will both the Needle and Index cut 68 degrees and the distance CE will be 8 Chains 72 Links which note in your Field-book as before 5. Lastly place your Instrument at E observing all the former cautions and direct the sights to A where you shall finde both the Needle and Index to cut 142 degrees 45 minutes and the measured distance EA to be 7 Chains 11 Links which note down in your Field-book And thus may you go about any field let it consist of never so many sides and angles observing alwayes this generall rule to lay the Index with the Box and Needle on the diameter of the Table and to turn the Table about till the Needle hangs directly over the meridian line in the Card and then fixing the Table turn the Index about till through the sights you espie the mark you looke for then will both the Index and the Needle cut the degrees which you must note in your Field-book so will the collected notes of this example stand as followeth  Degrees Minutes Chains Links A 218 10 9 65 B 298 30 9 28 C 15 40 5 70 D 68 00 8 72 E 142 45 7 11 Having thus collected your severall observations you may proceed to protract your work as is taught in the next Chapter which differeth nothing from that in the 36 Chap. ¶ It will be here objected by the affectors of the Peractor that here it is required that the Needle should play twice at each observation to which I answer it is true but if you neglect the latter of them it is both as speedy and as exact as the Peractor and if you have opportunity to observe both which you may conveniently do it will then be better CHAP. XXXVIII How to protract any observation taken as in the last Chapter YOu must first rule your paper or parchment all over with parallel lines or Meridians as is taught in the 36 Chapter and upon one of these Meridians assigne any point at pleasure as A then laying your Field-book before you place the center of the Protractor upon the point A the Scale thereof lying upon or parallel to one of the meridians ruled on your paper and because the degrees cut at A were above 180 degrees viz. 218 degrees 10 minutes therefore lay the Semicircle of the Protractor downwards and against 218 degrees 10 minutes of your Protractor make a mark through which mark and the point A draw the line AB containing 9 Chains 65 Links 2. Remove your Protractor to the point B which represents your second station or angle laying the Meridian line thereof upon or parallel to one of the Meridians drawn upon the paper and because the degrees cut at Bare above 180 lay the Semicircle downwards as before and against 298 degrees 30 minutes make a mark and through it draw the line BC containing 9 Chains 28 Links 3. Bring your Protractor to C and lay it parallel to some one of your Meridians and because the degrees observed at C were under 180 namely 15 degrees 40 minutes lay the Semicircle upwards and against 15 degrees 40 minutes make a mark drawing the line CD containing 5 Chains 70 Links 4. Place your Protractor as before upon the point D with the Semicircle upwards and against 68 degrees thereof make a mark and draw the line DE containing 8 Chains 72 Links Lastly Remove your Protractor to E placing it as before and against 142 degrees 45 minutes which were the degrees observed at your station at E make a mark and through it and the point E draw the line EA which if your work be true will passe through the point A and will contain 7 Chains 11 Links CHAP. XXXIX How to finde how many Acres Roods and Perches are contained in any piece of Land the plot thereof being first taken by any Instrument HAving shewn how to take the plot of any field or other inclosure severall wayes and also to protract the same upon paper it is now necessary to shew how the content thereof may be attained that is to say how many Acres Roods and Perches any field so plotted doth contain In the performance hereof you must consider that the originall of the mensuration of all superficiall figures such as Land Board Glasse or the like doth depend upon the exact measuring of certain regular figures as the Geometricall Square the Long Square or Parallelogram the Triangle the Trapezia and the Circle therefore if any plot of Land to be measured be not one of these figures it must before it can be measured be reduced into some of these forms I will therefore in the first place shew how to measure any of these figures severally by themselves and afterwards how to reduce any other irregular figure into some of these regular forms and lastly to measure them by the same rules and first Of the Geometricall Square A Geometricall Square is a figure consisting of four equall sides and angles as is the Square ABCD whose sides are all equall to the line QR which containeth six equall parts which may be attributed either to Inches Feet Yards Perches Chains or any other measure whatsoever Now to finde the superficiall content of such a Square you must multiply one of the sides in it selfe and the product of that multiplication shall be the content of the Square EXAMPLE Suppose the Square ABCD to be a piece of Land and the side thereof to contain 6 Perches therefore multiply 6 in it selfe and the product will be 36 so many Perches doth the square piece of Land contain Of the long Square A Long Square is a figure consisting of four sides as the figure ABCD the two opposite sides whereof are equall as the sides AB and CD and likewise AC and BD each of the shorter sides containing 7 Perches and the longer sides 13 Perches To finde the superficiall content of this long Square or Parallelogram you must multiply one of the longer sides by one of the shorter and the product will shew the superficiall content thereof Example The longer side of the Square contains 13 perches and the shorter 7 perches now if you multiply 13 by 7 the product will be 91 and that is the content of the square in perches Of the Triangle ALthough there be severall kindes of Triangles yet in respect they are all measured by one and the same rule I will therefore adde one example for all which is generall Halfe the length of the Base being multiplyed by the length of the perpendicular shall be equal to the area of the triangle Or Halfe the length of the Perpendicular being multiplyed by the whole Base will be the content of the triangle EXAMPLE Suppose you were to finde the area or content of the triangle BCD the Base thereof DB contaiking 58 perches and the perpendicular CA 24 perches Now if you multiply 12 which is half the length of the perpendicular CA by 58 the length of the whole base DB the product
and that it were required to finde the area or content thereof in Perches which to effect you must multiply the length by the breadth as is taught in the last Chapter therefore the length being 16 Unites 2 Primes and the breadth 1 Unite 3 Primes 2 Seconds these two numbers multiplyed together shall produce the area Set your numbers down as you are taught in the 5 Chapter of the 2 Book or as you see them stand in this Example with a prick over the head of every fraction 162̇ 13̇2̇ 324 486 162 21384 under these numbers draw a line and multiply them together in all respects as if they were whole numbers and then the work will stand thus the product of your multiplication being 21384. Now because in your two numbers viz. your multiplicand and your multiplyer there are three fractions namely one in your multiplicand and two in your multiplyer you must therefore with a dash of your pen cut off the three last figures of the product towards your right hand and then will your product stand thus 21 384 the three last figures whereof are the numerator of a fraction whose denominator is 1000 and the other two figures towards your left hand are Integers of your multiplication so that the sum of this multiplication is 21 perches and 384 1000 parts of a perch which is something more then a third part of a perch But to expresse the exact quantity of these fractions in a businesse of this nature were superfluous onely observe this one Rule for all namely that if the figures cut off come neere to a Unite that is when the figures cut off are neere as much as those underneath them or the first figure cut off is either 7 8 or 9 you may then increase your whole number by a Unite and not at all regard the fraction But for your further practise take another Example which let be a piece of land containing in breadth 5 Unites 6 Primes 3 Seconds and in length 15 Unites 4 Primes and 2 Seconds which place as before Now if you multiply these numbers one by another as if they were whole numbers then will they stand as in the margine the product being 868146 154̇2̇ 56̇3̇ 4626 9252 7710 868146 from whence take the four last figures because there are four fractions in your two numbers there remains 86 perches and 9146 10000 parts of a perch now because 8146 is neere to 10000 I adde 1 to 86 making it 87 perches dis-regarding the excesse as immateriall In like manner suppose the perpendicular of a Triangle should contain 1 Unite 3 Primes 2 Seconds and halfe the length of the base should contain 16 Unites 2 Primes these numbers being placed as those before and multiplyed one by another will produce this product 21384 from whence cut off the three last figures because there were three fractions in your numbers multiplyed and there will remain 21 perches and 384 1000 parts of a perch which being but of small value you may reject CHAP. XLI How to reduce any number of Perches into Roods and Acres or any number of Acres and Roods into Perches BY a Statute made the 33. of Edw. 1. an Acre of ground ought to contain 160 square Perches and every Rood of Land 40 square Perches and every Perch was to contain 16 foot and a halfe Now if any number of Perches be given to be turned into Acres you must divide the number given by 160 the number of perches contained in one Acre and the quotient shall shew you how many Acres are contained in that number of Perches and if any thing remain if it be under 40 it is Perches but if the remainder exceed 40 then you must divide it by 40 the number of perches contained in one Rood and the quotient shall be Roods and the remainder perches EXAMPLE Let 5267 perches be given to be reduced into Acres first divide 5267 by 160 and the quotient will be 32 and 147 remaining which divide by 40 the quotient will be 3 and 27 remaining so that the whole amounteth to 32 Acres 3 Roods and 27 perches Again let 5496 perches be given to be reduced into Acres first divide 5496 by 160 the quotient will be 34 and 56 remaining which 56 being divided by 40 the quotient will be 1 and 16 remaining so that the whole will be 34 Acres 1 Rood and 16 perches To reduce Acres into Perches THis is but the converse of the former for as before to reduce perches into Acres you divided by 160 you must now to reduce Acres into Perches multiply by 160. EXAMPLE Let 32 Acres 3 Roods and 27 perches be given to be reduced into Perches first multiply the 32 Acres by 160 and the product will be 5120 then multiply the 3 Roods by 40 the product is 120 these two products and the 27 perches being added together the summe will be 5267 5120 120 27 5267 and so many perches are contained in the foresaid number of Acres Roods and perches and thus much concerning the use of Master Rathborns Chain CHAP. XLII How to cast up the content of any piece of Land in Acres Roods and Perches by Master Gunters Chain IN measuring by Master Gunters Chain you are in your account only to take notice of Chains and Links as was before intimated in the description thereof Cap. 5. Lib. 2. Suppose then that the figure B were a piece of Land lying in a long square and that being measured by Master Gunters Chain should contain in length 9 Chains 50 Links and in breadth 6 Chains 25 Links Set your numbers down as before is taught and as here you see drawing a line under them then multiplying them together you shall finde the product to be 593750 9,50 6,25 4750 1900 5700 593750 from which product you must alwayes cut off the five last figures towards the right hands with a dash of your pen then will the product stand thus 593750 so is the 5 towards the left hand compleat Acres and the 93750 hundred thousand parts of an Acre which to reduce into Roods and Perches is easie by help of this Table For if you looke for 90000 under the title Links which is the first figure with Cyphers added Links R. P. 100000 4 0 90000 3 24 80000 3 8 70000 2 32 60000 2 16 50000 2 0 40000 1 24 30000 1 8 20000 0 32 10000 0 16 9375 0 15 8750 0 14 8125 0 13 7500 0 12 6875 0 11 6250 0 10 5625 0 9 5000 0 8 4375 0 7 3750 0 6 3125 0 5 2500 0 4 1875 0 3 1250 0 2 624 0 1 you shall finde against it 3 Roods 24 Perches then looke for 3750 and against it you shall finde 6 perches all which being added together as here you see the area or content of the whole piece will be 5 Acres 3 Roods and 30 Perches A. R. P. 5 00 00  3 24   6 5 03 30 Another Example Suppose the base of a Triangle
To reduce Acres into Perches and the contrary 248. 19. The use of a Scale of Reduction necessary for finding the Fraction parts of an Acre 250 20. Divers compendious rules for the ready casting up of any plain Superficies with divers other Compendiums in Surveying by the line of Numbers 251. 21. Of Satute and Customary measure to reduce one to the other at pleasure 254. 22. Of the laying out of common fields into furlongs 255. 23. Of Hils and Mountains how to finde the lengths of the horizontall lines on which they stand severall wayes 257 24. Of mountanous and uneven grounds how to protract or lay the same down in plano after the best manner giving the area or content thereof 258. 25. How to take the Plot of a whole Manner by the Plain Table three severall ways 260. Circumferentor 266. or Peractor 266. With the keeping an account in your Field-book after the best and most certain manner 270. and to protract any observations so taken 271. 26. Of inlarging or diminishing of Plots according to any possible proportion by Two Semicircles Mr. Rathborns Ruler A Line into 100 parts The Parallelogram 273. 27 Of conveying of water 276. FOrasmuch as the whole Art of Surveying of Land is performed by Instruments of severall kindes and that the exact and carefull making and dividing of all such Instruments is chiefely to be aimed at I thought good to intimate to such as are desirous to practise this Art and do not readily know where to be furnished with necessary Instruments for the performance thereof that all or any of the Instruments used or mentioned in this Book or any Mathematicall Instrument whatsoever is exactly made by Mr. Anthony Thompson in Hosier lane neer Smithfield London THE COMPLEAT SURVEYOR The First Book THE ARGVMENT THis first Book consisteth of divers Definitions Problemes Geometricall extracted out of the Writings of divers ancient and modern Geometricians as Euclid Ramus Clavius c. and are here so methodically disposed that any man may gradually proceed from Probleme to Probleme without interruption or being referred to any other Author for the Practicall performance of any of them Onely the Demonstration is wholly omitted partly because those Books out of which they were extracted are very large in that particular and also for the avoiding of many other Propositions and Theoremes which had the ensuing Problemes been demonstrated must of necessity have been inserted Also the figures would have been so incumbred with multiplicity of lines that the intended Problemes would have been thereby much darkened And besides it was not my intent in this place to make an absolute or entire Treatise of Geometry and therefore I have onely made choice of such Problems as I conceived most usefull for my present purpose and come most in use in the practice of Surveying and ought of necessity to be known by every man that intendeth to exercise himselfe in the Practice thereof and those are chiefly such as concern the reducing of Plots from one forme to another and to inlarge or diminish them according to any assigned Proportion also divers of the Problemes in this Book will abundantly help the Surveyor in the division and seperation of Land and in the laying out of any assigned quantity whereby large parcels may be readily divided into divers severals and those again sub-divided if need be Also for the better satisfaction of the Reader I have performed divers of the following Problemes both Arithmetically and Geometrically GEOMETRICALL DEFINITIONS 1. A Point is that which cannot be divided A Point or Signe is that which is void of all Magnitude and is the least thing that by minde and understanding can be imagined and conceived than which there can be nothing lesse as the Point or Prick noted with the letter A which is neither quantity nor part of quantity but only the terms or ends of quantity and herein a Point in Geometry differeth from Unity in Number 2. A Line is a length without breadth or thicknesse A Line is created or made by the moving or drawing out of a Point from one place to another so the Line AB is made by moving of a Point from A to B and according as this motion is so is the Line thereby created whether streight or crooked And of the three kindes of Magnitudes in Geometry viz. Length Breadth and Thicknesse a Line is the first consisting of Length only and therefore the Line AB is capable of division in length only and may be divided equally in the point C or unequally in D and the like but will admit of no other dimension 3. The ends or bounds of a Line are Points This is to be understood of a finite Line only as is the line AB the ends or bounds whereof are the points A and B But in a Circular Line it is otherwise for there the Point in its motion returneth again to the place where it first began and so maketh the Line infinite and the ends or bounds thereof undeterminate 4. A Right line is that which lieth equally between his points As the Right line AB lyeth streight and equall between the points A and B which are the bounds thereof without bowing and is the shortest of all other lines that can be drawn between those two points 5. A Superficies is that which hath only length and breadth As the motion of a point produceth a Line the first kinde of Magnitude so the motion of a Line produceth a Superficies which is the second kinde of Magnitude and is capable of two dimensions namely length and breadth and so the Superficies ABCD may be divided in length from A to B and also in breadth from A to C. 6. The extreams of a Superficies are Lines As the extreams or ends of a Line are points so the extreams or bounds of a Superficies are Lines and so the extreams or ends of the Superficies ABCD are the lines AB BD DC and CA which are the terms or limits thereof 7. A plain Superficies is that which lieth equally between his lines So the Superficies ABCD lieth direct and equally between his lines and whatsoever is said of a right line the same is also to be understood of a plain Superficies 8. A plain Angle is the inclination or bowing of two lines the one to the other the one touching the other not being directly joyned together As the two lines AB and BC incline the one to the other and touch one another in the point B in which point by reason of the inclination of the said lines is made the Angle ABC But if the two lines which touch each other be without inclination and be drawn directly one to the other then they make no angle at all as the lines CD and DE touch each other in the point D and yet they make no angle but one continued right line ¶ And here note that an Angle commonly is signed by three Letters the middlemost whereof sheweth
will be 696 and that is the area or content of the Triangle Or If you multiply 24 the whole length of the perpendicular by 29 the length of half the base the product will be 696 as before Or again If you multiply 58 the whole length of the base by 24 the whole length of the perpendicular the product will be 1392 the half whereof is 696 the area or content of the Triangle as before Of the Trapezia A Trapezia is a figure consisting of four unequall sides and as many unequall angles as is the figure ABCD. To measure this Trapezia you must first draw the diagonall line BD for by this means the figure is reduced into two Triangles as ADB and CDB then if you let fall the perpendiculars from the points A and C you may measure them by the last examples as two Triangles the sums whereof being added together will be the area or content of the whole Trapezia EXAMPLE Having drawn the line BD and so reduced the Trapezia into two Triangles and let fall the perpendiculars AE and CF upon the line BD which is the common base to both the Triangles you may finde the area of the whole Trapezia thus Suppose the perpendicular CF were 102 perches the perpendicular AE 118 perches and the base BD which is common to both Triangles 300 perches Now if according to former directions you multiply 300 the base by 59 halfe the perpendicular AE the product will be 17700 for the content of the Triangle ABD In like manner if you multiply 300 the Base by 51 halfe the perpendicular FC the product will be 15300 for the content of the Triangle BCD Now if you adde the contents of these two Triangles together namely 17700 and 15300 the summe of them will be 33000 and that is the content of the whole Trapezia ABCD. But this work may be performed with more brevity thus In respect the Base BD is common to both the Triangles you may therefore adde the two perpendiculars together the halfe of which being multiplyed by the whole Base the product will shew the content of the whole Trapezia EXAMPLE The two perpendiculars 118 and 102 being added together the summe of them is 220 the halfe whereof is 110 this number being multiplyed by 300 the whole length of the common base giveth 33000 the content of the whole Trapezia OR You may multiply the sum of the perpendiculars by the length of the Base and halfe that product will be the content of the Trapezia also Of irregular Figures how to reduce them into Triangles or Trapezias and to cast up the content thereof LEt ABCDEFGH be the figure of a Field drawn upon your Plain Table or otherwise protracted upon paper according to any of the former directions In regard that the Field is irregular that is to say it is neither Square Triangle or Trapezia it must therefore before it can be measured be reduced into some of these forms which to effect do thus draw lines from one angle to other as the lines AD DB AE AF and FH then will the whole figure be reduced into six Triangles as 1. the Triangle BCD 2. the Triangle ADB 3. the Triangle ADE 4. the Triangle AEF 5. the Triangle AFH 6. the Triangle FGH These six Triangles being measured severally according to the former directions and the contents of them all added together into one summe will shew the area or content of the whole field As Suppose the Triangle BCD should contain 72 Perches Suppose the Triangle ADB should contain 84 Perches Suppose the Triangle ADE should contain 110 Perches Suppose the Triangle AEF should contain 121 Perches Suppose the Triangle AFH should contain 165 Perches Suppose the Triangle FGH should contain 66 Perches These six numbers being added together make 618 perches and that is the area or content of the whole Field in perches But for an abreviation of this work you need not to finde the area of every Triangle but of every Trapezia as is before taught for the figure is as well divided into Trapezias as Triangles namely into the Trapezias ABCD ADEF AFGH By this means you neede but to finde the area or content of these three Trapezias which will abreviate nigh halfe of the Arithmeticall work for if you measure the three Trapezias severally as hath been taught in this Chapter you shall finde The Trapezia ABCD to contain 156 Perches The Trapezia ADEF to contain 231 Perches The Trapezia AFGH to contain 231 Perches These three numbers being added together produce 618 exactly agreeing with the former ¶ Here note that at any time when you reduce any irregular plot into Triangles your number of Triangles will be lesse by two then the number of the sides of your plot as in this figure the plot consisted of 8 sides and you see it is reduced into 6 Triangles Of the Circle THe proportion of the circumference of any Circle is to its diameter as 7 to 22. Now to finde the area or content of any Circle you must multiply the diameter thereof in it self and multiply that sum by 11 which product being divided by 14 shall give you the area of the Circle EXAMPLE In this Circle ABCD let the diameter thereof DB be 28 which multiplied in it selfe giveth 784 this number multiplyed by 11 giveth 8624 which being divided by 14 the quotient will be 616 and that is the area of the Circle The Circumference of a Circle being given to finde the Diameter MUltiply the Circumference by 7 and divide the product by 22 the Quotient shall be the length of the Diameter EXAMPLE Let the circemference of the Circle ABCD be 88 this multiplyed by 7 giveth 616 which being divided by 22 giveth 28 for the Diameter DB. CHAP. XL. Of the manner of casting up the content of any piece of Land in Acres Roods and Perches by Master Rathborns Chain IN the 5. Chapter of the 2 Book you have a description of Chains in generall and more particularly of Master Rathborns and Master Gunters In the measuring of Land by Master Rathborns Chain you call every Pole or Perch thereof which is divided into 100 Links a Unite and every ten of those Links you call a Prime and every single Link you call a Second Now because there are divers that fancie this Chain rather then any other because it giveth the content of any Superficies measured therewith in its smallest denomination namely in Perches and parts of Perches so that when any Superficies is cast up and brought to Perches it may easily be reduced into Roods and Acres Now for their sakes that affect this Chain I will shew the use thereof and afterwards of Master Gunters Chain leaving every man to take his choice and use that which liketh him best Suppose that the figure B were a piece of Land lying in a long square which being measured by Master Rathborns Chain should contain in length 16 Unites 2 Primes and in breadth 1 Unite 3 Primes 2 Seconds
will reach from 12 Chains 50 Links to 11 Acres 37 parts 4. Having the Base and perpendicular of a Triangle given in Perches to finde the content in Acres As 320 to the Perpendicular So the length of the Base to the content in Acres So in the Triangle LAB if the line BD be taken for the perpendicular of the Triangle then the length of the base being 50 perches and the perpendicular 36 2 5 the area will be found to be 5 Acres 22 parts which is 2 Roods 30 perches then If you extend the Compasses from 320 to 36 2 5 the perpendicular the same extent will reach from 50 the length of the base to 5 Acres 22 parts 5. The Base and perpendicular of a Triangle being given in Chains to finde the content in Acres As 20 to the perpendicular So the Base to the content in Acres So in the former figure if AB 12 Chains 50 Links be taken for the Base and BD 4 Chains 55 Links for the perpendicular of the Triangle ALB the area by this proportion will be found to be 5 Acres 68 parts that is 5 Acres 2 Roods 30 perches therefore If you extend the Compasses from 20 to 4 Chains 55 Links the same extent will reach from 12 Chains 50 Links to 5 Acres 68 parts which is 2 Roods 30 perches 6. The Area or superficiall content of any piece of Land being given according to one kinde of Perch to finde the content thereof accoading to cnother kinde of Perch As the length of the second perch To the length of the first perch So the content in Acres To a fourth number And that fourth number to the content in Acres required Suppose the figure B were a piece of Land which being plotted and cast up by a Chain of 16 foot and a halfe to the Perch should contain 8 Acres and that it were required to finde how much the same piece would contain if it were measured with a Chain of 18 foot to the perch if you work according to the proportion here delivered you shall finde it to contain 6 Acres 72 parts for If you extend the Compasses from 18 to 16½ that extent will reach from 8 to 7.30 and from 7.30 to 6.72 and so many Acres would the figure B contain if it were measured by a perch of 18 foot 7. Having the length of the Furlong to finde the breadth of the Acre As the length of the furlong in Perches to 160 So is 1 Acre to the breadth in Perches So if the length of the furlong be 50 perches the breadth for one Acre will be 3.20 for If you extend the Compasses from 50 the length of the furlong in perches the same extent will reach from 1 Acre to 3.20 perches But if the length of the Furlong be given in Chains then As the length of the Furlong in Chains is to 10 So is 1 Acre to the breadth of the furlong in Chains So the length of the Furlong being 12 Chains 50 Links the breadth thereof will be found to be 00 Chains 80 Links for If you extend the Compasses from 12 Chains 50 Links to 10 that extent will reach from 1 Acre to 80 Links which is the breadth of the furlong required CHAP. XLIV How to reduce one kinde of measure into another as Statute measure to Customarie measure BY the 6 Prop. of the last Chapter you may perform this work by the line of Numbers as is there taught but however it will not be amisse in this place to shew how to performe the same Arithmetically that the reason thereof may the better appear Now whereas by the forementioned Statute an Acre of ground was to contain 160 square perches measured by the Pole or Perch of 16 foot and a halfe but in many places of this Nation through long custome there hath been received other quantities called Customarie as namely of 18 20 24 and 28 foot to the Pole or Perch It is therefore necessary for a Surveyor to know how readily to reduce Customarie measure to Statute measure and the contrary Suppose then that it were required to reduce 5 Acres 2 Roods 20 Perches measured by the 18 foot Pole into Statute measure you must seeke out the least proportionall terms between 18 foot and 16 foot and a halfe which to perform do thus Because 16 and a halfe beareth a fraction reduce 16 and a halfe into halves and that both your numbers may be of one denomination you must reduce 18 the customary Pole into halves also then will your numbers stand thus 33 36 which abreviated by 3 by saying how many times 3 in 33 the quotient will be 11 and again how many times 3 in 36 the quotient will be 12 so will the two proportionall terms between 16 and a halfe and 18 be 11 and 12. This done reduce your given quantity 5 Acres 2 Roods and 20 perches into perches which makes 900 perches Now considering that what proportion the square of 11 which is 121 bears to the square of 12 which is 144 the same proportion doth the Acre of 16 foot and a halfe to the Perch bear to the Acre of 18 foot to the Perch Now because the greater measure is to be reduced into the lesser multiply the given quantity 900 perches by 144 the greater square and the product will be 129600 which divided by 121 the quotient will be 1071 9 â—… perches which being reduced into Acres giveth 6 Acres 2 Roods 31 perches and 9 â—… parts of a perch according to statute measure But on the contrary suppose it had been required to reduce Statute measure into Customary measure then you must have multiplyed 900 perches your given quantity by 121 the lesser Square because the lesser measure is to be reduced into the greater the product will be 108900 which divided by the greater Square 144 the quotient will be 756¼ perches which reduced into Acres is 4 Acres 2 Roods 36 perches and a quarter The same manner of work is to be observed in the reducing of any Customarie quantity whatsoever CHAP. XLV How to lay out severall Furlongs in Common-fields unto divers Tenants HAving plotted the whole Field Common or other Inclosure with its particular bounds as you observe them in the survey of the whole Mannor or if you only survey that particular you must take speciall notice of all the bounds thereof then provide a Book or paper which must be ruled or divided into 8 Columns in the first whereof towards the left hand is to be written the Tenants name and the tenor by which he holds the same Land the two next Columns are to contain the length of every mans Furlong in Chains and Links In the two next Columns is expressed the breadth of every mans Furlong in Chains and Links as by the Letters over the head of each column doth appear In the three last Columns is to be expressed the quantity of each tenants Furlong in Acres Roods and Perches In the laying out of
having at each end thereof a Semicircle is inferiour to none but the Instrument being very chargeable and the use thereof very intricate and tedious I shall wholly omit to speak any more of it There is another way also which Master Rathborn used which was with a Ruler by him invented for that purpose which would indifferent well reduce a plot from one bignesse to another according to some particular proportions The making of this Ruler is so well known and the use thereof so apparent that I shall not need to say any thing concerning the description or use of it I only intimate that there is such a Ruler that those which please may have it made Another way is by one line divided into 100 or 1000 equall parts only which by the help of Arithmetick will perform this work very well but this as being very tedious I neglect To passe by these and divers others which I could name I shall say somthing of the Parallelogram which for generality exactnesse and dispatch surpasseth all the rest unto which in my opinion there is none comparable Of Parallelograms there are diverse sorts but that which I shall instance in consisteth but of four Rulers only the making whereof is well known to the Instrument maker and the manner of using it is as followeth Take the plot which you would reduce and fasten it to a Table with Mouth-glew then by it upon the same Table fasten your fair paper or parchment upon which you would have your new plot then having fitted your Parallelogram according to the proportion into which you would have your plot reduced fix the Parallelogram to the Table by a point for that purpose then put your drawing pen into some one hole on one of the sides of the Parallelogram and upon it a plummet of lead or brasse to keepe the pen down close to the paper when it is moved thereupon and here note that at any time when the Parallelogram is thus fitted the point that sticketh in the Table the Pen which is to draw and the Tracer which you must move along the lines of your old plot will lie alwayes in a right line but this by the way Your Parallelogram being fixed to the Table and the pen in its true place fitted to draw take the Tracer in your right hand and with it lightly go over all the lines of your old plot so shall the motion thereof occasion the pen to draw upon your clean paper or parchment the true and exact figure of your former Plot though of another bignesse which will be in proportion to the greater according to the situation of the sides of the Parallelogram which will better appeat by the sight of the Instrument then words can possibly explain it CHAP LII How to draw a perfect draught of a whole Mannor and to furnish it with all necessary varieties also to trick and beautifie the same in which as in a Map the Lord of the Mannor may at any time by inspection only see the symetry scituation and content of any parcell of his Land HAving protracted your plot according to your intended bignesse and written the content of each Close about the middle thereof you may about the bounds of every field or Inclosure with a small Pensill and some transparent green colour neatly go over your black lines so shall you have a transparent stroke of green on either side of your black line which will adde a great lustre and beauty to your Plot. Then in your Wood-land grounds draw diverse little Trees in the most materiall places and shadow your mountanous and uneven grounds with hils and valleys expressing all kinde of Bogs Groves High-wayes Rivers c. distinguishing them by lively colours according to their similitudes Then in some convenient place of the Plot without the Inclosures draw a Circle and therein describe the 32 points of the Mariners Compasse according to the situation of the grounds with a Flower-de-luce at the North part thereof Then in some other convenient place of your plot make a Scale equall to that by which your plot was protracted Lastly in some other convenient place towards the upper part thereof draw the Coat of Arms belonging to the Lord of the Mannor with Mantle Helme Crest and Supporters or in a Compartment but be sure you blazon the Coat in its true Colours THE Mannor of Lee. These things being well performed your plot will be a neat Ornament for the Lord of the Mannor to hang in his Study or other private place so that at pleasure he may see his Land before him and the quantity of all or every parcell thereof without any further trouble Also in your plot must be expressed the Mannor-house according to its symetry or situation with all other houses of note also all Water-mils Wind-mils and whatsoever else is necessary that may be put into your Plot without confusion For farther explanation of what hath been delivered in this Chapter I have here added the figure of a small Mannor which will be sufficient for example sake CHAP. LIII How to finde whether water way be conveyed from a Spring head to any appointed place THere is an Instrument called a Water-Levell for the performance hereof the making whereof is sufficiently known Now if it were required to know whether water may be conveyed in Pipes or Trenches from a Spring head to any determinate place observe the following directions Place your Water-Levell at some convenient distance from the Spring head in a right line towards the place to which the water is to be conveyed as at 30 40 60 or 100 yards distant from the Spring-head Then having in a readinesse two long streight poles which you may call your station staves divided into Feet Inches and parts of Inches from the bottome upwards being thus provided cause one whom you may call your first assistant to set up one of the said staves at the Spring head and require another which you may call your second assistant to erect the other staffe beyond your Instrument at 30 40 60 or 100 yards forward towards the place to which the water should be conveyed These station staves being erected perpendicular and your Water-Levell in the mid way precisely horizontall go to the end of the Levell and looking through the sights cause your first assistant to move a leafe of paper up and down your station staffe till through the sights you see the very edge thereof and then by some known signe or sound intimate to him that the paper is then in its true position then let this first assistant note against what number of Feet Inches and parts of an Inch the edge of the paper resteth which he must note down in a paper Then your Water-Levell remaining immoveable go to the other end thereof and looking through the sights towards your other station staffe cause your second assistant to move a leafe of paper along the staffe till you see the very edge thereof