apprehended at the first sight I will therefore instance in the Circumferentor as being most generall Let the example of the last Chapter serve where the figure ALMNPQSTVXGHK represented part of a Mannor Then having provided your field-Field-book ready ruled you must at the head of one of the leaves thereof write the Title of the Mannor the County in which it is and who is Lord thereof As The Mannor of Elsmore in the County of S. for the Honourable R. B. Lord thereof Then beginning with your first Close write over the head of your field-Field-book the Tenants name the name of the Close and the tenour by which he holds the same so for the first Close Henry Grey Casbey Close Pasture Free Under this draw a line quite through your Book then beginning to survey this Close place your Instrument at A and direct your sights to L noting the degrees there cut which let be 160 degrees 45 minutes which 160 degrees 45 minutes must be noted in the first and second Columns of your Field-book then measure the distance AL 8 Chains 68 Links which place in the third fourth Columns 2. Remove your Instrument to L and direct the sights to M the needle cutting 181 degrees 30 min. and the line LM containing 6 Chains 55 Links which note down in your Field-book 3. Place your Instrument at M and direct the sights to N the needle cutting 233 degrees and the line MN 7 Chains 27 Links which note in your field-Field-book And in regard you are to leave the hedge or bounder ALMN adjoyning to Wisby Common which appertaineth to another Mannor and therefore only the name inserted for your remembrance when you come to protraction you must draw a line quite through your Field Book and in the last Column thereof write Wisby Common which denotes unto you that you are to leave the bounder of Wisby Common 4. Place your Instrument at N and direct the sights to O the needle cutting 355 deg 40 min. and the distance NO being 4 Chains 45 Links which note in your Field-book as before 5. Place your Instrument at O and direct the sights to C the needle cutting 309 degrees 30 minutes and the line OC containing 6 Chains 64 Links which note in your field-Field-book Now because at these two observations you went against the hedge or bounder of Banton plain you must against them write in your Field-bok Banton plain and because you are now to leave the hedge or bounder of Banton plain draw a line quite through your Field-book 6. Place your Instrument at C and direct the sights to B the needle cutting 54 degrees 00 minutes and the distance CB being 8 Chains 5 Links the degrees and minutes must be noted in the first and second columns of your Field-book and the Chains and Links in the third and fourth 7. Remove your Instrument to B and direct the sights to A the needle cutting 19 degrees 30 minutes and the distance BA being 6 Chains 43 Links the degrees and minutes must be noted in the first and second Columns of your field-Field-book and the Chains and Links in the third and fourth Now because at these two last observations you went against the hedge or bounder of Bay Wood you must therefore against them write Bay Wood and because you have now finished your first Close you must draw a double line through your Book for your remembrance Then consider which parcell is next fittest to be taken in hand which let be Bay Wood and withall at what angle thereof it is most meet to begin which suppose C and here for your help when you come to protraction you must expresse in the title of this second Close at what angle you begin the same unlesse you had begun it where you ended the last at A and then it is not materiall wherefore seeing you are best to begin at C looke in your field-Field-book on the work of the last Close what degrees and minutes the needle cut at C which were 54 degrees and 8 Chains 5 Links therefore against that number make this ☉ or the like mark and write the Title for your second Close thus Samuel White Bay-wood by Lease begin at ☉ By this means you shall readily know when you come to protraction where to begin with this prcell and in the margine place 2 for the number of your second parsell and then proceed in your work of surveying this parcell as before you did for the other till you have gone round about the same ending at A where you first began noting down all your observations both of lines and angles with the particular bounders as you go along in your Field-book in all respects as you did those of the first Close and in thus doing you shall finde that at your first observation from C to E that you went partly by the hedge or bounder of Banton plain and partly by the hedge or bounder of Church-field and therefore against the degrees of that observation write Banton plain and Church-field there drawing a line then at your two next observations at E and F you went along the hedge or bounder of Church-field and at the three last observations at G H and K you went against the hedge or bounder of Wisby Common there finishing your second parsell wherefore draw a double line quite through your Field-book These two parcels being finished consider which is next fittest to be taken in hand and where to begin it which suppose Banton plain and to begin at N wherefore looke in your field-book what degrees the needle cut when you made observation at N in the surveying of Gosby Close and left the bounder of Wisby Common which degrees you shall finde to be 355 degrees 40 minutes and 4 Chains 45 Links therefore at the end of that line where you finde 355 degrees 40 minutes and 4 Chains 45 Links make this + or some other mark for a remembrance when you come to protraction then for the next parcell write in your Field-book George Burton Banton plain for two lives begin at ✚ This being done place your Instrument at N and direct the sights to P the needle cutting 220 degrees 20 minutes and the line NP containing 9 Chains 32 Links which note in your field-Field-book and because at this observation you went by the hedge or bounder of Wisby Common and are now to leave it therefore draw a line and write Wisby Common and in this manner must you go about this parcell also till you come to close at D and having finished draw a double line Then considering that Church field is next fitest to be surveyed and that it is most convenient to begin the same at Q therefore looke what degrees the needle cut at Q in the surveying of Banton plain which were 15 degrees 40 minutes â—nd 10 Chains 75 Links against which in your Fild-book make this ♓ or the like mark for your remembrance and for your next Close â—rite in your Field-book as
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
severall parcels in this kinde you will have use only of your Chain then when you begin your work you must first write the name of the field and in the first columne of your Booke or paper you must write the Tenants name and the tenour by which he holds the same from what place you begin to measure and upon what point of the compasse you passe from thence and observing this direction in all the rest you may if need require bound every parcell This being noted in your Book observe the species or shape of the Furlong whether it be all of one length or not if of one length then you need take the length thereof but once for all but if it be irregular that is in some places shorter and in others longer then you must take the length thereof at every second or third breadth and expresse the same in your Book under the title of length As for the expressing of the severall breadths you need but to crosse over the whole Furlong taking every mans breadth by the middle thereof and entering the same as you passe along but in case there be a considerable difference at either end then I would advise you to take the breadth at either end and adde them together into one sum then take the half of that summe for your mean or true breadth and enter it in your book or paper under the title of breadth In this manner you may proceed from one Furlong to another till you have gone through the whole field which when you have done and noted down the severall lengths and breadths in your book you may multiply the length and breadth of every parcell together as is taught before and so shall you have the quantity of every parcell by it selfe which quantity must be noted downe in the three last columns of your Book as in the following example appears Mordon Field The Tenants names and tenour Length Breadth Content C. L. C. L. A. R. P. Abel Johnson from the pond S. E. free 32 76 3 45 11 1 12 Nicholas Somes for three lives 30 12 2 63 7 3 30 Robert Dorton for Life 28 60 8 12 23 0 36 James Norden at Will 25 11 12 35 31 0 2 CHAP. XLXI. To finde the horizontall line of any hill or mountain THis proposition differeth nothing from those formerly taught in the taking of Altitudes Wherefore suppose you should meet with a hill or mountain as ABD the thing required is to finde the length of the line BD on which the mountain standeth First place your Instrument at the very foot of the Hill exactly levell then let one go to the top of the hill at A and there place a mark which must be so much above the top of the hill as the top of the Instrument is from the ground then move the Label up and down till through the sights thereof you see the top of the mark at A and note the degrees cut by the Label on the Tangent line for that is the quantity of the angle ABC which suppose 47 degrees then by consequence the angle BAC must be 43 degrees the complement of the former to 90 degrees then measure the side of the hill AB which suppose to contain 71 Feet then in the Triangle ABC there is given the side AB 71 foot and the angle BAC 43 degrees together with the right angle ACB 90 degrees and you are to finde the side BC which to perform say As the Sine of the angle ACB 90 degrees Is to the side AB 71 feet So is the Sine of the angle BAC 43 degrees To the side BC 48½ feet Then because the hill descends on the other side you must place your Instrument at D observing the angle ADC to contain 41 degrees and the angle DAC 49 degrees and the side AD 80 feet now to finde the side CD the proportion will be As the Sine of the angle ACD 90 degrees Is to the side AD 80 feet So is the Sine of the angle CAD 49 degrees To the side CD 60½ feet Which added to the line BC giveth 109 feet which you may reduce into Chains by dividing it by 66 and this line must be protracted instead of the hypothenusall lines AB and AD. Another way There is another way also used by some for the measuring of horizontall lines which is without the taking of the Hils altitude or using of any Arithmeticall proportion but by measuring with the Chain only the manner whereof is thus Suppose ABC were a hill or mountain and that it were required to finde the length of the Horizontall line thereof AC At the foot of the hill or mountain as at A let one hold the Chain up then let another take the end thereof and carry it up the hil holding it levell so shall the Chain meet with the hill at D the length AD being 60 Links then at D let the Chain be held up again and let another carry it along levell till it meet with the side of the hill at E the length being 54 Links then again let one stand at E and hold up the Chain another going before to the top of the hill at B the length being 48 Links these three numbers being added together make 162 Links or 1 Chain 62 Links which is the length of the horizontall line AC This way of measuring is by some practised but the other in my opinion is far to be preferred before it only when you are destitute of better helps you may make use hereof ¶ But if the hill or mountain should have a descent back again on the other side you must then use the same way of working as before and adde all together for the horizontall line CHAP. XLVII How to plot Mountanous and uneven grounds with the best way to finde the content thereof FOr the plotting of any mountanous or uneven piece of ground as ABCDEFG you must first place your Instrument at A and direct the sights to B measuring the line AB then in regard that from B to C there is an ascent or hill you must finde the horizontall line thereof and draw that upon your Table accounting thereon the length of the hypothenusall line then measure round the field according to former directions and having the figure thereof upon your Table reduce it into Trapezias as into the Trapezias ABEG BCDE and the Triangle GEF then from the angles A C E and F let fall the perpendiculars AK CH EI and FM Now in regard there are many hils and valleys all over the field you must measure with your Chain in the field over hill and dale from B to D and to the line BD set the number of Chains and links as you finde them by measuring which will be much longer then the streight line BD measured on your Scale then by help of your Instrument finde the point H in the line BD and measure with your Chain from C to H over hill
followeth Thomas King Church field by Lease begin at ♓ Then placing your Instrument at Q direct the sights to S noting the degrees cut and the length of every line measured with your particular bounders as you did in the other Closes before till you come to inclose at G and when you have done draw a double line quite through your field-Field-book and write the title of the next Close to be surveyed in this manner John Nichols Odcumb Close Free begin at Then placing your Instrument at T direct the sights to Y and note the degrees cut and the lines measured as in those before till you have gon round the field to G. And thus if there were never so many Inclosures you may without confusion easily distinguish the work of the one from the other and be able remembring the premises to draw a plot thereof at any time remembring alwayes that those numbers in the Margent of your Book ought to be placed severally in your Plot in those Closes they represent The Mannor of Elsmore in the County of S. for the Honourable R. B. Lord thereof 1 Henry Grey Cosbey Close Pasture Free 160 45 8 68 Wisby Common 181 30 6 55 233 00 7 27 355 40 4 45 + Banton plain 309 30 6 64 54 00 8 5 ☉ Bay Wood. 19 30 6 43 2 Samuel White Bay Wood by Lease begin at ☉ 320 00 10 22 Banton plain Church field 15 30 5 50 Church field 337 45 6 68 87 30 6 84 Wisby Common 113 30 6 73 153 30 6 69 3 George Burton Banton plain for 2 Lives begin at + 220 20 9 32 Wisby Common 299 30 10 50 The Forrest 15 40 10 75 ♓ Church field 53 30 5 3 4 Thomas King Church field by Lease begin at ♓ 316 20 13 12 The Forrest 17 15 10 83 Church Lane 56 00 6 15 Odcumb Close 24 10 6 38 5 John Nichols Odcumb Close Free begin at 334 30 7 3 Church Lane 48 30 6 25 101 30 6 18 These Instructions being sufficient for the application and use of the Field book I shall desire all men to make frequent triall and practise thereof and compare the Book with the Plot and protracting the same according to the directions hereafter given you will finde it to be most exact and facile Here by the way I might give directions whereby to take in divers severals at once if the bounders be regular which will much ease you both in surveying and protracting but by small practise this and divers other abreviations will appear of themselves I have here added one leafe of your Field-book as it ought to be ruled which take for an example it being the collections of the work of this Chapter with the severall lines angles and bounders as you observed them in your Survey CHAP. L. How to protract or draw the plot of a whole Mannor or of divers inclosures the observations of the severall angles lines and bounders being noted in your Field-book PRovide a Skin of Velom or Parchment or divers sheets of paper neatly fastned together with Mouth-glew according to the magnitude or greatnesse you intend to have your Plot which paper or parchment let be ruled all over with 〈◊〉 parallel lines representing Meridians as is taught in the 36 Chapter of this Book the distance of which lines one from another must not exceed the breadth of the Scale of your Protractor Now suppose you were to protract the observations of the last Chapter laying your Field-book before you consider which way your plot will extend and accordingly begin your work as at the point A upon which point A place the center of your Protractor turning it about till the correspondent divisions at each end of the Scale of the Protractor lie directly upon one of the parallel meridians and staying the Protractor there look in your Field-book what degrees and minutes the needle cut at your first observation at A which were 160 degrees 45 minutes therefore against 160 degrees 45 minutes of your Protractor make a mark and through that mark and the point A draw the line AL containing 8 Chains 68 Links Then place the center of the Protractor upon the point L in all respects as before and finding your next degrees and length to be 181 degrees 30 minutes and the length 6 Chains 55 Links therefore against 181 degrees 30 minutes of your Protractor make a mark and through it draw the line LM containing 6 Chains 55 Links Then place the center of the Protractor upon the point M and looke in your Field-book what degrees were cut at M protract those degrees as before and draw the line MN containing 7 Chains 27 Links Then place the center of the Protractor upon the point N the degrees cut being 355 degrees 40 minutes and the line NO containing 4 Chains 45 Links and because against these 355 degrees 40 minutes you finde in your Field-book this mark + there placed you must therefore with Black lead or the like make the same mark at the point N upon your paper to signifie that you must there begin to protract some other Close In this manner must you proceed with all the other lines and angles as you finde them noted in your Field-book till you have gone over your first Close and closed your plot at A. Having thus finished your first inclosure you must deale in the same manner with the second third and fourth and so on were there never so many And to know where to begin to protract your second inclosure you must have recourse to your Field-book where you shall finde this mark ☉ at which you must begin your second inclosure which is Bay Wood and the like mark upon your paper at the point C which is your remembrancer to put you in minde that at the point C you must begin to protract your second Inclosure as you did your first Close ¶ In this manner of protracting there is no difference nor cautions to be observed more then those already hinted in Chap. 36 and 38 of this Book viz. that if the degrees to be protracted be under 180 to lay the Semicircle of the Protractor upwards or from you and if they be above 180 to lay the Semicircle downwards CHAP. LI. The figure of any plot being given how to inlarge or diminish the same according to any assigned proportion IT may so fall out that when you have taken the plot of a whole Mannor upon your Plain Table in divers sheets of paper or observed the angles and afterwards protracted them as in the two last Chapters it may so fall out that your plot may be either bigger or lesser then is desired now if at any time it be required to inlarge or diminish any plot according to any proportion this Chapter will accomplish your desire The Instruments for the performance hereof are divers as was intimated in the 9 Chapter of the 2 Book Now for generality and exactnesse the two Indexes there spoken of