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-line of the breadth as before then set up two sticks exactly in the 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
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
Basis by one third of the Altitude the solid Content of the Figure is had which you may value at such a price as Fire-wood beareth with you I will give you one Example and it shall be of an Ash which was felled in a place called the Old Orchard by the Stables at Cashiobury This tree I observed by several of the Rules before and found it to be 80 foot high from the ground to the top-shoot I also observed the height of the Timber to be 56 foot long by the same Rules then setting a Ladder to this Tree about 25 foot high I girthed it with a pack-thred which place I took for the middle girth being the Tree did not taper and it girthed 64 Inches upon the Bark But most men that buy timber by the foot have the Bark taken off at the girthingplace or an Allowance for the Bark but you may readily know the girth of the Tree under the Bark though the Tree be standing or lying without ever taking off the Bark or making Allowance by ghess as some doe which to perform find with your Penknife or Prickers the thickness of the Bark or you may cut a hole thorow the Bark in the girthing-places or two or three holes and then observe the mean thickness As on the foresaid Tree the Bark was half an Inch thick doubled makes one Inch so then the tree is less by one Inch in the Diameter when the Bark is off then by this general Rule as 22 is to 7 so is the Circumference to the Diameter Examp. by the Line of Numbers Extend your Compasses from 22 to 7 the same extent will reach from 64 to 20 and near a half for the Diameter of the Circumference of 64. Examp. by Arithmetick As 22 to 7 so is 64 to 20 8 22 the Diameter But the Bark taking one Inch off from this Diameter it is then 19 Inches and 8 22 then to find the true Circumference under the Bark agreeing to this Diameter say thus As 7 to 22 so is 19 8 22 to 61 the Circumference or near it For if you extend the Compasses from 7 to 22 the same will reach from 19 8 22 to 61 very near Or you may turn this 8 into a Decimal Fraction for as 22 is to 100 so is 8 to 36 of 100 and near a ½ Thus by four turns of your Compasses on the Line of Numbers you may in a moment find the Circumference under the Bark which here we find to be 61 then according to the customary way of measuring though not the true way take one fourth part of the Circumference and say As 12 is to this ¼ part of the Circumference in Inches so is the Length in feet twice repeated to the content in feet or parts Examp. The fourth part of 61 is 15 and ¼ Inches extend your Compasses from the point 12. on your Line of Numbers to 15 ¼ that extent will reach from 56 to 91 foot and neer a half being twice turned to the Right hand which must alwayes be if the ¼ of your Circumference be more than 12 Inches if less then to the Left hand Thus having found the Timber of this Tree to be 91 foot and a half which must be valued according to the worth of Timber in the place where you are here I will value it at 12 d. the foot though it was sold with courser Timber at an under-price this at 12 d. the foot comes to 4 l. 11 s. 6 d. Now to measure the head of this Tree according to our supposed Rule aforesaid if you take 56 the Length of the Timber from 80 the height of the Tree there remains 24 foot for the head This 24 foot which is the head two parts of it I measure as a solid Cylinder and one part as a Cone for if you girt all the boughs a little above where they break out from the Timber and adde the several girths together they will girth more than the Timber where the head was cut off two parts of the 24 foot is 16 which I measure by the same Rule I did the Timber by the Line of Numbers and the same Girt As 12 is to 15½ the square in Inches So is 16 the Length in feet twice repeated to 26 foot ¾ for the ⅔ of the Head Now for the ⅓ of the Head which must be measured as a solid Cone we must find the Basis and multiply the Content thereof by one third of the Altitude The Circumference of the Basis was 61 but I will take it now for 60 Inches then as before As 22 is to 7 so is 60 the Circumference to the Diameter which is 19 and a little more that which is more I neglect as not worth minding in such a business as this Half 60 is 30 half 19 is 9 and ½ Ex. to work it by the Line of Numbers Extend the Compasses from 1 to 9 and ½ the same will reach from 30 to 285 the Content in Inches of the Basis then ⅓ of 8 foot is 32 Inches Then say As 1 to 32 so is 285 to 9120 Inches which divided by 1728 the In. in one foot square is 5 foot and ¼ and a little more this added to 26 foot ¾ make 32 foot for the Head which at a Groat per foot is 10 s. 8 d. But this must be valued according the Countrey you are in So according to these Rules this Tree was worth 5 l. 2 s. 2 d. there was of the Head one Stack and near a quarter and 12 Faggots it cost 3 s. per Stack to cut out and was worth in the place where it stood 10 s. You see how near the Rule agrees with this tree but if the tree stands hanging down hill it will then endanger the Timber in falling or if you fear the Timber to be faulty or some of the Arms blown off you must judge-accordingly c. It is oft found in your great Elms and Ashes that they be hollow within and yet good Timber on the out-sides especially some length of them toward or at the lower end Now I will shew you how you may judge very near the Quantity of Timber that is in one of these trees or a piece of them according to the customary way Examp. A piece of a Tree 12 foot long and hollow and decayed wood at one end 12 Inches Diameter at the other end hollow and decayed 6 Inches Diam The piece was 26 Inches Diameter under the Bark First I measure the piece as if all sound Timber then the hollow and decayed by its Diameter that being deducted from the piece sheweth how much found Timber there is in foot and parts measured the customary way As 7 to 22 so 26 to 81 5 7 the Circumference the ¼ of it is 20 and ¼ and somewhat more as 12 to 20 ¼ in Inches so is 12 the Length in feet twice Repeated to 39 foot and ½ the Content as if it were all sound Then for the hollow
I take the mean Diameter to be 9 In. As 7 to 22 so 9 to 28 and 2 7 the Circumference of the hollow ¼ is 7 In. then as 12 to 7 so 12 foot to 4 and ¼ near which taken from 39 foot and ½ leaves 35 foot and ¼ for the sound Timber of that piece CHAP. XXXVIII Of making Walks Avenues or Lawns AS for making of Walks in Gardens I shall not speak of that in this place because I have resolved to keep my walk without the walls there are several Books of Gardening that have many Drafts and Knots in them but they be all done by ghess and none of them fitted to a scale to inform what Ground they be most proper for so that they be as fit for Butter-Prints as for Knots in a Garden Most Walks that are made abroad they either terminate or end or lead to the Front of a House or Door or Garden-gate or other Gate High-way or Wood c. Now if you would make a Walk from any one of these and have resolved upon the Center or Middle Line of the Walk as the Middle of a Door in the Front of a house or the like there pitch up a straight stake and then from the square of the Front c. raise a Perpendicular from this Stake and at a convenient distance in this perpendicular Line set up another stake let these two stakes be two little stakes at first but that at the Centre alwayes the highest these two stakes being thus fixed and you fully concluding them to be in the Mid-line then come to the Centre-stake and having in readiness a Quantity of Stakes according to the Length of your Walk bid one of your assistance go as far as you can well see back-sight and fore-sight and there by the motion of your hand or hat and his own back-sight let him fix upright one stake as exactly as may be in the Line then take up the two little stakes and at the Centre fix in a stake six foot high straight and upright with paper on the top and exactly in the place where the little stake stood Thus having got two stakes placed the Middle-stake and the Centre-stake you may if your Walk be level and the ground clear and the Walk not above one mile long set up one stake at the End in the Mid-line looking over the head of that stake and the other moving it till these three stakes be in a Right Line so may you have the middle line of your walk by these three stakes exacter than by more for the fewer stakes you use in your mid-line the better because that if you be but once a little amiss the more stakes are used you will be so much the further out of the right way And note it is better to take your sight over the head of your stakes than to look by their sides therefore you must have the Center stake highest the next a little shorter and so the next shorter than that c. but if your Ground be not level then order your stakes accordingly as thus And if your Ground be not level or be of such a length that you cannot well see from End to End then you must place down more stakes viz. between the Middle-stake and Centre-stake one and between the Middle and End-stake one if need require more I have oft made use of a sight-stake which I had only to find the place where my other stakes should stand this stake was made with a slit in the head half a foot deep which I looked through over the heads of the rest till I found the place where to set my stake right in the Mid-line It is of good use and Fig. 13. may somewhat represent it you may make it to slide up and down the better to come to the Level of the head of the stakes See Fig. 13. When you take sight to set any stake true in a Line with others stand at a little distance with your Eye from the head of the stake so shall you set it Exacter in the Line than when your Eye touches the head of the stake set your stake so that you may onely see three stakes in a Line let your Walk be of what length it will Having thus staked out your Mid-line strain a Line in this Mid-line and lay a square to that Line so set off the breadth of your Walk exactly square to your Middle-line then set up stakes as you did against every stake in the Middle of the Walk and when you have got the Lines true where your Trees must stand then drive down Oak-stakes in the Line to the head and then it is but putting down high stakes by these when you come to set your Trees Then having resolved on the distance to set your Trees at and provided good store of small stakes take your Chain and not a Line for that will retch and shrink and with your help set little stakes downright in this Line and square where you would have every Tree to stand these stakes are to make your holes by which I would have at least three foot wide and two foot deep and the holes made a Quarter of a Year before you set your Trees if it were a year 't were the better keeping the Mould turn'd over now and then and mixing it with Earth or Dung if need be then when the time of Planting is come begin betimes however on dry ground set up Stakes by every Oak-stake you left in the Row before having pruned the Roots and Heads to an equal height set them right one Tree against another square And if your Trees be not all of one Size set the greatest first right one against another and so lesser and lesser by degrees minding that both Rows go on square together and be sure you mind to let your Trees be at equal distance from End to End then if you have a point fixed at both Ends you must run over that distance you resolve to plant your Trees at before you set your Stakes and if you find it is over or short of equal distances then must you adde or substract this odde open to or from the rest to make them all of equal distance See Chap. 33. Now having your Trees and all things in Readiness set them by the Stakes standing in the Rows minding to set every Tree to range with the Stakes by back-sight and fore-sight Cover and part the Roots with fine Mould and when they be all covered lay on some Rotten Dung over that Mould and then cover that Dung with a little Mould this Dung will keep them from friezing in Winter and from drying too much in Summer and also well prepares the water for the Roots Thus having set them take care to fence them in at such places where need is so will you as well as I reap a great satisfaction if you let not the Dung touch the Roots Do not mask a fine Front nor vail a
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-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
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
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-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
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
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