which you would take your Observations Hauing placed your Semi-circle at F turn it about the North-Point of the Card from you till through the Fixed-Sights Note that I call them the Fiexed-Sights which are on the Fixed-Diameter you espy the mark at G. Then screw fast the Instrument which done move the Index till through the Sights thereof you see the mark at A and the Degrees on 〈◊〉 â—â—â—b there cut by it will be 20. Move again the Index to the mark at B where you will find it to cut 40 deg Do the same at C and it cuts 60 deg likewise at D 77 and at E 100 deg Note down all these Angles in your Field-Book next measure all the Lines as from F to G 14 Chain 60 Links from F to A 18 Chain 20 Links from F to B 16 Chain 80 Links from F to C 21 Chain 20 Links from F to D 16 Chain 95 Links from F to E 8 Chain 50 Links and then will your Field-Book stand thus Angles Degrees Minutes Chains Links G 00 00 14 60 A 20 00 18 20 B 40 00 16 80 C 60 00 21 20 D 77 00 16 95 E 10 00 8 50 To Protract the former Observations Draw a Line at adventure as G g upon any convenient place on which lay the Centre of your Protractor as at F keeping the Diameter thereof right upon the Line G g. Then make marks round the Protractor at every Angle as you find them in the Field-Book viz. against 20 40 60 77 and 100 which done take away the Protractor and applying the Scale or Ruler to F and each of the marks draw the Lines FA FB FC FD and FE Then setting off upon these Lines the true distances as you find them in the Field-Book as for the first Line F 〈◊〉 Chain 60 Links for the second FA 18 Chain 20 Links c. make marks where the ends of these distances fall which let be at G A B C c. Lastly Between these Marks drawing the Lines GA AB BC CD DE EF FG you will have compleated the Work. When you Survey thus without the help of the Needle you must remember before you come out of the Field to take a Meridian Line that you may be able to make a Compass shewing the true Situation of the Land in respect of the four Quarters of the Heavens I mean East West North and South which thus you may do The Instrument still standing at F turn it about till the Needle lies directly over the Flower-de-Luce of the Card there screw it fast Then turn the moveable Index till through the Sights you espy any one Angle As for Example Let be D Note then what Degrees upon the Limb are cut by the Index which let be 10 deg Mark this down in your Field-Book and when you have Protracted as before directed lay the Centre of your Protractor upon any place of the Line FD as at ☉ turning the Protractor about till 10 deg thereof lye directly upon the Line FD. Then against the end of the Diameter of the Protractor make a mark as at N and draw the Line N ☉ which is a Meridian or North and South Line by which you may make a Compass Note that you may as well take the Plot of a Field at one Station standing in any Side thereof as in an Angle For if you had set your Instrument in a the Work would be the same I shall forbear therefore as much as I may Tautologies How to take the Plot of a Field at two Stations provided from either Station you may see every Angle and measuring only the Stationary Distance Let CDEFGH be supposed a Field to be measured at two Stations first when you come into the Field make choice of two Places for your Stations which let be as far asunder as the Field will conveniently admit of also take care that if the Stationary Distance were continued it would not touch an Angle of the Field then setting the Semicircle at A the first Station turn it about the North Point from you till through the Fixed Sights you espy the Mark at your second Station which admit to be at B there screw fast the Instrument then turn the Moveable Index to every several Angle round the whole Field and see what Degrees are cut thereby at every Angle which note down in your Field-Book as followeth Angles Degrees Minutes  C 24 30  D 97 00  E 225 00 First Station F 283 30  G 325 00  H 346 00  Secondly measure the Distance between the two Stations which let be 20 Chains and set it down in the Field-Book Stationary Distance 20 Chains 00 Links Thirdly placing the Instrument at B the Second Station look backwards through the fixed Sights to the First Station at A I mean by looking backward that the South Part of the Instrument be towards A and having espyed the Mark at A make fast the Instrument and moving the Index as you did at the First Station to each Angle see what Degrees are cut by the Index and note them down as followeth and then have you done unless you will take a Meridian Line before you move the Instrument which you were taught to do a little before Angles Degrees Minutes  C 84 00  D 149 00  E 194 00 The Second Station F 215 00  G 270 00  H 322 00  How to Protract or lay down upon Paper these foregoing Observations First draw a Line cross your Paper at pleasure as the Line IK then take from off the Scale the Stationary Distance 20 Chains and set it upon that Line as from A to B so will A represent the First Station B the Second Secondly apply your Protractor the Centre thereof to the Point A and the Diameter lying streight upon the Line BK mark out round it the Angles as you find them in the Field-Book and through those Marks from A draw Lines of a convenient Length Thirdly move your Protractor to the Second Station B and there mark out your Angles and draw Lines as before at the First Station Lastly the places where the Lines of the First Station and the Lines of the Second intersect each other are the Angles of the Field As for Example At the First Station the Angle C was 24 Degrees 30 Minutes through those Degrees I drew the Line A1 At the Second Station C was 84 Degrees Accordingly from the Second Station I drew the Line B2 now I say where these two Lines cut each other as they do at C there is one Angle of the Field So likewise of DE and the rest of the Angles if therefore between these Intersections you draw streight Lines as CD DE EF c. you will have a true Figure of the Field This may as well be done by taking two Angles for your Stations and measuring the Line between them as C and D from whence you might as well have seen all
in your Field-Book the length of any Line you may set it thus if you please with a Stop between the Chains and Links as 15 Chains 15 Links 15.15 or without as thus 1515 it will be all one in the casting up Of Instruments for the taking of an Angle in the Field There are but two material things towards the measuring of a piece of Land to be done in the Field the one is to measure the Lines which I have shewed you how to do by the Chain and the other to take the quantity of an Angle included by these Lines for which there are almost as many Instruments as there are Surveyors Such among the rest as have got the greatest esteem in the World are the Plain Table for small Inclosures the Semicircle for Champaign Grounds The Circumferentor the Theodolite c. To describe these to you their Parts how to put them together take them asunder c. is like teaching the Art of Fencing by Book one Hours use of them or but looking on them in the Instrument-maker's Shop will better describe them to you than the reading one hundred Sheets of Paper concerning them Let it suffice that the only use of them all is no more or chiefly at most but this viz. To take the Quantity of an Angle Plain Table Place the Table already fitted for the Work with a Sheet of Paper upon it as nigh to the Angle A as you can the North End of the Needle hanging directly over the Flower de Luce then make a Mark upon the Sheet of Paper at any convenient place for the Angle A and lay the Edge of the Index to the Mark turning it about till through the Sights you espy B then draw the Line AB by the Edge of the Index Do the same for the Line AC keeping the Index still upon the first Mark then will you have upon your Table an Angle equal to the Angle in the Field To take the Quantity of the same Angle by the Semicircle Place your Semicircle in the Angle A as near the very Angle as possibly you can and cause Marks to be set up near B and C so far off the Hedges as your Instrument at A stands then turn the Instrument about 'till through the fixed Sights you see the Mark at B there screw it fast next turn the moveable Index 'till through the Sights thereof you see the Mark at C then see what Degrees upon the Limb are cut by the Index which let be 45 so much is the Angle BAC How to take the same Angle by the Circumferentor Place your Instrument as before at A with the Flower de Luce towards you direct your Sights to the Mark at B and see what Degrees are then cut by the South End of the Needle which let be 55 do the same to the Mark at C and let the South End of the Needle there cut 100 substract the lesser out of the greater the remainder is 45 the Angle required If the remainder had been more than 180 degrees you must then have substracted it out of 360 the last remainder would have been the Angle desired This last Instrument depends wholly upon the Needle for taking of Angles which often proves erroneous the Needle yearly of it self varying from the true North if there be no Iron Mines in the Earth or other Accidents to draw it aside which in Mountainous Lands are often found It is therefore the best way for the Surveyor where he possibly can to take his Angles without the help of the Needle as is before shewed by the Semicircle But in all Lands it cannot be done but we must sometimes make use of the Needle without exceeding great trouble as in the thick Woods of Jamaica Carolina c. It is good therefore to have such an Instrument with which an Angle in the Field may be taken either with or without the Needle as is the Semicircle than which I know no better Instrument for the Surveyors use yet made publick therefore as I have before shewed you How by the Semicircle to take an Angle without the help of the Needle I shall here direct you How with the Semicircle to take the Quantity of an Angle in the Field by the Needle Screw fast the Instrument the North End of the Needle hanging directly over the Flower de Luce in the Chard turn the Index about till through the Sights you espy the Mark at B and note what Degrees the Index cuts which let be 40 move again the Index to the Mark at C and note the Degrees cut viz. 85. Substract the Less from the greater remains 45 the Quantity of the Angle Or thus Turn the whole Instrument 'till through the Fixed Sights you espy the Mark at B then see what Degrees upon the Chard are cut by the Needle which for Example are 315 turn also the Instrument till through the same Sights you espy C and note the Degrees upon the Chard then cut by the Needle which let be 270 substract the Less from the Greater as before in working by the Circumferentor remains 45 for the Angle Mark if you turn the Flower de Luce towards the Marks you must look at the Norh end of the Needle for your Degrees Besides the Division of the Chard of the Semicircle into 360 Equal Parts or Degrees It is also divided into four Quadrants each containing 90 Degres beginning at the North and South Points and proceeding both ways 'till they end in 90 Degrees at the East and West Points which Points are marked contrary viz. East with a W. and West with an E because when you turn your Instrument to the Eastward the End of the Needle will hang upon the West Side c. If by this way of division of the Chard you would take the aforesaid Angle direct the Instrument so the Flower de Luce from you 'till through the fixed Sights you espy the Mark at B then see what Degrees are cut by the North End of the Needle which let be NE 44 next direct the Instrument to C and the North End of the Needle will cut NE 89 substract the one from the other and there will remain 45 for the Angle But if at the first sight the Needle had hung over NE 55 and at the second SE 80 then take 55 from 90 remains 35 take 80 from 90 remains 10 which added to 35 makes 45 the Quantity of the Angle Moreover if at the first Sight the North End of the Needle had pointed to NW 22 and at the second NE 23 these two must have been added together and they would have made 45 the Angle as before Mark if you had turned the South part of your Instrument to the Marks then you must have had respect to the South End of your Needle Although I have been so long shewing you how to take an Angle by the Needle yet when we come to Survey Land by the Needle as you shall see by and by we
having found the place for B there make an Angle of 51 Degrees drawing the Line 'till it intersect AC c. You may also survey a Field after this manner by setting up a Mark in the middle thereof and measuring from that to any one Angle also in the Observations round the Field having respect to that Mark as you had here to the Angle A. It is too tedious to give Examples of all the Varieties besides it would rather puzzle than instruct a Neophyte How to take the Plot of a Large Field or Wood by measuring round the same and taking Observations at every Angle thereof by the Semicircle Suppose ABCDEFG to be a Wood through which you cannot see to take the Angles as before directed but must be forced to go round the same first plant the Semicircle at A and turn the North End of the Diameter about 'till through the fixed Sights you see the Mark at B then move round the Index till through the Sights thereof you espy G the Index there cutting upon the Limb 146 Degrees 2. Remove to B and as you go measure the Distance AB viz. 23 Chains 40 Links and planting the Instrument at B direct the North End of the Diameter to C and turn the Index round to A it then pointing to 76 Degrees 3. Remove to C measuring the Line as you go and setting your Instrument at C direct the North End of the fixed Diameter to D and turn the Index till you espy B and the Index then cutting 205 Degrees which because it is an outward Angle you may mark thus › in your Field-Book 4. Remove to D and measure as you go then placing the Instrument at D turn the North End of the Diameter to E and the Index to C the Quantity of that Angle will be 84 Degrees And thus you must do at every Angle round the Field as at E you will find the quantity of that Angle to be 142 Degrees F 137 G 110 but there is no need for your taking the last Angle nor yet measuring the two last Sides unless it be to prove the Truth of your Work which is indeed convenient When you have thus gone round the Field you will find your Field-Book to be as followeth Angles Lines  Deg. Min.  Ch. Lin. A 146 00 AB 23 40 B 76 00 BC 15 20 C 205 00 › CD 17 90 D 84 00 DE 20 60 E 142 00 EF 18 85 F 137 00 FG 13 60 G 110 00 GA 19 28 To protract this draw a dark Line at adventure as AB upon which set off the Distance as you see it in your Field-Book 23 Chains 40 Links from A to B then laying the Centre of your Protractor upon A and the Diameter upon the Line AB the North End or that of 00 Degrees towards B on the outside of the Limb make a Mark against 146 Degrees through which Mark from A draw the Line AG so have you the first Angle and first Distance 2. Place the Centre of the Protractor upon B and turn it about until 76 Degrees lyes upon the Line AB there hold it fast and against the North End of the Diameter make a Mark through which draw a Line and set off the Distance BC 15 Chains 20 Links 3. Apply the Centre of the Protractor to C the Semicircle thereof outward because you see by the Field-Book it is an outward Angle and turn it about 'till 205 Degrees lye upon the Line CB then against the Upper or South End of the Diameter make a Mark through which draw a Line and set off 17 Chains 90 Links from C to D. 4. Put the Centre of the Protractor to D and make 84 deg thereof lye upon the line CD then making a mark at the end of the Diameter or 0 deg Through that mark draw a line and set off 20 Chains 60 Links viz. DE. 5. Move the Protractor to E and make 142 deg to lye upon the line ED. Then at the end of the Protractor make a mark as before and setting off the distance 18 Chains 85 Links draw the line EF. 6. Lay the Centre of the Protractor upon F and making 137 deg lye upon the line EF against the end of the Diameter make a mark through which draw the line FG which will intersect the line AG at G So have you a true Copy of the Field or Wood But you may if you think fit to prove your Work set off the distance from F to G and at G apply your Protractor making 110 deg thereof to lye upon the line FG. Then if the end of the Diameter point directly to A and the distance be 90 Chain 28 Links you may be sure you have done your Work true Whereas I bid you put the North end of the Instrument and of the Protractor towards B it was chiefly to shew you the variety of Work by one Instrument for in the Figure before this I directed you to do it the contrary way and in this Figure if you had turned the South-side of the Instrument to G and with the Index had taken B and so of the rest the work would have been the same remembring still to use the Protractor the same way as you did your Instrument in the Field Also if you had been to have Surveyed this Field or Wood by the help of the Needle after you had planted the Semicircle at A and posited it so that the Needle might hang directly over the Flower-de-Luce in the Card you should have turned the Index to B and put down in your Field-Book what Degrees upon the Brass Limb had then been cut thereby which let be 20. Then moving your Instrument to B make the Needle hang over the Flower-de-Luce and turn the Index to C and note down what Degrees are there cut So do by all the rest of the Angles And when you come to Protract you must draw Lines Parallel to one another cross the Paper not farther distant asunder than the breadth of the Parallelogram of your Protractor which shall be Meridianlines marking one of them at one end N for North and at the other S for South This done chuse any place which you shall think most convenient upon one of the Meridian lines for your first Angle at A and laying the Diameter of your Protractor upon that Line against 20 deg make a mark through which draw a line and upon it set off the distance from A to B. In like manner proceed with the other Angles and Lines at every Angle laying your Protractor Parallel to a North and South Line which you may do by the Figures gratuated thereon at either end alike When you have Surveyed after this manner how to know before you go out of the Field whether you have wrought true or not Add the Sum of all your angles together as in the Example of the precedent Wood and they make 900. Multiply 180 by a number less by 2 than the number
the Off-sets in Perpendicular-lines although it be the best way for you may take the Angles with the Index from any part of the Line This way was chiefly intended for such as were not provided with Instruments for instead of the Semi-circle with a plain Cross only you may lay out a Square the rest of the Work being done with a Chain How by the help of the Needle to take the Plot of a large Wood by going round the same and making use of that Division of the Card that is numbred with four 90s or Quadrants Let ABCDE represent a Wood set your Instrument at A. and turn it about till through the Fixed Sights you espy B then see what Degrees in the Division before spoken of the Needle cuts which let be N. W. 7 measure AB 27 Chains 70 Links then setting the Instrument at B direct the Sights to C and see what then the Needle cuts which let be N. E. 74 measure BC 39 Chains 50 Links in like manner measure every Line and take every Angle and then your Field-Book will stand thus as followeth hereunder Lines Degrees Minutes Chains Links AB N. W. 7 00 28 20 BC N. E. 74 00 39 50 CD S. E. 9 00 38 00 DE N. W. 63 20 14 55 EA S. W. 74 80 28 60 To lay down which upon Paper draw Parallel Lines through your Paper which shall represent Meridian or North and South Lines as the Lines NS NS then applying the Protractor which should be gratuated accordingly with twice 90 Degrees beginning at each End of the Diameter and meeting in the middle of the Arch to any convenient place of one of the Lines as to A lay the Meridian Line of the Protractor to the Meridian Line on the Paper and against 7 Degrees make a Mark through which draw a Line and set off thereon the Distance AB 28 Chains 20 Links Secondly apply the Centre of the Protractor to B and turning the Semicircle thereof the other way because you see the Course tends to the Eastward make the Diameter thereof lye parallel to the Meridian Lines on the Paper which you may do by the Figures at the Ends of the Parallelogram and against 74 Degrees make a Mark and set off 39 Chains 50 Links and draw the Line BC the like do by the other Lines and Angles until you come round to the place where you began This is the most usual way of plotting Observations taken after this manner and used by most Surveyors in America where they lay out very large Tracts of Land but there is another way though more tedious yet surer I think first made Publick by Mr. Norwood whereby you may know before you come out of the Field Whether you have taken your Angles and measured the Lines truly or not and is as followeth As Radius or Sine of 90 Degrees viz. the Right Angle C is to the Logarithm of the Line AB 20 Chains So is the Sine of the Angle CAB 20 Degrees to the Difference of Longitude CB 6 Chains 80 Links Secondly to find the difference of Latitudes or the Line AC say As Radius is to the Logarthm Line AB 20 Chain so is the Sine Complement of the Angle at A to the Logarithm of the Line AC 18 Chains 80 odd Links Example of the foregoing Figure In the precedent Figure I find in my Field-Book the first Line to run NW 7 Degrees 28 Chain 20 Links now to find what Northing and what Westing is here made I say thus As Radius 10,000000 Is to the Logarithm of the Line 28 Chains 20 Links 1,450249 So is the Sine of the Angle from the Meridian viz. 7 Degrees 9,085894 To the Logarithm of the Westing 3 Chains 43 Links Again As Radius 10,000000 Is to the Logarithm 28 Chains 20 Links 1,450249 So is the Sine Complement of 7 Degrees 9,996750 To the Log of the Northing 27 Ch. 99 Lin. And having thus found the Northing and Westing of that Line I put it down in the Field-Book against the Line under the proper Titles NW in like manner I find the Latitude and Longitude of all the rest and having set them down the Field-Book will appear thus Lines Degrees Minutes Chains Links N S E W AB NW 7 00 28 20 27 99 .. .. .. .. 03 43 BC NE 74 00 39 50 10 89 .. .. 37 97 .. .. CD SE 9 00 38 00 .. .. 37 53 05 95 .. .. DE NW 63 20 14 55 06 53 .. .. .. .. 13 00 EA SW 74 00 28 60 .. .. 07 88 .. .. 27 49    45 41 45 41 43 92 43 92 This done add all the Northings together also all the Southings and see if they agree also all the Eastings and Westings and if they agree likewise then you may be sure you have wrought truly otherwise not Thus in this Example the summ of the Northings is 45 Chains 41 Links so likewise is the summ of the Southings also the summ of the Eastings is 43 Chains 92 Links so is the summ of the Westings Therefore I say I have surveyed that Piece of Land true But because this way of casting up the Northing Southing Easting or Westing of every Line may seem tedious and troublesome to you I have at the End of this Book made a Table wherein by Inspection only you may find the Longitude and Latitude of every Line what quantity of Degrees soever it is situated from the Meridian Moreover I am also obliged to shew you another way of plotting the foregoing Piece of Ground according to the Table in the Field-Book of NS EW as hereunder Then through B draw another North and South Line parallel to the first as NBS is parallel to NAS and taking with your Compasses the Northing of the second Line viz. 10 Chains 89 Links set it upon the Line from B to ☉ 2 take also the Easting of the same Line viz. 37 Chains 97 Links and setting one Foot of the Compasses in ☉ 2 with the other sweep the Arch cc also take with your Compasses the length of the second Line viz. 39 Chains 50 Links and setting one Foot in B cross the former Arch with another dd and that intersection is your third Angle viz. C. It would be but tautologie in me to go round thus with all the Lines for by these two first you may easily conceive how all the rest are done But let me put you in mind when you sweep the Arches for the Easting and Westing to turn your Compasses the right way and not take East for West and West for East Nor can I commend to you this way of plotting the former being as true and far easier yet when you plot by the former way it is very good for you to prove your Work by the Table of difference of Latitude and Longitude before you begin to protract and when you find your Field Work true you may lay it down upon Paper which way