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-line from a strait-line in any Garden Walk House-end or the like See Fig. 34. Examp. If you be desired to set off a square-line at B. from the Line A. B. take six Foot Yards or Rod and Measure from B. to C. in your 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
So doth your Walnut Chesnut Horse-Chesnut Peaches Almonds Apricocks Plumbs c. and the onely difference from Beans and Pease is that these Stone-fruits put forth at the small ends and the other alwayes at the sides In like manner there be several sorts of Trees and most sorts of Plants that be small which put forth Root at the small end and as soon as that Root hath laid hold of the ground they then send out two false Leaves nothing like those that grow on the Tree or Plant which two false Leaves are the seed which divides into two parts and so stand some small time on the top of the ground and then between these two false Leaves comes forth a Shoot which produceth leaves like those of the Tree or Plant from whence it came Of this way of growth there be an infinite number both of Trees and Plants as the Elm Ash Sycamore Maple Pear Apple Quince and the most sorts of the seeds of Trees which are not environed by Stones or Shells of seeds the Melon Parsnip Carrot Carduus Angelica and indeed most sorts of seeds CHAP. V. Of the several wayes to raise Forrest-trees or others and how to perform the same by Laying THose sorts of Trees which will grow of Cuttings are the easiest to raise by Layings some of which sorts you may see in the next Chapter Now touching the best time for laying your Layers of Trees observe that if they be Trees that hold their Leaf all Winter as Firres Pines Holly Yew Box Bayes Lawrels Elix c. Let such be laid about the latter end of August But if they be such as shed their Leaf in Winter as Oak Elm Line Sycamore Apple Pear Mulberry c. let such be laid about the middle of October I do grant that you may lay at any time of the Year but these times I take to be the best for then they have the whole VVinter and Summer to prepare and draw Root in at that time of the year the Sun having so much power on the sap of the Tree as to feed the Leaf and Bud but not to make a shoot and if that little sap that rises be hindred as it is by some of the following wayes of laying the Leaves and Buds yet gently craving of the Layer makes the Layer prepare for Root or put forth root a little to maintain it self being it finds it cannot have it from the Mother-plant and being it wants but little Nourishment at that time of the Year I think it is better to lay Layers of Trees and to set Cuttings than at other times In Summer when the sap is much abounding or in VVinter when the sap stirres little or in the Spring when the sap begins to rise for then it comes too suddenly to draw sap from the Layer before it hath drawn or prepared for root for Nature must be courted gently though I know in small Plants the Spring or Summer doth very well for they being short-lived are therefore the quicker in drawing root and besides that Trees are many times laid as they are not As for those Trees that are apt to grow of Cuttings take but some of the boughs and lay them into the Ground covering them about half a foot with fresh fine Mould leaving them with the end of your Layer about one foot or a foot and a half out of the ground keeping them moist in Summer and in Twelve Months time you may remove them if rooted if not let them lie longer Another way is take a Bough you intend to lay and cut it half way through right cross the wood then slit it up towards the end half a foot or according as your Layer is in bigness lay the slitted place into the ground and you shall find that slitted place take root if laid as the former and so ordered This way you may encrease many fine Flowers and small Plants but they being out of my Element at this time I shall not speak of the ordering them for fear I seem tedious to some Another way to lay a Layer of a Tree is take a piece of VVyer and tie it hard round the bark of the place you intend to lay into the ground twisting the ends of the VVier that it may not untie prick the place above the VVier thorough the bark with an Aul in several places then lay it into the ground as the first A fourth way of Laying of trees is Cut a place round about one Inch or two where you find it most convenient to lay into the ground and so proceed as is shewed in the first way of Laying A Fifth way to lay some sorts of Trees is to twist the place you intend to lay into the ground as you do a withe and lay it as is shewed in the first way of Laying by this way and the first you may furnish your Woods and Hedges For they being easie any ordinary man will perform the same Thus you may from one Stub as a Sallow or the like between one Fall and another of your VVood for a Rod square of Ground and more if that one Stub produce but strong shoots fill it well with Wood For when the Stub hath got two or three years shoot then lay round it as before at large is shewed there letting them remain to produce new Stubs But if you would increase by laying some young Trees from an high Standard whence you cannot bend the boughs down to the ground then you must prepare either Box Basket or Pot and fill them full of fine sifted Mould putting a little rotten VVillow-dust with this Earth for that keeps Moysture to help the Layer to draw root then set the Pot or Box thus fill'd with Earth upon some Tressel or Post as your Ingenuity will direct you then lay your Bough by the second third or fourth way of Laying leaving not too much head out because the wind will offend it if you doe and by its own motion be likely to rub off the tender young Root and thus lay your Hops this way These things observed you may raise many choyse Trees as Mulberry Hors-Chesnut c. These Rules may instruct you sufficiently concerning the propagation of Trees by Laying but let me tell you it is hard to raise a fine straight Tree by a Layer or Cutting I have hinted at the Reasons before Note the smaller your Boughs be Set them the less out of the ground and keep them clean from VVeeds that they spoyl not your Layers Alsonote that the harder the VVood is then the young VVood will take root best laid in the ground but if a soft VVood then older boughs will take Root best Now you that be Lovers of wood make use of these sure Directions and if you repent then blame me CHAP. VI. Of those sorts of Trees that will grow of Cuttings and how to perform the same IF your Ground be moist you may Set with success any sort of Willow Sallow or Osier
from it till the next Year or rather longer then take it up at a fit Season and you will find it will at those ends where the Roots were cut off have drawn many tender young Roots apt to take and sufficient for the Tree wheresoever you shall transplant him further to facilitate the Removal of such great Trees or small ones that are ticklish to Remove for the Adornment of some particular place or the rarity of the Plant there is this Expedient A little before the hard Frosts surprise you make a Trench about your Tree at such distance from the stemme as you judge sufficient for the Roots dig this so deep till you come lower than the side-roots if your Ground be a dry Ground water the Hill of Earth the Frosts will lay hold on it the more but commonly in Winter before Frosts we have showers saves you that Labour then lay some Litter in the bottom of your Trench which will keep that part from freezing in case you have Occasion to undermine it more to loosen it when you take it up as is very likely you will Thus let it stand till some hard Frost do bind the Earth firmly to the Roots and then convey it to the Pit or Hole prepared for its new station having before covered the Earth by with some Horse-Litter to keep that Earth from freezing which Mould will then be ready to cover that clod round the Root of the Tree and the ends of the Roots and so secure it the better and that Litter will do well to lay round the Tree on the top of the Ground But in case the Tree be very great and the Mould about the Roots be so ponderous as not to be removed by an ordinary force you must then have a Gin or Crane such a one as they have to Load Timber with and by that you may weigh it out of its place and place the whole upon a Trundle or Sledge to convey it to the place you desire and by the afore-said Engine you may take it off from the Trundle and set it in its hole at your pleasure By this Address you may transplant trees of a great stature without the least Disorder and by taking off the less of their Heads which is of great Importance where this is practised to supply a Defect or remove a Curiosity I do suppose that one of these small Cranes or Gins would be very useful to those that have a great many pretty big trees to take up in their Nurseries especially such as have strong and tough Roots for if the Ground were but well loosened round the Roots and a Rope well fastened a little above the Ground to the stemme of the tree I dare engage that this way one Man with a Lever shall draw up more than ten Men And besides this will draw upright which is better than drawing on one side as many are forced to do You must have on the lower end of the three Legs pieces of Plank to keep it from sinking too far into the loose Ground I have now one a making and hereafter I shall be able to give you a better Account of it than now the onely Inconvenience I think of at present is in fastening the Rope about the Tree so that it may not slide or gall the tree but a piece of good Leather about four or five Inches broad with three or four Straps to come through so many holes when it is fastened to the Rope they may all be strained alike this I suppose will do your work The afore-said Learned Author Adviseth you before you take up trees to mark them all on one side the better to place that side to point to the same Aspect it did before For Oaks growing on the North side of an Hill are more Mossie than those that grow on the South-side this I grant because that side is Colder and Wetter for it is Cold and Wet Ground that breeds Moss most and that gets from the Ground upon the Trees Also he says that Apple-trees standing in a Hedge-row after the Hedge was taken away the Apple-trees did not thrive so well as they did before for want of the shelter of the Hedge I say that if the Hedge-row had drawn up the Apple-trees so as to make them top-heavy they might not thrive so well but if they were not the shelter being taken away they would thrive the better unless by thriving he means growing in height See Lord Bacon's Natural History p. 113. For a tree pent up cannot spread But as for placing the South-side of a tree South again this is not to the purpose for the greatest time that Trees grow in is from the Suns entring into Aries to his entring into Libra and all that time that is half a Year the Tree hath the Sun on the North-side both Morning and Evening and the North side hath the benefit of warming it self later in the Evening and earlier in the Morning having two hours time earlier and two later in the height of Summer more than the South-side Again you shall have the Cold be as much on the South-side of a Wall or Tree in the Night as on the North if the Wind blow on the South-side therefore I do Judge that to place a Tree the South-side South again signifieth little though the same Author saith p. 88. and the Author of the Book Called Mathematical Recreations p. 75. saith That a Tree groweth more on the South-side than on the North I have oft Observed the Annual Circles and have found as many nay more to the contrary for thus I have always found on a Tree near the Ground the Annual Circles have been the greatest on that side from which most of the great Roots came As if a Tree grow on the South-side of a Bank you shall find the Circles on that Tree to be greatest on the North-side c. but higher on a Tree the Circles are ever greatest on that side the Tree where there is a great Bough breaks out for the Sap has great recourse thither many times by sudden cold some is stayed by the way and so increaseth that side of the Tree most For I take the Sap of a Tree if the Weather be open that is of those Trees that shed their Leaves to be still ascending into the Head though it be Mid-winter though there do not rise enough to keep the Leaves on nor to make it bud forth yet it is plain that it keeps the buds full and fresh and increaseth the growth of the Tree for that same pory substance of the Tree which is between every Annual Circle that is made by the Winter-sap and the milder the Winter is the greater you shall find this to be as is visible in Ash Oak Elm c. The other which is more hard and clear is increased by the Sap in Summer and the more feeding the Summer is by showers the more shall the Circles increase on dry Ground and according
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
a mile two Trees as at Figure 2 is ½ a mile three Trees as at Figure 3 is ¾ of a mile See Fig. 21. Though the Figure doth not show well because the smallness of the Paper will not allow Room to draw the distance of miles as the Trees are according to Scale though my scale is here for the distance of the Trees 160 foot for one Inch yet I presume where this is really acted in Walks it will do well I here begin at the Centre-tree in the Semi-circle and in the Right-hand Row shewing how the ¾ of the mile may be set out and shewed by the Semi-circles on the sides at the other End I begin at the Centre of the Circle and so shew the ¼ ½ and ¾ how they may be set out on the other side Or if you please you may have a Tree in the Mid-line of your Walk at every quarter of a mile with a Circle to break round that Tree three times the breadth of the Walk which Tree must be pruned up high or else it will hinder the Prospect of your Walk I fansie the other way is best as let a Tree stand at every ¼ of a mile as you see in the Figure See Fig. 22. Thus having shewed you how Walks may end in Circles or Semi-circles I shall now shew how Walks may end or come into an Oval and how it sometimes happens that an Oval is the best Figure that Walks can End in If three Walks meet acutely at one place then it will be necessary to have the Mid-line of the three Walks meet at a Tree in the side of an Oval for if you make that poynt the Centre of a Circle it will be too large 't is possible larger than your Ground will permit as at Cashiobury where the three Walks meet by Hemsted High-way for if I had made the Circle from the aforesaid Centre and made the Semi-di3ameter so large as to have in the Circumference the two Trees marked A. A. which rangeth for both Walks then would this Circle have been too great and beside could not be made within the Pale Now I having Orders from my Lord that the Mid-line of these three Walks should meet at a Tree as in Fig. 23. they doe at B. and that I should make the Figure so large as that the Wood which is between the Middle-walk and the two out-side Walks should end at a Tree which should stand exactly in the Range of Trees for the Middle-walk and also for the in-side Rows of the two out-walks by considering I found the Oval to suit best with this ground so I having these two Trees as at A. A. and the Poynt as at B. which I took for the Breadth of the Oval accordingly I made it See the Figure Length of the Oval is 205 foot Breadth 124 foot Middle-walk 50 foot the side-walks each 40 foot wide having wood between the VValks and round the Oval See Fig. 23. Now having the two Trees as at A A. and the Centre-tree of the three Walks B. from the Mid-line of the middle-walk and in the middle of that Line between A A. and B. draw a perpendicular Line which sheweth the Length of the Oval at each End set a Tree as C. C. then divide the distance between the Centre-tree at B. and the End-trees at C. C. which let be at such a distance as may best suit with the six Trees between D. and C. on each side here the Trees between B. and C. are ten foot ten Inches distance and the Trees between D. and C. are 10 foot 9 Inches distance Let alwayes the Trees that make either Oval or Circle stand pretty nigh they shew this or any other Figure the better For this no certain distance can be given but they must be set at such a distance as the Arch-line can be divided into c. I shall shew you how to know the Length of an Arch-line and how to make an Oval or other Figure hereafter This Oval and Walks are surrounded with Wood and also between the Walks ending at a Tree as at A A. you may make broader at your pleasure or you may alter the Oval in shape or bigness as your Ground and Fancy shall direct you Your Oval may be surrounded with a double or treble Row of Trees if you fansie it and indeed if it be in a place where it is not encompassed with wood it is very proper An Oval or a Circle are very good Figures for Ponds though they be not in use Now for making Walks to end in a Triangle this may be several wayes according to your Fancy or Ground But I confess I never yet saw or heard of any Walk in England or elsewhere that ended in such a Figure But why may not the best of Figures be neglected by the Ingenious Survey or both at home and abroad as well as we see many Excellent things known to several ingenious men which are practised by few Having made at the End of Walks Semi-circles Circles and Ovals of several sorts and notwithstanding that I had at the end of the three VValks that goe from the Garden to the Bowling-green that end next the Garden a Figure given me by a worthy person but how proper for that place I shall not now speak I nevertheless neglected that and made the Triangle as is shewed by Figure 24. The trees I set the closer because this being a Front of the house intended to be hid at a distance all but the breadth of the VValks therefore I chose this Figure as much proper for such a design See Fig. 24. This Line according to Scale is the Length of the Garden-walk the Break in the middle against the great Walk is a Grate which is intended to front it This Figure might be much improved if it were made a little larger so that the inner Row of the Triangles might range a little without the End of the Garden wall and at that end a walk to take it to goe by the Garden-side so might you have a convenient by-way without the VValls from the 20 foot VValk along either VValk of the Triangles to the walk by the Garden-side c. There are several other sorts of Triangles proper for VValks to end in but for Shade I preferre this or the next following if you would have the Trees to shew the shape of their heads then a single Row is best as the out-Row of the Triangle-walk See Fig. 25. For a Court you would have shaded with Trees this Figure will do well In this last Figure you may let the little VValk end Parallel with the VVall and have no VValks by the side-walls or you may make onely one VValk on each side As for making of the Triangle at the End of your Walk it may be Analogically according to your Ground though these two be made obtuse the perpendicular half the Length of the Base there be several sorts of Triangles or triangular Figures