the World and ye Are the green shoots of Him th' Original Tree Encourage then this innocent old Trade Ye Noble Souls that were from Adam made So shall the Gard'ners labour better bring To his Countrey Profit Pleasure to his King CHAP. XII Of Raising and Ordering the Ash AND as for Raising the Ash I shall give you the same Rules as I did to the aforesaid Honourable Person the same time before the Discourse of Forrest-trees was written Let your Keyes be thorow ripe which will be about the middle or end of October or November When you have gathered them lay them thin to dry but gather them off from a young straight thriving Tree My Reason to gather them off a young thriving tree is because there will the Keyes or seeds in the Keyes be the larger and solider therefore by consequence they are the abler to shoot the stronger and to maintain themselves the better and longer Though I know by experience that the seeds of some old Plants will come up sooner so the seed be perfect than the seed of young Plants and also that old seed so it will but grow will come up sooner than new Seed My aforesaid Reasons do in part demonstrate this Or thus Nature finding her self weak doth like a provident Mother seek the sooner to provide for her weak Children for Nature is one in divers things and yet various in one thing Now if you gather them off from a straight tree 't is the likelier they will run more up and grow straighter than those which be gathered off a Pollard or crooked tree for it is well known and might be proved by many Instances that Nature doth delight in Imitation and the Defects of Nature may be helped by Art for the great Alterations which many times we find visible in many Vegetables of the same species they all proceed either from the Earth the Water or the Heavenly Influences but the last is the greatest Author of Alteration both in Sensibles Vegetables and Animals However Like still produceth its Like and since there is such plenty of Forrest-trees that bear seed you may as well gather all sorts of Keyes and Seeds off or under such Trees as not As for the time of sowing them let it be any time between the latter end of October and the last of January for they will lie till Spring
a great Bearer and a Tree that doth not last very long my Ground being also a shallow Ground I think of 22 foot asunder to plant these Trees at or as neer that as the Ground will permit Then Secondly I go round my Ground and observing my Fence well and finding no great Trees in it I then resolve to set my Trees at six foot from my Fence but note if there be great Trees in your Hedge that fences your Ground then this is too nigh then I set off six foot at one Corner of my Orchard and six foot at the other Corner of the same side which is the East side then I set off six foot at one Corner of the West side it matters not which only that End which is the Levellest is the best for Measuring Having set these three stakes I strain a Line from one stake to the other on the East side then I lay a square to this Line removing it along the Line till I find the other End of the Square point exactly against the Stake on the west side then laying a Line right square to that Line till you come at the Stake on the VVest side I then measure by this Line as many 22 foots as I can noting how many times 22 foot I find and what you find is over or more than 11 foot then make your distance the less to make that up the equal distance for one Tree more but if it be less than half the distance your Trees are to stand asunder then adde that which is under the 11 foot to the number of Trees that be to stand asunder Observe but this and then you need not fear that your Trees will stand too far off on one side and too near on the other it being the same Charge to plant in good Order as at Random as too many doe nay many times less Charge and how much more pleasing Order is I leave them to judge to whom the great God of Order hath given a great delight to imitate him in his glorious works But as for this my piece of Ground which I pitch on only for Example viz. One Acre and a Square I must find the square Root of 160 Rod or as near it as my Chain will give and then substract but the 12 foot out for the distance of the Trees from the Fence and divide the Remainder by 22 the Quotient tells you how many Trees will stand in a Row the over-measure substracted from or added to as your Reason teacheth you Note this that it is most commonly the best way for your Rows to goe the longest way of your Ground for though your Trees stand 22 foot asunder yet your Rowes in their straight Lines will not stand so far Now to find the square Root there are very many Rules but none that are to my Apprehension so exact and easie as by Logarithmes find but the Logarithme of your Number then take half that Log. the Number answering is the square Root Exam. The Log. of 160 is 2. 204 11998. The half of this Log. is 1. 10205999. The nearest Number answering this Logarithme is 12 Rod 65 100 that is 12 Rod 65 Links of a one Pole-Chain divided into 100 parts The Proof may appear by these three Examples following By this it doth plainly appear that 12.65 is the nearest Number that can be found by your Decimal Chain it is but 225 10000 more and by Logarithmes but 2 of a Link put into 100 parts therefore exact as need be for this purpose unless it were for Calculation in Astronomy or the like And you see that 12.64 multiplyed in it self amounts to 159 Rod and 7696 10000 so that I take 12 Rod and 65 of 100 to be Length or Breadth it being a Square they both be as one Now being the Question is propounded in Feet we must turn this 12 Rod and 65 100 into feet also but note you may work the same by the Links of your Chain better than by foot Measure but some 't is possible have not a Chain therefore observe both wayes and first by Foot measure 12 Rod multiplyed by 16 Foot and a half shew the Feet in 12 Rod. Then for the 65 Links of one Rod put into 100 parts or if it be your four Pole-Chain as is most usual now put into 100 Links then are these 65 Links but 16 Links and a 1 49 by that Chain then by the Rule of Three say if 25 the Links in one Rod be equal to 16 foot and a half the feet in one Rod how many feet are equal to 16 Links and a Quarter The Question ranks it self thus in Decimal Fractions As 25 is to 16. 50 so is 16. 25 to 10 foot 725 1000 of a foot Do you desire to know what this Fraction 725 1000 is in Inches or Barley-Corns which be the lowest vulgar terms in surveying to satisfie you and also my self and likewise to instruct those that desire to learn this Excellent Rule the Rule of Three which rightly for its excellent Use is called the Golden Rule Observe this if one foot or 12 Inches be put into 1000 parts as here it is and must be being 't is the Integer or whole summe of 725 the Rule orders it self thus as 1000 is to 12 Inches so is 725 to 8 Inches 700 1000. Now to know what this 700 1000 is in Barley-Corns do as before say thus If 1000 be equal to 3 Barley-Corns what is 700 equal unto I say as here you see it proved that 700 is equal to two Barley-corns and one tenth part of one for 100 is one tenth of 1000. By this it doth plainly appear that if 12 Rod 65 100 be turned into feet it maketh 208 foot 8 Inches 2 Barley-corns and one tenth of a Barley-corn So that you see the square Root of an Acre is near 208 foot 8 Inches two Barley-corns neglecting 1 10 because 65 100 is somewhat too much Now from this 208 foot 8 Inches I take the 12 foot for the Trees to stand off from the Fence there remains 196 foot 8 inches then I divide this by 22 the distance the Trees are to stand asunder So I find there may stand ten Trees for here you see there may be open places and 20 foot 8 inches for one more so there wants but one foot 4 Inches or 16 Inches to make 10 Trees in a Row for there is alwayes a Tree more than the open Note that in planting of Walks this is of good use that as I said before to make one Tree more this 16 inches I divide by 9 being there are 9 opens between the ten Trees the Quotient is near 2 inches which substract from 22 foot and there remains then 21 foot 10 Inches and so much must every Tree stand asunder the proof is as followeth Here you see that'tis 196 foot and 6 Inches it wants but 2. In. Then to know what distance your Rows may stand asunder the Rule is If
you make an Equilateral Triangle the perpendicular of that is the distance between the Rows which Triangle I have drawn by the same scale of the Orchard See Fig. 4. See Chapter the 44 th The breadth of my Paper 6 inches the Plat 196 foot and 66 of 100 for the 8 inches my Scale is neer 33 parts in one inch but I take 32 because it is an even number See Fig. 4. If you will trye the Perpendicular of this Triangle 't is but 19 foot so that there are 3 foot between every 2 Rowes saved by Planting your ground this way more than those that plant their Ground to have every 4. Trees to make a Square the Trees standing in both at the same distance But finding that but little Paper beareth the full breadth of 6 inches the quarter of a sheet and this being less square by twelve foot than my full Draught should be this being only for the square of the Trees I draw and proportion my Scale to the breadth of 5 Inches and a half 208 foot divided by 5 and ½ sheweth that your Scale must be one Inch divided into 37 parts and better but for fear this Scale should be too great I draw my Plat by the Scale of 40 in one Inch so if you divide 208 the breadth of the Ground by 40 it gives 5 Inches and 8 40 and so broad must the Plat be as you may see by the Figure Thus may you enlarge your Draught or diminish it on your Paper as your pleasure is But 't is better to draw all your Draughts as large as your Paper will give you leave the distance of the Trees in the Draught is 21 foot 10 Inches asunder See Fig. 5. By this you see that if you plant your Trees triangle this Acre of Ground hath 11 Rowes and 104 Trees but if you begin either side with 10 as before I began with 9 then will there be in this ground 105 Trees but to know how many Rowes you may have in any ground doe thus and you may presently satisfie your self you see the ground from one out-side Row to the other is 196 foot 8 Inches which divided by 19 the distance that the Rowes be asunder neglecting the Fraction as needless now gives 10 distances Alwayes remember that there is one Rowe or in a Range of Trees one more than the Distances in this Draught the Trees stand at the same distance but square See Fig. 6. By this last Draught it appeareth that if you set the Trees at the same distance and set them square that then there will be but 9 Rowes and 90 Trees in this square Acre of Ground but if you plant them Triangle then will it hold 14 or 15 Trees more But if your Plat of Ground be a long square or any other Irregular Figure then will your Triangle-way hold a great many more in proportion to the Quantity of Ground besides it makes many more Rowes therefore more pleasing to the Eye Note this well for setting your Trees exactly having found the distance they are to stand asunder and likewise how many Rows with a Line laid or stakes true set where your first Row must goe the said stakes will be of good use to set the Trees by when your holes be made having resolved on which side you will begin which alwayes let be the side you find most in sight set down your two Corner-stakes for the first and last holes to be made then with your Assistants measure exactly in your Row by the Line 21 foot and Ten inches but in case there should be odde measure then proportion it as is shewed before by making one Hole more or less as you see cause Then having two men to assist you with a Chain for Line will reach or shrink measure exactly the distance of two Trees let one hold at one Tree and one at the next in the Row you standing at the Angle with the Chain equally stiffe put down a stake at the Angle and so go on to the next two Trees pitching down your stakes perpendicular And also considering the Thickness of your Stakes thence let your two men go to the next and you setting down one at the Angle till you have staked out the whole Ground this doe when you come to set your Trees being carefull to keep your Chain strained both sides alike and to allow for the crookedness of your Trees and when you have got two Rows planted then your Eye will assist you well enough to observe the Rowes as you go on Note also that if your Ground be large and a square then your best way will be to find the middle Row and set that off square from that side of your Ground you mind most or find to be straightest there begin to mark out your holes and also to plant your Trees but if your Ground be Irregular or have an Angle on one side then begin on your straight side and run the odde measure into the Angle as far as is convenient to plant in such a Ground you need but find what distance your first Row must be set at But if your Ground have both the sides straight then it will be convenient to set the side-rowes at equal distance from your Fence Thus you may well perceive that it is but measuring the length and breadth of your Ground and proportion one to the distance your Trees be to stand at the other to the distance the Rows are to be asunder and you may proceed to stake out your Ground After this method you may plant any sort of Forrest trees in Groves The best way is to stake out your whole Ground before you plant a Tree or make one hole by so doing you may well perceive where a fault is and easily mend it in time though some are of opinion otherwise but I shall leave them to their own Judgement and satisfie my self with Experience and Reason But for fear any thing should be dubious to you that I have writ observe but the setting out of these two Rows and then I hope it will be plainly demonstrated to you how to proceed Suppose the Length of your Ground should be the length of the Line marked at the End thus See Figure 7. Having staked out your first Row as before is shewed and having the Chain exactly the distance of two Opens then bid one of your men take one End and the other man the other End you holding exactly the Middle bid one hold at the stake one the other at the stake two then pitch you down your stake right at the Angles as the pricked Line sheweth So let your two men remove from stake to stake and you from Angle to Angle till you have staked out your Rowe and then let them come to that Row you last set out and goe on to another so proceed till you have staked out your whole Ground Thus much for planting Trees in Orchard fashion I have been the larger to
pleasant Prospect as too many doe by making the Walks too narrow If you make any Walk that leads to any pleasant Front of a House or other Object if it be but half a mile long let it be at least forty foot wide but if longer more as 50 or 60 foot wide or the breadth the length of your Front But if you be for walks of shade then make three Walks the middle one 40 the two out-side walks each 20 foot or 50 and 25 the out-side walks or divide your Front into two parts and let the middle be as broad as both the side-walks so that if you make three walks together let the middle one be as much as both the other so will the Trees range much the better whether you set them square or triangular but however keep to one of them though I think the square to be the best because then four Trees in the four Rows end all together fit to end in either Semicircle segment of a Circle Oval Triangle or Circle for all walks of any Length especially in Parks should end in some one of these Figures or lead into some other walk but where they doe fall into another walk there should be a Circle to receive them or else they seem much defective I shall now endeavour to shew you how to make a walk through a wood and then I will give you an Example of some of the Figures that Walks ought to end in Suppose you were to clear a Walk or Line through a Wood for to run the Mid-line true about three yards wide having the Centre given doe as before run your Mid-line as far as you can into the wood and at one yard distance on each side the Mid-line two other Lines Run these Lines also as far as you can into the wood keeping them just one yard distant and setting up stakes as you proceed into the wood with large whites all of a bigness as half a sheet of white Paper on every Stake spread abroad when any of these three Lines come to a Tree run on the other two till you are past the Tree and then set him off again in its place parallel to his fellowes and so proceed till you be through the Wood marking that wood which must goe down then when your under-wood is stocked up run out your Line again still when you come to a Tree set off Parallels and when past set off into your true Line again This way I cut a straight Line through the Wood-walk at Cashiobury from the North front over one wall and several Hedges neer a mile long and when I came to stake it out true there was at the very end not four foot difference as the ingenious Hugh May Esq can witness and several others This way of staking out a walk by three Lines is worth your practising in setting out of Walks that go through Hedges or Bushes be sure to carry on the Mid-line of the walk and the two Lines where the Trees must goe together now and then measuring to see if they keep their equal distances and that which is amiss you will soon find and may as soon rectifie it again There is another way of carrying a straight Line through a Wood which Reason taught me and by Experience I have found true the place where the middle of the walk should poynt to being given there hang up a large Candle and Lanthorn and having found the Mid-line some 20 30 or 40 yards from that there hang up another they must both hang pretty high but let that next the House or Center be the higher having thus placed your two Lights and in a clear calm night but not too light goe with your Man to the further side of the wood till you make both these Lights in one Line and then walk on keeping them so marking the Trees on each side of you quite through the Wood order them to be cut down at leisure so shall you have a straight Line cut through the Wood. But if you are to make a walk from Gate to Gate so that you are tied to such a Center at each End if your walk be so that you can see from End to End it is then but setting up two Stakes one at each end by the sight of which cause a third to be set up in the middle But if you cannot see to the far End for Hill Wood or the like then you must cause an high Pole with a white on the top to be set up at the End by that and your Centre-stake cause your Assistants to set up as many as you think convenient in the mid-Mid-line but if that wood be so high that you cannot see a high Pole at the End then run it over as near as you can by ghess take notice of the Length and of your Error at End and ¼ and ½ and ¾ each at a Quarter of the Length of your walk set off a quarter of your Error c. And thus bring your Line till it ranges exactly from one point to another from Gate to Gate then set off the two Lines where the Trees must goe as is before shewed by the square and if for three walks then the four Rows of Trees if there be three Walks let the Middle-walk be just as broad as both the other which is the best Form or else all three of equal breadth so may you set your Trees not onely square but they will answer one another several wayes beside as square from A. to B. and other wayes as B. to C. and to D. so that every Tree must keep his Row Range Square and equal Distance c. See Fig. 14. The pricked Lines shew how the sight will take the Trees as square from A. to B. and Angle-wayes from C. to B. or C. to D. c. Thus have I shewed you how to stake out the Mid-line and the two side-lines of your walk I wish Sir E. T. Sir W. B. and Sir R. B. had seen these Directions before they had planted their walks I do judge they then would have done them better For Errors in planting make too many worthy Persons forbear Now as for the Figures which walks ought to end in I have named them before and if you observe most Plants especially Trees which make your Walks the most of them end in a Circular figure and therefore I will shew you some wayes how Walks ought to end in a Circle For a walk ending bluntly without any Figure or entring into another may be compared to a Tree with the Head off and what difference there is let those which well observe the Objects of Nature judge Let the Circle be three times the Breadth of your walk if conveniently you can or bigger if you have Room After you have found the Mid-line and resolved upon the Centre as at A. and of the Bigness of your Circle next consider of the Distance of your Trees round the Circle run that distance
over first and if you find an odde Tree let it stand in the Mid-line and in the Circumference as at B. but if no odde Tree then let the Mid-line pass tween two Trees adding or substracting the odde Inches till you find the equal distance your Trees must stand at c. See Fig. 15. Let the Trees in your Circle stand not much above half the distance that the Trees are in the Rowes as in the last they were 16 foot â—ere Trees in the walk 24 foot but in the Oval thicker that they may shew the Figure the better A fine Tree in the Centre of all Circles doth well See Fig. 16. Two Walks meeting in a Point let that be the Centre of the Circle as at A. and there a Tree Two Walks crossing one another where the Mid line meets let that be the Centre of a Circle as B. Note That if your Circle be divided into two parts by Walks as the Circle A. find a distance that the Trees in each part may stand as neer that distance as may be there they be near 11 foot both and the Circle B. neer 10 foot asunder Now the smaller parts the Circle is put into the thicker set your Trees round it as B. is put into four parts by the two Walks crossing it set these parts the thicker that they may shew the Figure the better Of three Walks going up to a Circle as they doe to the Bowling-Green at Cashiobury which Green is 80 yards or 240 foot diameter with a border 16 foot wide planted with three Rowes of Spruce-firs set in the year 1672. being set Circular and Triangular see the Figure there are 90 trees in the outer Row and 90 Trees in the innermost Row and 89 in the middle Row which is 269 trees I lost not one of these except one that was stollen See Fig. 17. To plant such a Border first with a Line on the Centre B. mark out the Circle where the inner Row should goe then set two Trees in the Circle and in the Rows of the VValk as at A. A. then having resolved of the distance to set them at run that Distance over from A. A. and the odde Inches or parts adde or substract according to the Number of the Opens to or from the Measure you first resolved on as is shewed before c. 1. Next I shall shew you some wayes how VValks may come into or end in a Semi-circle or Segment of a Circle c. as A. being a Gate B. C. is a Hedge or Pale A. is the Centre of the middle of the VValk and Circle See Fig. 18. Or thus The Centre at A. and then three Trees or more to go to the Pale parallel to the Walk as 1 2 3. 2. How three Walks may come into a Semi-Circle See Fig. 19. This may be continued on with three or more Trees parallel to the Mid-line as in Fig. 19 c. 3. How three Walks may break into a Semi-circle at three several places and how to make the Semi-circle so great as that you may have just so much Wood on all sides of the Walks as the Walks are broad or to order it to what proportion you please Suppose the three Walks to be each forty foot wide which makes 120 foot then there is to be 40 foot without one side-walk and 40 foot without the other side-walk and 40 foot between each of the side-walks and the Middle-walk which is four times 40 foot that is 160 foot so that the 120 foot makes 280 foot for the Arch of this Semicircle then find the Semi-diameter to the Arch of this Circle and strike the Arch from the Centre Ex. The Semi-circumference being 280 the Circumference is then 560. Then as 22 is to 7 or if you will be more Exact as the Learned Oughtred in his Circles of Proportion pag. 43. saith as 3.1416 is to 1. so is the Circumference to the Diameter but the other is a standing Rule nigh enough for our purpose As 22 to 7 so 560 to 178 4 22 the Diameter if you turn this Fraction into Inches it will be two Inches and near half of a Barley-Corn so then the whole Diameter will be 178 foot 2 Inches the half is 89 foot one Inch With this 89 foot one Inch being the Semi-diameter draw the Arch of your Semi-circle which Arch shall be 280 foot and from the Centre by which you drew this Arch may be the Mid-line of your three Walks as is described in the Figure See Fig. 20. Let the Centre A. be in a straight Line with the pricked Line B. B. and parallel to the Middle-walk C. the Line B. A. B. may be if Convenience serve 50 or 60 foot from the wall pale hedge and that to goe parallel to that Line and where the wall or pale ends there may be a Row of Trees continued so far as you please or can c. At the Centre A. let be some fine Tree set or some Figure c. I once saw a Semi-circle set out somewhat like this where I saw a great deal of measuring before they could proportion it exactly to such a place as was intended I took my Pen and by these Rules I told them justly how far they should goe More I could say if I thought it not unseasonable now Here you see how to proportion a Semi-circle which you may enlarge with three four or five Trees on each side and parallel to the Middle-walk as is in the second Figure of Semi-circles but be mindfull to make such a Figure for your Walks to end in and of such a bigness as is most convenient to your Ground the Arch of the Semi-circle may be one Row of Trees as in the Figure or two three four or more as you please but three Rows set triangular do very well 4. How and where a Semi-circle is proper on the side of a Walk c. Suppose you have a Walk a Mile in length or more it is no wayes improper but pleasant and satisfactory to have your Walks shew you every ¼ of a Mile ½ of a Mile and ¾ c. to the End or from each End or from one End back to the other as if you begin at the Centre-tree in the Semi-circle at A. then at ¼ of a Mile at the Figure 1. make a Semi-circle to break out on the Right hand the Centre-tree to be exactly in the Row of the Walk and just a quarter of a mile as is shewed in the Figure as well as the Largeness of our Paper would bear by the Semi-circle Figure 1 then at the half mile let two Trees stand in a Semi-circle at Figure 2 one to stand in the Row that makes the walk which two Trees is half a mile and at three quarters three Trees still minding that one be in the Row or Walk the Centre-tree of your Circle and the exact distance So one Tree the Centre of the Semi-circle as at Figure 1. is a ¼ of
D E. is but 290 Pole which wants 62 Pole and a half of the half of the Field therefore take 62. 50 from the Triangle A C D. by the Rules delivered in the 38 th Fig. and there will be added the Triangle A D H which being added to the Triangle A D E will divide the Figure into two equal parts the thing desired See Fig. 41. Thus may you take half from any irregular Figure or more or less than half and from what Angle desired which will assist you well how to fell your Woods by the Acre or to know how far you shall go into a Field to take off any parts the fourth Rule which I found by my Practice I commend for very good One Example I shall give you more which shall be according to my fourth Rule I try'd it in a Field near to Cashiobury-Park this I was ordered to doe by my Lords Steward Mr. Sydenham to take off three Acres from a small Field as exactly as I could at one End appointed by him First I measured that End and found it to be 37 pole and ¾ but observing the Hedges I found them to splay off a little so that about 6 Rod and a half or little more would be the middle which I set off at each End and found that Line to be 38 Pole long then I divided 160 the Poles in one Acre by 38 the Poles of the End of the Field the Quotient was 4 and 8 38 which 8 of 38 I must turn into parts of my Chain that is into Decimal parts thus As 38 is to 8 so is 100 to 21 and 2 of 38 which 2 is not considerable So that if the Chain be divided into 100 Links you must then goe 4 Pole and 21 Links at each End for to make one Acre of Ground but if your Chain be a four pole Chain divided into 100 Links then with such a Chain you must goe 4 pole 5 links and ¼ and a little more to make one Acre at 38 Pole long Then for three Acres I must goe in breadth 12 Pole 63 100 to make three Acres and a little more see it proved Here you may see that 12 Pole 63 100 multiplyed by 38 Pole gives 479 Pole and 94 100 which being divided by 160 the Poles in one Acre gives in the Quotient 2 and 159 so then if you adde but 6 of 100 to the 94 it is just three Acres for whereas I take in the Decimal parts but 21 100 I should take the 21 Links and the 22 th part of one of these Links which niceness may be dispensed with From what hath been said you may measure any standing Wood or part thereof especially if these parts be near to a Square or Triangle if not you may Reduce them to one of these Thus having spoke something how superficial Figures are to be measured I shall give an Example or two of the Chain and it shall be of the Four-pole Chain divided into 100 parts as suppose the Figure A B C D. See Fig. 42. This Figure may be measured several wayes as first it may be put into two Triangles and so measured or else you may measure both the Ends and half them and so measure the Length in the middle you may measure also both the sides and half them and then measure the breadth in the middle But for Example First I measure the side A B. and find it to be 15 Chains and 80 Links of the Four-pole Chain the End B C. is 6 Chains 74 Links the other side C D. is 12 Chains 50 Links and the other End D A. is 6 Chains Then adde the two sides together of which take the half that half is the mean Length both sides added together make 28 Chains 30 links half of which is 14 Chains 15 links then adde the Ends together viz. 6 Chains and 6 Chains 74 links the total of both is 12 chains 74 links then half of the Ends added together is 6 chains 37 links Then multiply the mean Length by the mean Breadth and cut off 5 Figures to the Right hand and whatsoever Figures Remain to the Left hand are Acres and those 5 Figures cut off are parts of an Acre Thus may you know the Content of a Field without Division as in the last Examp. 14. 15 multiplyed by 6. 37 gives 901355 then if you take off five figures as the fractional parts there remains 9 which is nine Acres two Pole and above ⅛ of a Pole But you may easily know the fractional part of any Decimal fraction thus This belongs to 100000 for if the Decimal fraction have 5 Figures the Integer is 6 the fraction 4 then the Integer 5. c. Then work it by the Rule of Three or by your Line of Numbers thus As 100000 is to 1355 so is 160 the square Poles in one Acre to 2 Poles and neer ¼ but that you may be the better satisfied in this most useful Rule if 100000 be Equal to one Acre or 160 Pole So that when any Fraction is repair but to these Rules and you may see what Number of poles is equal to it you may proportion it to half-poles c. for Not onely to prove this but also to shew you how much readier this way is than the 100 Links to bring it into Rods or Poles then divide it by 160 to bring the aforesaid Measure to the one Pole Chain and 100 multiply 14. 15 by 4 it gives 56. 60 and 6. 37 multiplyed by 4 gives 25. 48 which being multiplyed one by the other gives 1442 1680 10000 I will neglect the Fraction as being not ¼ of a Pole and divide 1442 the Poles in that Measure by the sq Poles in one Acre 160 Pole and the Quotient is 9 and 2 over that is 9 Acres 2 Pole and a little more as before But how much the other way is readier than this I leave the Reader to judge Example the Second How to measure a Triangle with the Four-pole Chain and never use Division As in the Triangle A B C. the Base A C. is 40 Pole and the pricked Perpendicular Line is 20 the half is 10 Pole Now when you have even Poles as in this Examp. you must adde two Cyphers to the length and two to the breadth or else you cannot take off the 5 Figures or 5 Cyphers as is before shewed then taking the 5 Cyphers off after Multiplication there remains 40 which sheweth you that such a Triangle that hath such a Base and such a Perpendicular containeth four Acres of Ground And if you work it the common way you will find it to be true See Fig. 43. But to assist you yet further to turn  M. C. X.  ac ro p. ac ro p. ro po 1 6. 1. 0 0. 2. 20 0. 10 2 12. 2. 0 0. 1. 0 0. 20 3 18. 3. 0 1. 3. 20 0. 30 4 25. 0. 0 2. 2. 0 1. 0 5 31. 1. 0 3. 0. 20 1. 10
6 37. 2. 0 3. 3. 0 1. 20 7 43. 3. 0 4. 1. 20 1. 30 8 50. 0. 0 5. 0. 0 2. 0 9 56. 1. 0 5. 2. 20 2. 10 Poles into Acres observe this Table The Denominations of the several Numbers are known by the Marks under which they are set as all under Ac. are Acres under Ro. are Roods under Po. are so many Pole and so the first Column under M. answereth to Thousands that under C. to Hundreds that under X. to Tens and the odde Pole if any be are set down under Pole As e. g. 1442 Pole To know how many Acres by this Table first for the One thousand in the Table under M. is 6 Acres one Rood set that down as you see in the preceding Page then four Hundred under C. and against 4 is 2 Acres 2 Roods set that down then in the Table under X. and against 4 is one Rood set that down then the odde Poles set down alwayes under the Poles as 2 under Poles then summe them up and you shall find it is 9 Acres 2 Pole as before This Table being so plain there needs no more Examples A Table of superficial long Measure from an Inch to a Mile according to the Standard of England Inch.       12 A foot      36 3 A yard     45 3 ¾ 1 ¼ Ell.    198 16 ½ 5 ½ 4 ⅖ Pole   7920 660 220 176 40 Furlong  63360 5280 1760 1408 320 8 Mile A Table of square Measure Acres 4 160 4840 43560  Rood 40 1210 10890   Pole 30 ¼ 272 ¼    Yards 9     Feet An Example of the Table of long Measure Suppose you were to find out how many Inches were in a Pole long look under Inches and against Pole there is 198 and so many Inches are in a Pole long and 16 ½ Foot 5 ½ Yards And in the Table of Square Measure to know how many square Yards is in a Pole look against Pole and above Yards there is 30 ¼ the square yards in a Pole There be several other sorts of superficial Measures as Pavings Plaisterings Wainscotings and Painting which are to be measured by the Yard square and may be measured by some of the Rules before shewed your readiest way is by the Yard divided into ten parts so will you odde Measure come into Decimal Fractions which are as easily cast up as whole Numbers Or if you measure by the Foot Rule have it divided into 10 parts and when you have found the Content in feet divide it by 9 the Quotient will shew you how many yards and if any remain they be feet Some sorts of Work are measured by the square of 10 foot the side so that such a Square is 100 foot for ten times Ten is a Hundred By this Measure is your Carpenters Work measured as Floors Partitions Roofs of Houses So also is Tiling and Slatting measured this is very ready to measure and to cast up for if you multiply the Breadth by the Length so many hundreds as you find so many Squares are there and what remains are parts of a Square Board and Glass c. are measured by the foot which may be divided into ten parts which will be much easier to count up But if you would be more fully satisfied in the Rules of Surveying see the work of Mr. Leyborn Mr. Wing Mr. Rathborn c. Having the Length of a Field to know what Breadth will make one Acre of Ground by the Four-pole Chain and Line of Numbers Ex. The Length is 12 Chains 50 Links to find the Breadth to make that Length just one Acre do thus Extend your Compasses from 12.50 the Length to 10 that Extent will reach from one to 80 which is the Breadth in Links to make one Acre for if you multiply 12.50 by 80 it yields 100000 from which if you take off five Cyphers there remains one which is one Acre c. CHAP. XLI Of Measuring Holes and Borders that be under a Pole broad by which you may the better lett or take them to doe by the Pole-square c. with several Tables of Measures HOles for to set Trees in are seldome made under one foot Diameter or above eight foot Diameter the Depth may be reduced to a foot deep The Rules to measure any Circle by are the same which is thus To take the Semi-circumference and the Semi-diameter and multiply these Halfs the one by the other sheweth the superficial Content or Area of that Circle This you may work either by the Pen or Line of Numbers As by the line of Numbers thus The Diameter being four foot extend the Compasses from 1. to 4. the Diameter keep your Compasses fixed and alwayes on the Number 7854 set one point and turn twice to the Right hand but if they fall off at the End at the second turn then must you set them on the first part of the Line when you have turned them once c. Having taken the distance of 1 to 4. and set one poynt on the standing Number 7854 the other poynt goes to 31 and neer ½ thence if you turn another turn it will go off from the Line therefore you must find the poynt 31 and near ½ on the first part of the Line and set one poynt there the other will reach to 12 and about 58 100 which tells you that in a Circle of 4 foot Diameter there are 12 superficial square feet and a half and better Now to work it according to the Rule above by the Line if you multiply the Semi-diameter by the Semi-circumference it giveth the Content the same way I shall do it with my Pen Example First having the Diameter I must find the Circumference Extend the Compasses from 7 to 22. the same will reach from 4 to 12. 58 the Circumference then ½ of 12. 58 is 6 29 100 the Semi circumference which multiply by 2 the Semi diameter Extend the Compasses from 1 to 2 the same Extent will reach from 6. 29 to 12. 58 as before that is twelve foot and a half and 8 100 You here may see how easily and readily the Golden Rule and Multiplication may be performed by the Line of Numbers which I use the oftener that you might take the more notice of the Easiness of it to work any of the Rules of Arithmetick by Being once perfect in this you will soon understand the Sector with its excellent uses in the Mathematicks performed by Lines and Compasses but according to the last Rule see the same Question wrote with the Pen that you may see the Agreement that is between Geometry and Arithmetick Example 144 Which 741 Barly-corns is above half a foot as was shewed before but in finding the Circumference I adde a Cypher to 4 which makes it 40 from that I take 6 times 7 which is 42 and should be
pole as in the first Example then always such a Figure ends in ¾ of a pole as that doth But if a Figure be two pole and ¾ one way and two pole and ¼ the other as the last was it ends always in such a Decimal as this 1875 that is half a quarter and half half a quarter that is ⅛ and 1 16 parts of a pole square This way may you cast up the Content of a Ground very speedily and Exact if the middle Length and middle Breadth fall out in ¼ ½ or ¾ of a Pole and this way you may summe up a Field before you do it decimally And then one will be good proof to the other which with little Practice will make you so perfect that in small Fields you will readily tell the Content without Pen or Rule only by Memory These Rules may also be done by two turns of your Compasses on the Line of Numbers and there is no way so ready if once you come but to understand that most usefull Line well For as the distance of one of the Numbers to be multiplyed is from one at the End of your Line the same distance is the product from the other Number Example of the Second Figure As One is to Two and a half the same Extent of your Compasses will reach from 2 and a half to 6 ¼ the Product A Table of Board-Measure by having the breadth of the Board in Inches against which is shewed the Quantity of one foot thereof in Length The use of this Table Bredth of the board in Inches The quantity of one foot in Length  f.pts. 1 0.083 2 0.167 3 0.250 4 0.333 5 0.417 6 0.500 7 0.583 8 0.667 9 0.750 10 0.833 11 0.917 12 1.000 13 1.083 14 1.167 15 1.250 16 1.333 17 1.417 18 1.500 19 1.583 20 1.667 21 1.750 22 1.833 23 1.917 24 2.000 25 2.083 26 2.167 27 2.250 28 2.333 29 2.417 30 2.500 31 2.583 32 2.667 33 2.750 34 2.833 35 2.917 36 3.000 Having taken the Breadth of the Board in Inches see what Number answereth it in this Table and what Number you find against the Breadth in Inches multiply by the Length of the Board or Glass and cut off the three last Figures to the Right hand thereby you shall have the Number in feet and the parts cut off are parts of a foot Example A Board ten Inches broad and ten foot long against 10 you see is 0.833 which multiplyed by 10 gives 8330 then taking off 3 Figures there remains 8 that is 8 foot and 33 100 But if you would measure this Board by the Line of Numbers then set one point of your Compasses on 12 extend the other to the breadth in Inches the same Extent will reach from the length in feet to the Content For as 12 the side of a superficial foot square is to the breadth in inches which here is 10 so is the length in feet which in this Example is 10 to the Content in feet and parts which is 8 foot 33 100 Note this for a general Rule that if the Breadth be less than 12 Inches then must you turn the Compasses to the left hand on your Rule and if more than 12 then turn your Compasses from the Length in feet to the Right hand Learn but to read your Line well and this Rule then may you measure any Board or Pain of Glass as easily as to tell ten c. CHAP. XLII Of measuring Timber and other solid Bodies with several Tables usefull thereunto c. IN Board Glass Land c. we onely took notice of the Length and Breadth which was sufficient to find the superficial Content but to measure solid Bodies we must take notice of the Length Breadth and Depth Most of solid Figures are measured by finding first the superficial Content of the Base or one End and multiplying that by the Length if both Ends alike but if tapering then by ⅓ of the Length and as superficial Measure hath 144 square Inches in one foot and 72 square Inches in half a foot and 36 square Inches in a Quarter So In solid Measure 1728 square Inches make one foot And 8.64 square Inches make half a foot And 432 square Inches make a quarter of a foot For every Inch square is like a Die and so is a foot of solid Measure supposed to be for what it wants either in Breadth or in Thickness it must have in Length so that in what form soever your solid Body is that you measure there must be 1728 solid Inches to make a foot for 12 the side of a foot multiplyed by 12 gives 144 for one side and 144 multiplyed by 12 another side gives 1728 the Cube-square Inches in a Cube-square foot Now to find the solid Content of any piece of Timber or Stone that hath the sides equal first find the superficial Content of the End in Inches and parts and multiply that by the Length in Inches the Product is the Content in solid Inches Then divide that summe by 1728 the Inches in a foot the Quotient sheweth you the Content in solid feet and what remain are Inches If you would work this by the Line of Numbers the Rule is thus Extend the Compasses from one to the Breadth in Inches The same Extent will reach from the Depth to the Content of the End Then extend the Compasses from one to this Content of the End Keep your Compasses fixed and that Extent will reach from the Length to the Content in solid Inches But if your solid Figure hath both Ends alike and in form of a Regular Polgone that is a piece of Timber hewed into 5 6 7 or 8 equal sides c. which is called by some A prisme then take the Semi-circumference and multiply that by the Radius or Semi-diameter that product by the Length giveth the Content But if your solid Figure be a Cylinder that is a round piece of Timber or Stone having both Ends equal Diameter as a Roller c. here take the Semi-circumference multiply it by the Semi-diameter and the Area of that by the Length giveth the solid Content Now many of the Bodies of our Timber-trees will be near this form of a Cylinder but Custom hath got such footing though very false that men will not measure their Timber the true way but will still keep their Error which is to gird the middle of the Tree about with a Line and take the fourth part thereof for the true square and so measure it as a four-square piece of Timber but how false that is may appear by the ensuing Tables Whoever is pleased to trye will find that there may be four Slabs taken off to bring that to a Square and that squared piece then will be near equal to the Measure they first measured the piece of Timber by so that when they have brought their piece square by hewing or sawing they then have the Measure that it was measured for when it
was Round But several men have demonstrated this false Rule to be false near ⅓ as Mr. Wing Mr. Philips and others Yet Custom doth and will keep its Road. I have already shewed how to measure Timber by the Customary way by the Line of Numbers in Chap. 35 and 36. before-going and for further satisfaction I referre you to these Tables following A Table shewing the solid Content of one foot Length of any piece of Timber according to the superficial Content taken at the End thereof The Inches at the End f. pts 1 0.007 2 0.014 3 0.021 4 0.028 5 0.035 6 0.042 7 0.049 8 0.056 9 0.062 10 0.069 20 0.139 30 0.208 40 0.278 50 0.347 60 0.417 70 0.486 80 0.556 90 0.625 100 0.694 200 1.389 300 2.083 400 2.778 500 3.472 600 4.167 700 4.861 800 5.556 900 6.250 1000 6.944 2000 13.888 3000 20.833 4000 27.778 5000 34.722 6000 41.666 7000 48.711 8000 55.555 9000 62.500 10000 69.444 20000 138.888 Finding the superficial Content at the End of your Timber-stick or Stone c. let it be Round or Square so it hath but the same Compass from one end to the other against that Number is the feet and parts of one foot Length and by multiplying that by the Length of your Stick sheweth the Content in square feet Example The superficial Content at the End being 200 Inches and 5 foot long against 200 is 1 foot 389 parts which multiplyed by 5 the Length yieldeth 6 foot and 945 parts that is near 7 foot of Timber But if the Number that is at the End be not in the Table then adde two Numbers together and then take the Number which answereth them and adde them together and multiply the Length by that summe as before c. A Table shewing the true Quantity of one foot length in any true squared piece of Timber for Inches and half Inches from half an Inch square to 36 Inches square I. fo pts  0.002 1 0.007  0.016 2 0.028  0.043 3 0.062  0.085 4 0.111  0.140 5 0.174  0.210 6 0.250  0.293 7 0.340  0.390 8 0.444  0.502 9 0.562  0.627 10 0.694  0.765 11 0.840  0.919 12 1.000  1.085 13 1.174  1.266 14 1.361  1.460 15 1.562  1.668 16 1.778  1.891 17 2.007  2.127 18 2.250  2.377 19 2.507  2.641 20 2 778  2.918 21 3.062  3.210 22 3.361  3.516 23 3.673  3.835 24 4.000  4.166 25 4.340  4.513 26 4.694  4.877 27 5.063  5.250 28 5.445  5.670 29 5.840  6.043 30 6.250  6.460 31 6.673  6.890 32 7.111  7.333 33 7.562  7.780 34 8.028  8.263 35 8.507  8.750 36 9.000 If you would enlarge this Table further the Rule is this As the square of 12 Inches which is 144 is to 1000 So is the square of another Number to another Example As in 36 the Square of it is 1296 then as 144 is to 1000 So is 1296 to 9 foot c. as is in the Table The Vse of the Table The Square of a piece of Timber being found in Inches and the Length thereof in Feet to know the Content take the Number answering to the Square of Inches out of the Table and multiply it by the Length in feet Example A piece of Timber 18 Inches square and 25 foot long the Number answering to 18 Inches square is Which multiplyed by 25 the Length Which is 56 foot and one quarter A piece 18 Inches square at the End and one foot long is 2 foot and 1 40. A Table shewing by the Compass of Round Timber what is contained in a Foot length thereof Co. fo pa. 10 0.055 11 0.066 12 0.079 13 0.093 14 0.108 15 0.124 16 0.141 17 0.159 18 0.179 19 0.200 20 0.221 21 0.243 22 0.267 23 0.292 24 0.318 25 0.343 26 0.374 27 0.403 28 0.433 29 0.465 30 0.497 31 0.531 32 0.566 33 0.602 34 0.639 35 0.677 36 0.716 37 0.756 38 0.798 39 0.840 40 0.884 41 0.929 42 9.974 43 1.021 44 1.070 45 1.119 46 1.169 47 1.220 48 1.273 49 1.327 50 1.381 51 1.437 52 1.496 53 1.552 54 1.612 55 1.671 56 1.732 57 1.795 58 1.860 59 1.923 60 1.988 61 2.056 62 2.124 63 2.193 64 2.264 65 2.335 66 2.406 67 2.480 68 2.555 69 2.631 70 2.707 71 2.785 72 2.864 73 2.945 74 3.026 75 3.108 76 3.191 77 3.276 78 3.362 79 3.449 80 3.537 81 3.625 82 3.715 83 3.807 84 3.866 85 3.990 86 4.084 87 4.183 88 4.279 89 4.377 90 4.475 91 4.576 92 4.677 93 4.780 94 4.882 95 4.987 96 5.093 97 5.200 98 5.307 99 5.416 The Vse of this Table is as followeth Look for the Compass of the Tree in Inches and in the Column annexed you have the Quantity of Timber in one Foot length which multiply by the Number of feet that the Tree is in Length and the Product is the Content thereof Example The Circumference or Compass of a Tree 47 Inches and 12 foot long the Number against 47 Inches is 1.220 So there is so much in one foot Length Which multiplyed by 12 gives the Content That is 14 foot and above half a foot This Table shews how many Inches in Length make one Foot of Timber according to the Compass of the piece of Timber from 10 Inches Compass to 100 Inches Compass Co. In. pts 10 217.15 11 179.46 12 150.80 13 128.49 14 110.79 15 94.312 16 84.822 17 75.137 18 67.020 19 60.151 20 54.286 21 49.228 22 44.865 23 40.904 24 37.690 25 34.743 26 32.122 27 29.787 28 27.697 29 25.820 30 24.127 31 22.596 32 21.206 33 19.936 34 18.784 35 17.736 36 16.755 37 15.862 38 15.038 39 14.276 40 13.572 41 12.916 42 12.310 43 11.744 44 11.211 45 10.723 46 10.262 47 9.830 48 9.425 49 9.044 50 8.686 51 8.349 52 8.030 53 7.730 54 7.447 55 7.178 56 6.924 57 6.684 58 6.455 59 6.238 60 6.030 61 5.836 62 5.649 63 5.471 64 5.301 65 5.140 66 4.985 67 4.837 68 4.696 69 4.561 70 4.432 71 4.308 72 4.198 73 4.075 74 3.965 75 3.861 76 3.760 77 3.663 78 3.569 79 3.479 80 3.393 81 3.310 82 3.230 83 3.152 84 3.078 85 3.006 86 2.936 87 2.869 88 2.804 89 2.742 90 2.681 91 2.622 92 2.566 93 2.511 94 2.458 95 2.406 96 2.356 97 2.307 98 2.261 99 2.216 100 2.171 The Vse of this Table Having taken the Circumference of the Tree in Inches look that Compass in the Table and against it you may see how many Inches or parts of an Inch make one Foot of Timber then with a Ruler or a pair of Compasses which are better measure how many times you can find that in the Length of the piece of Timber and so many Foot is in that piece of Timber This is a most usefull Table to measure your Timber-trees by Example The Compass of a Tree being 84 Inches about then