A treatise of practical surveying; which is demonstrated from its first principles. The whole illustrated with copper-plates. The third edition. By Robert Gibson. 1768
Gibson, Robert.
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I 2 — — $5. ©: 1 2 7 4 „ 2 0 9 — 3H 209 wH = oO 500 | —— TW. 7 1 87 4995 5700 1 4103 5564 429 5628 3502 41; — ws <a  | 7 23120] 4598 0 | "AM T1082 2} 3338 47½3 | : I 5 952 | 1 3 | 2] -1522] 4916 ü I; 3297 4720 3 I 3 —. — eee 1779 4920 7. % 32550 4727 8 of 17 1 1 3214] - o7 5 00 2| 3473| -4741 1 3j 3131 -474 | 5 1 yu | 3] -1607] 4935 72 of.zogo|.4755] Heres pagan r 4935} | 2007 68 | "EY | 49414 | - 3007 7s | 2] -1475] 4945 * — 4350 4945 73. of 292 4781 2 | 3 - | 11 2892 1588 1 I 2 4950} | 2] 2340 4794 | 2 _ _ | 3] U 4 | 3] -1262 4000 5 1 | * of 9 4 |%: of oily axbol 4 2672 4512 | : TY = | 9255 2 :., ——I_.z63ol_8z3Þ__|_____ 3}.1959| e — — — — 264 A Table of Latitude and Departure. Deg. N 8. E N |Deg Qu —— ä üũ�Nä 8 — ZE A. 1045| 4972 0 1] 1002 4974 11 | 2| 909580 497 2 | 3| -o915] 4979 3] 85. ol 0871 -4981 88. 0 | 1].o — — — 264 A Table of Latitude and Departure. Deg. N 8. E N |Deg Qu —— ä üũ�Nä 8 — ZE A. 1045| 4972 0 1] 1002 4974 11 | 2| 909580 497 2 | 3| -o915] 4979 3] 85. ol 0871 -4981 88. 0 | 1].o — — — — 264 A Table of Latitude and Departure. Deg. N 8. E N |Deg Qu —— ä üũ�Nä 8 — ZE A. 1045| 4972 0 1| 1002 4974 11 | 2| 909580 497 2 | 3| -o915] 4979 3] 85. ol 0871 -4981 88. 0 | 1].o — — — — 828 4923 | 2 2| 0784 | -4984 | 2 3| -0741 | -49860 | 3 86. o| 0697 4988 89. 0 1 0654 | 4989 | 2 3| -0666 | 4992 | 3 . 90. 0 [ 255 ] A TABLE for changing Degrees taken by the Circumferentor to those of the Quartered Compasses, and the contrary. | Degrees | Cir. QC. | Degrees | "Ir. A 2.56 Aube for changing Degrees, &c. A Table for Changing Degrees, &c. 257 The above Table is so plain in itself, that it needs no further Explanation than this, that Cir. at the Top of the Column stands for Circumference, and Q. C. for Quarter Compasses. To perform the foregoing Table by Numbers. To change Degrees of the Circumference to those of the Quarter Compasses, without the foregoing Table, and the contrary. 1. If the Degrees are less than 60, they are that Number in the NW Quadrant. 2. If the Degrees are between 60 and 180, take them from 180, and the Remainder is the Degrees in the SW Quadrant. 3. If the Degrees are between 180 and 270, take 180 therefrom, and the Remainder is the Degrees in the SE Quadrant. 4. If the Degrees are between 270 and 360, take them from 360, and the Remainder is the Degrees in the NE Quadrant. 5. If the Degrees are between 270 and 360, take them from 360, and the Remainder is the Degrees in the NE Quadrant. 5. If the Degrees are between 240 and 300, take them from 360, and the Remainder is the Degrees in the NE Quadrant. 1. Change 564 taken by a Circumference, to Degrees of the — Comp. An Answer NW 56 2. Change 126+ to Degrees of the — 0 An Answer SE val 16 4. Change 324Ô to Degrees of the Quarter'd Compals. 360 3243 Answers NE 355 The contrary of the former. Again to change Degrees taken by the Quarter'd Compasses to those of the Circumferentor. 1. If the Degrees are in the NW Quadrant, they are a like Number by the Circumferentor. 2. If the Degrees are in the SW Quadrant, take them from 180, for the Degrees by the Circumference. 3. If the Degrees are in the SE Quadrant, add 10 them to 180, their Sum will be those for the Circumference. 4. If the Degrees are in the NE Quadrant, take them from 360, the Remainder will be those for the S 60 Circumference. 5. Nis 360, S180, W go, and E 270 Degrees. MY | This is so plain it requires no Example. Having the Angles of the Field taken by a Theobaldite, Semicircle, or Plane Table given, to reduce them to Angles from the Meridian, or to those taken by the Circumference. The Angles of the Field, with the Bearing of the Bust, or any other Stationary Line from the Meridian being given; the Bearings of all the other Stationary Lines may be found by these two Rules. Rule I. If the Angle of the Field at any Station be more than 180, take 180 from it, and add the Remainder to the Bearing at the foregoing Station; the Sum it less than 360 will be the Bearing at the present Station or of the next Line: But if the Sum be more than 360, take 260 from it, and the Remainder will be the present Bearing. Rule II. If the Angle of the Field be less than 180, take it from 180, and from the Bearing at the foregoing Station take the Remainder, and you will have the Bearing of the present one: But if the Bearing at the foregoing Station be less than the first Remainder, to this foregoing Bearing add 360, and from that Sum take the first Remainder, and this last Remainder will be the present Bearing. An Example will render this Matter familiar and easy. Required to change the following Angles of the Field, to Bearings of the Needle from the North, the Bearing of the first Stationary Line being 571 N g Puch. The Manner of finding the Bearings. 200—180 = 20, 262 = 20, 28 270 70 180 90, 282-90 = 372, 37 2—360 = 12 80 1 122360 = 372, 372—1002 80-98-82. 272—32 = 180-100 80, 190—80 = 230 30-180 50, 3 110 80-9090, 1 0-90 = 80-82 = 93, (70-82) = 360+-70 = 9 = 2 1911691—180 8 11.113322 343 180—180 = 21, 283—21 a — The last found bearing being the same as that taken at the first Station by the Needle, shows that all the Angles of the Field were truly taken. The like we may also be confirmed of by adding up the Angles of the Field; for if their Sum be equal to twice as many right Angles as there are Stations or Sides in the Figure lens by 4, they are truly taken. By Scholium, P. 157. 8 22 twice the Number of Stations Having found the Bearings from the North, as by the Circumference, the Bearings by the Quarterd Compasses are easily obtained as before. And thus a Map can be more accurately protracted than from the Angles of the Field, and its Area may be had by Calculation. If you have all the Angles of the Field without any Bearing given, you may in the like Manner reduce them to Bearings, which will answer for Proportion by Parallels, by finding the Area by Calculation; by supposing the Bearing of the first Stationary Line to be any Number less than 360, and thence you may also know, if the Angles of the Field be truly taken. For though the Bearings of the several Stationary Lines be false ones, yet the Map will be equal in all Repects to one protracted from Bearings taken by the Needle, and therefore the Area of each will be the same: But you will be at a loss for the Situation of the Land surveyed, with respect to The foregoing Rules demonstrated. Plate XI. Fig. 1. Let i, 2, 3, 4, 5, Sc. represent a Plot of Ground, and let the Lines pass through every Station representing Meridian Lines. The Arc NSo at the first Station, will be the Bearing of the Line 12, from the North, as if taken by the Circumference, which Arc is equal to the Arc Nr Sq at the second Station, made by producing the Line 12, from the Parallel Position of the Needle. And the Arc Nr Sq at the second Station, — which is a semicircle, is 0q, but Nr Sq, which was shown to be equal to the Bearing at the first Station, which will be the Bearing of the Second Stationary Line. Thus if from Nr Sq 2005, the Angle of the Field at the second Station, rSq = 180? be taken, the Remainder oq will be 20%. But Nr Sq = 262, the Bearing of the first Stationary Line oq, which is 20% = Nr Sq = 282, the Bearing of the second Stationary Line. Again at the third Station Nr Sq = Nr Sq, the Bearing of the second Stationary Line, and rSq No the Angle of the Field at the third Station; if then from it the semicircle rSq be taken, the Remainder will be qNo, to which if Nr Sq be added, the Sum will be the entire Circle + No, therefore if the Remainder No will be the Bearing of the Space. The third section will be manufactured with little consideration when every Line is continued, and the Circles drawn as in the Scheme. SECT. The Circle, or 360, be taken therefrom, the Re- Containing the Nature of Off-ſets and Interſeftions. The Methods of enlarging, diminishing, and constructing Maps, with the Method of tracing the Down (or any other) Surveys. Also the Vulturian of the Compass and its Uses in Surveying. How to reduce one Measure to another in six Problems, with three other very useful Problems; and the whole concludes with some necessary Derections concerning Surveys in general. WOT FF.-SETAS5 In taking Surveys, it is unnecessary and unusual to make a Station at every angular Point, because the Field Work can be taken with much greater Expedition, by using Off-sets and Intersections, and with equal certainty. Off-sets are perpendicular Lines drawn or measured from the angular Points of the Land, that lie on the right or left Hand to the Stationary Distance, thus, Plate XI. Fig. 2. Let the black Lines represent the Mearings of a Farm or Town-Lard: And let it be the first Station, then if you have a good View to 2, you omit the angular Points between 1 and 2, and take the Bearing and Length of the Stationary Line in 1 2, and insert them in your Field-Book: But in changing from 1 to 2, stop at 4 opposite. Title to the angular Point, and in your Field-Book insert the Distance from 1 to 2, which admit to be 4C. 25L. as well as the Measure of the Off-set ad, which admit to be 1C. 12L. thus: By the Side of your Field-Book in a Line with the first Station say, at 4C. 25L. 10. 12L. that is, at 4C. 25L. there is an Off-set to the left Hand of 1C. 12L. This done, proceed on your distance Line to, opposite to the Angle, and measure each, supposing then to be 7C. 40L. and 8C. 40L. Say (still in a Line with the first Station in your Field-Book) at 10L. 40L. that is at 7C. 40L. there is an Off-set to the left of 3C. 40L. proceed then with your distance Line to, opposite to the Angle, and measure each; supposing then if to be 13C. and 10C. 25L. say in the same Line as before, at 13C. 10L. 25L. Then proceed from 5 to 2, and you will have the Measure of the entire Stationary Line 2, which insert in its proper Column by the Bearing. In taking Off-sets, it is necessary to have a Perch Chain, or a Staff of half a Perch, divided into Links for measuring them; for by these Means the Chain in the Stationary Line is undisturbed, and the Number of Chains and Links in that Line from whence, or to which, the Off-sets are taken may be readily known. Having arrived at the second Station if you find Your View will carry you to 3, take the Bearing from 2 to 3, and in measuring the Diagram. An instance Line, Of OFF-SETS. Stop at 1 opposite to go to, admit all to be 4C. 101. and the Off-set is 1C. 20L. then in a Line with the second Station in your Field-Book, say at 4C. To L. RIC. 20L. that is the Off-ſet is a right Hand one of 100. Again at m, which supposes to be 100. 2;3L.. from 2; take the Off-ſet mh of 100, 15L. and in a Line with the second Station tay, at 100. 25L. RIC. 15L.. In the same Line when you come to the Mearing at 1, infert the Distance 21, 13C. 10L. thus, at 130. 10L.o; that is at 130. 10L. there is one Off-ſet. At n, which is 150. from 2, take the Off-ſet nk 45 L. and still opposite to the Second Station lay at 150. 15L. Let the Line 36 repreſent the Mearing, which by Means of Water, Bryars, or any other Impedi- ment cannot be meaſured. In this Cate make one or more Stations within or without the Land, where the Diſtances may be meaſured, and draw a Line from the Beginning of the firſt to the End of the laſt Diſtance thus: Make Stations at 3, 4, and 5, taking the Bearings, and meaſuring the Diftances as uſual, which inſert in your Field-Book, and draw a Mark like one Side of a Parentheſis from the third to the fifth Station, to ſhew that a Line drawn from the third Station to the fartheſt End of the fifth fta- tionary Line will expreſs the Mearing. Thus, No. Sta. Deg. 8 1 1722 5.45 4 200 13-25 \s5 250 3.36 Suppcfe the Point p of the Mearing to be inac- cettibie, by Means of the Lines 6p or py, being overflowed, or that a Quarry, Furze, Sc. might prevent you taking their Lengths : In this Cate take the Bearing of the Line 67, which inſert op- poſtc polite to the ſixth Station in your Ficld-Book with the other Bearings; then direct the Index to the Point p, and inſert its Bearing on the left Side of the Field-Book, oppolite to the lixth Station, annexing thereto the Words, ut. for Mearing , and having meaſured and inſerted the Diſtance 6 7, tet the In- dex in the Direction of the Line 7p, and inſert its Bearing on the left of the ſeventh Station of the Field-Book, annexing thereto the Words Int. for Mearing; the Croſſing or Inter ſection of theſe two Bearings will determine the Point p, and of courſe the Mearing 657 is alſo determined. If your View will then reach to the first Station, take its Bearing, stationary Line, and Off-sets, as before, and you have the Field-Book completed. Thus, The FIE L D-BO OK. Remarks and Interest. So. Peg. C. I. | OFF-SETTS. — — —— — —— — 313 Int. to a Tower | 1 [358 22.12 4.. | 1 12L. at 7C. gol. J. | 3 qo. at r3C £ 8 | oC. 2560. 2312 Int. to Ditto. 2 [2972 21.12 At 4C. 10L. RIC. 20L. at 10(,. 25h. RIC. — wa — — 153 L. at 130. 10L o. at 150. L. 45L. 1 ( 3 [172z; 5-45 4 1200 | I 3.25 a 5 [2509 | 3-36 1555 Int. for Measuring 6 [125 | 15.15 274 Int. for Measuring 7 [1054 15.10, 4: 10. 20l. L 2C. 20l. 32L at 11C. 25L, o at 12C. 23L. R36L. at 7C. 45L L 2C. Close at the top Station. If you would lay down a Tower, House, or any other remarkable Object in its proper Place; from | Mm 2 any '. N 4 af 4. "x [5 4 FR ' g . Ts Ty q 3 | : 1 —— — ns gy n_— -1 = ova 1 * = - — — 177 — = 2 — * = C3 hk — 5 —— 2 — 7 3 2 - - — 4 * * c = i. - 7 - - — _ — = *.. — 1 "4 : pd 4 » . 2 E CE < - — — 7  dale TINS in N. 88 t: lutcricction will determine the a ER you are to insert it, in the Manner that the. 7 is set out in the Figure, from the Interjections taken at the first and second Statious of the above Figure. Book. A Protraction of this will render all plain, on which lay off your Off-tets and Interjections, and proceed to find the Content by any of the Methods in Section the gih. The foregang Field-Book may be other kept 1.5 - emarks and Interjections | Deg. | Otf-tet | C. J. Otf-ſet i Hog | Cc | |. * | E. L. | 318 Int, to a Tower | 1 355 | 1.12 | 4-3 | | | 3.40 [7- BE 2.2 30 2534 kat. for Dia | 22974 | 410] 120 t. 201 (26134109 =; nt. % Venting Colt at the first Station. Of OFF-SETS. 269 Floto to cast up Off-sets by the Pen. Plate XI. Fig. 2. 12—1f = 2f, if —te=fe, 1e—1d=ed. Then 1d x Adar da, by Prob. 6, Page 182, and 2d x dateb=adeb by Lemma, Page 226, also 2 fe x ebtfc = befc, and f x + fe=cf2; the Sum of all which will be 1abc21; the Area contained between the Stationary Line 12, and the Mearing, 1 abc 2. In the same Manner you may find the Area of 2thg2, of ik gi, as well as what is without and within the Stationary Line 71. If therefore the left Hand Off: gets exceed the right Hand ones, it is plain, the Excess must be added to the Area within the Stationary Lines, but if the right Hand Off- gets exceed the left Hand ones, the Difference must be deducted from the said Area; if the Ground be kept on the right Hand as we have all my supposed, or in Words thus. To find the Contents of Off-Off-Off-Off-Off. From the Distance Line, take the Distance to the preceding Off-Off, and from that the Distance of the one preceding it, Sc. in Four-Pole Chains; so will you have the respective Distances from Off-Off to Off-Off-Off, but in a retrograde Order. 2. Multiply the last of the Remainders by the first Off-Off-Off, the next by the Sum of the For the first and second, the next by half the Sum of the second and third, the next by half the Sum of the third and fourth, &c. The Sum of the first will be the Area produced by the Off-sets. Thus, in the foregoing Field-Book, the first stationary Line is 22C. 12L. or 11C. 12L. of 4 Pole Chains. See the Figure. From 11. 122 1,2 6.50=1f 3.90 ie Take 6.50=1f 3.90 ie 2.25 81 4.62=2f 2.60 1.65=ed C. L. 14=2.25x 32L. half the first Off-ſet= 7200 ed=1.65x1C. 26L. ⁊ the Sum of the 1. & 2d 2.0790 ef = 2. 60 Xx 1C. 32L. = the Sum of 2d & 3d 3. 4320 2f = 4.62 x 3) L. half the last Off-ſet 1.7094 Content of left Off-ſets on the first Diſt, ——— in Square Four-pole Chains 7.9404 In like Manner the rest are performed. The Sum of the left Hand Off-ſets will be 14.0856 And the Sum of the right Hand ones 3.6825 Excess of left Hand Off-ſets in Squ. 4 Pole C. 10.4031 Acres 1.04031 16124 4 Perch 6.449 Excess of left Hand Off-ſets above the right Hand ones, 1 A. OR. 6P. to be added to the Area within the stationary Lines. 7 L 16124 4 Perch 6.449 Excess of left Hand Off-ſets above the right Hand ones, 1 A. OR. 6P. to be added to the Area within the stationary Lines. 7 L Of INTERSECTIONS. How to find the Area of a Piece of Ground by Interjections only, when all the Angles of the Field can be seen from any two Stations on the vast Side of the Ground. Plate XIT. Fig. 1. E T ABCDEFGA be a Field, H and I two Places on the outside of it, from whence an Object at every Angle of the Field may be seen. Take the Bearing and Diſtance between H and I, and ſet that at the Head of your Field-Book, as in the annexed one. Fix your Inftrument at H, from whence take the Bearings of the ſeveral an- gular Points, A, B, C, D, Fc. as they are here re- preſented by the Lines HA, HB, HC, HD, Se. Again fix your Inſtrument at I, and take Bearings to the ſame angular Points, repreſeated by the Lines IA, IB, IC, ID, Sc. and let the firſt Bearings be entered in the ſecond Column, and the ſecond Bearings in the third Column of your Field-Book : Then it is plain that the Points of Interſection, made from the Bearings in the ſecond and third Columns of every Line, will be the Angular Points of the Field or the Points A, B, C, D, Sc. which Points being joined by right Lines, will give the Plan APCDEFGA required, Of INTERSECTIONS. Bea. 180 Di 28C. of the Sta. H an dl. | 1 ä i | No. {Bear | f | Bear. | 2612 | 2654 248 | 2283 | 2152 | 2082 3311 3173 3074 289 2622 2862 220 | 300 The fame may be done from any two Stations within-ſide of the Land, from whence all the An- gles of the Field can be ſeen. This Method will be found uſeful in Caſe the ſtationary Diſtances from any Cauſe prove inacceſſi- ble, or ſhould it be required to be done by one Party, when the other whoſe Poſſeſſion it is, refuſes to admit you to go on the Land. To find the Content of a Field by Calculation, whick was taken by luterſection. In the Triangle AIH, the Argles AIH, AIH, and the Bate HI being known, the Perpendicular Aa, and the Segments, of the Bate Ha, Al may be obtained by Trigonometry: And in the same manner, the other Perpendiculars which Cc, Dd, Ef, Gg, and the several Segments at h, c, d, e, /, If therefore the several Perpendiculars be supposed to be drawn in the Scheme, which are here omitted to prevent Contusion arising from a Multiphaty of Lines, it is plain that if from the beginning, there be taken BAG Feb, the Remainder will be the Map ABCDEFGA. As before, Half the Sum of Bb, and Cc, multiplied by bc, will be the Area of the Trapezium bBC, after the same Manner, Half the Sum of Cc, and Dd, multiplied by cd, will give the Arca of the Trapezium cCDd,; and again, Half the Sum of Dd, and Ee multiplied by de, gives the Area of the Trapezium bBCDEe; and the Sum of the three Trapezia will be the Area of the Figure bBCDEe. Again, in the same Manner, Half the Sum of bB, and all multiplied by ab, will give the Area of the Trapezium bBAa; and Half the Sum of aA, and 26, by ag, gives the Trapezium aAGg, to the add the Trapezium gGF, and fFe, which are found in the like Manner, and you will have the Figure bBAGFEeb, and this taken from 4BCDEeb, will leave the Map ABCDEFGA. Q. E. F. It will be sufficient to protract this Kind of Work, and from the Map to determine the Area, as well as in Plate X, Fig. 3, to find the Areas of the Pieces 24563, and 6p76, from Geometrical Construction. How to determine the Station where a Fault has been committed in a Field-Book, without the Trouble of going round the whole Ground a second Time. From every fourth or fifth Station, if they be not very long ones, or oftener if they are, let an Interference be taken to any Object, as to any particular Part. Part of a Cane, House, or Cock of Hay, etc. or if all these be wanting, to a long Staff with a white Sheet or Napkin set thereon to render the Object more conspicuous, and let this be placed on the Summit of the Land, and let the respective Interjections so taken be inserted on the left Hand Side of the Field-Book, opposite to the Stations from whence they were respectively taken. In your Protraction as you proceed, let every Interjection be laid off from the respective Stations from whence they were taken. In your Protraction as you proceed, let every Interjection be laid off from the respective Stations from whence they were taken, and let these Lines be continued if they all converge or meet in one Point we thence conclude all is right, or so far as they do converge; but if we find a Line of Interjection to diverge or fly off from the rest, we may be sure that either a Mistake has happened between the Station, the foregoing Interjection was taken at, and the Station from whence the Interjection Line diverges; or there must be an Error in the Interjection; but to be assured in which of these the Fault is, protract on to the next Interjection, and having set it off, if it converges with the rest, the foregoing one did not, we may conclude the Fault was committed in taking the last Interjection but one, and none in any Station, and that so far is true. As is protracted; but if this as well as the foregoing Interference diverge, or fly from the Point of Concourte or converging Point of the rest, the Error must have its Rise from some Station or Stations, at or after that, from whence the last converging Interference Line was taken; so that by going to that Station on the Ground and proceeding on to that where the next, or from whence the following diverging Interference was taken we can readily and with little Trouble (at all to Rights. But in most tracts of Land, one object cannot be seen from every Station, or from perhaps one fourth of them; in this Case we are under the Necessity to move the Pole after we begin to lose sight of it to some other Part of the Land, where it may be seen from as many more Stations as possible; which is easily done by viewing the Mearing before it be surveyed. The Pole then being fixed in an advantageous Place, the first Interjection to it is best to be made from the same Station from whence the last one was taken, and then as often as may be thought convenient as before; in like manner the whole may be done by the Removal of the Pole. When we here speak of Stations we do not mean such as are usually taken at every particular Angle of the Field: For it is to be apprehended, that every skilled Surveyor, particularly such who use Calculation, will take the longest Distances possible, not only to lessen the Number of Stations, for the Use of either Protraction or Calculation, but with greater certainty to account for the Land passed by, on the right Hand or on the left, which is taken by Off-ſers: And surely it will be allowed that any Meaſure taken on the Ground and the Content Then arithmetically computed, will be much more accurate than that which is obtained from any Geo-metrical Production. From what has been said it is plain, that from this Method any Fault committed in a Survey can be readily determined, and therefore must be much preferable to the present Method of taking Diagonal. Of Interesse, or the Bearings and Lengths of Lines across Land, to accomplish that End; which Last Method is too frequently used by Surveyors to approximate or arrive near the Content, which will ever remain uncertain, let these Diagonals be ever so many, till the Station or Stations wherein the Error or Errors were committed, be found; and the Fault or Faults be corrected. Where one Diagonal is taken it may perhaps close or meet with one Part of the Survey and not with the other; in this Case, if the Surveyor would discover his Error, he must survey that Part of the Land which did not close, and this may be half or more, of the whole. And should the Diagonal close with neither Part, but be too long, or too short, or should it fall on either Side of the assigned Point it was to close with, he ought to go over the whole, and make a new Survey of it in order to discover its Error. A Number of Diagonals are frequently taken, the Sum of the Lengths of which very often exceeds the Circuit of the Ground, and after all they are but Approximations, and the Content remains uncertain as before; therefore he who returns a Map, made up by the Assistance of Diagonals, where there remains a Miscellaneum in any one Part, runs the Rienzo of being detected in an Error, and must suffer Uneasiness in his Mind, as he cannot be certain of the Return he makes. The frequent Miscellaneums which are botched up by Diagonals, occasion the many and frequent ROWE | | scandals - Of INTERSECTIONS. Of INTERSECTIONS. Sandalous Broils and Animosities between Surveyors, which tend to the Loss of Character of the one or the other, and indeed often to the Discharge of both, as well as to that of the Science they profess. But these may be easily remedied by Interjections, and the Bearing or Line be adjusted where the Fault was committed, and till this be found, nothing can be certain. To enlarge or diminish MAPS, Elo to enlarge or diminish a Map, or how to reduce a Map from one Scale to another: Also the Manner of uniting separate Maps of Lands which Join each other, into one Map of any assigned AY the you would enlarge, over the Paper on which you would enlarge it, and with a fine projecting Pin, prick through every angular Point of your Map, join these Points on your Paper, (laying the Map you copy before you) by penciled or popped Lines, and you have the Copy of the Map you are to enlarge: In this Manner any Protrachon may be copied on Paper, Vellum, or Parchment for a fair Map. If you would enlarge a Map to a Scale which is double, or treble, or quadruple to that of the Map to be enlarged; the Paper you must provide for its Enlargement must be two, or three, or four Times as long as broad as the Map; for which Purpose in large Thirgs you will find it necessary to join several sheets of Paper, and to cement them with white paper or Paper, but the former is best. Then pitch upon any Point in your copied Map, for a Center; from whence if Directions be taken to its extreme Points, and thence if those Directions be taken in a right Line with (but from) the Center, and the same. To enlarge or diminish Maps. 279 the same last Points fall within your Paper, the Map may be encrusted on it to a Scale as large again as its own; and if the like Distances be again set outwards in right Lines from the Center, and if the like Distances be again set outwards in right Lines from the Center, and if the like Distances be again set outwards in right Lines from the Center, it will contain a Map encrusted to a Scale three Times as large as its own, c. Plate XII. Fig. 2. Let the pricked or popped Lines represent the Copy of a Down or old Survey, laid down by a Scale of 80 Perches to an Inch, and let it be required to enlarge it to one laid down by 40 to an Inch. Pitch upon your Center as, from whence through a lay the fiducial Edge of a thin Ruler, with a fine pointed pair of Compasses, take the Distance from a to the Center, and lay it by the Ruler's Edge from a to A: In the like Manner take the Distance from the next Station to the Center, and lay it over in a right Line from DD to B. and join the Points A and B by the right Line AB: In the like Manner set over the Distance from every Station to the Center. From that Station outwards, and you will have every Point to enlarge to the joining of these constantly as you go on by right Lines, will give you the enlarged Map required. In taking the Directions from every Station to the Center, let one Foot of the Compass in the Station, and the other very lightly over the Center-Point, so lightly as scarcely to touch it, otherwise the Center-Point, will become so wide that it may occasion several Errors in the enlarged Map: For if you err from the exact Center but a little, that Error will become double, or treble, or quadruple, as you enlarge to a Scale that is double or treble or quadruple, of the given one; therefore great Accuracy is required in enlarging a Map. When you have done with a Station, give a Dash with a Pen or Pencil to it, such as at the Station and by this Means you cannot be disappointed in misusing a Station, or in laying your Ruler over one Station twice. From what has been said it is plain, that if a Map is to be enlarged to one whose Scale is double the given one, that the Diastruces from the respective Stations to the Center, being set over by the Ruler's Edge, will give the Points for the enlarged one. And thus may a Map be enlarged from a Scale of 160 to one of 80, from one of 80 to one of 40, from one of 20 to one of 10 Perches to an Inch, Sc. For to enlarge to a Scale that is double, the Number of Perches to an Inch, for the enlarged Map must be Half of those to an Inch for that to be enlarged: To enlarge to a Scale that is triple the given one, the Number of Perches to an Inch for the enlarged Map, will be one third of those for the other; if to a Scale that is quadruple the given one, the Number of Perches to an Inch, for the enlarged Map, will be one fourth of those for the other, therefore if you would enlarge a Map which is laid down by a Scale of 120 Perches to an Inch, to one of 40 Perches to an Inch; the Distance from the several Stations to the Center, being set twice beyond the said Stations, will mark out the several Points required, for these Points will be three Times further from the Center than the stationary Points of the Map are. In the same Manner, if you would enlarge a Map from a Scale of 160, to one of 40 Perches to an Inch, to enlarge or diminish Maps. To enlarge or diminish Maps. To enlarge or diminish Maps. To enlarge or diminish Maps. To diminish the Size of the Map. A When a Map is enlarged to another, whoſe Scale is double or treble, or quadruple Fc. of the given one, every Line, as well as the Length and Breadth of the enlarged Map will be double, or treble, or quadruple, Sc. thole of the given one, for it muſt be eaſy to conceive that thoſe Maps are like : But the Area, if the Scale be double, will be four Times; if treble, nine Times; if quadruple, ſix- teen Times that of the given Figure; that is, it will contain four, nine, or ſixteen Times as man ſquare Inches as the given one (for it has been ſhewn that like Polygons are in a duplicate Pro- portion with their homologous Sides.) Yet theſe Figures being caſt up by their reſpective Scales, will produce the fame Content. Thus much is ſufficient for enlarging Maps, and. from hence, diminiſhing of them will be obvious; for one fourth, one third, or half the Diſtances from the ſeveral Stations to the Center, will mark out Points, which, if joined, will compoſe a Map | ſimilar to the given one, whoſe Scale will be four Times, three Times, or twice as ſmall as the given one, ; Thus, if we would reduce a Map from 40 to 80, from 20 to 40, from 10 to 20 Perches to an Inch, Sc. half the Diſtance of the Stations from the Center will give Points requiſite for drawing the Map; if we would reduce from 40 to 120, from 20 to 60, from 10 to 30 Perches to an Inch, Sc. one third of the Diſtances to the Center, will give the Points for the Map: And if we would reduce | 8 Oo from 282 To enlarge or diminiſh Maps. From 40 to 160, from 20 to 80, from 10 to 40 Perches to an Inch, Sc. one fourth of the Diſtances to the Center, will give the Points for the Map. By the Methods here laid down, I have reduced a Map from a Scale of 40 to one of 20 Perches to an Inch, which contained upwards of 1,200 Acres, and constructed of 224 separate Divisions, without the least Confusion from the Lines; for none can arise if the Methods here laid down be strictly observed. I have also from the same Methods reduced a large Book of Maps, each of which was an entire Skin of Parchment, and the whole contained upwards of 46,000 Acres, to a Pocket Volume; and afterwards connected all these Maps into one Map, which was contained in one Skin of Parchment: Therefore upon the whole I do recommend these Methods for reducing Maps to be much more accurate than any of the Methods commonly used, such as surveying of Paper, using a Parallelogram, proportional Compasses, or any other Method I ever met with, though the Figures to be reduced were ever so numerous, irregular, or complicated. How to unite Separate Maps of Lands which join each other, into one Map of any assigned Size. If there be several large Maps contained in 2 Books, each of which supposes to take up a Skin of Parchment. archment, or a Sheet of the largest Paper; which Maps of Lands join each other; and it be required to reduce them to such a small Scale, that all of them when joined together may be contained in To enlarge or diminish Maps. 283 in one Skin, half a Skin, or any subscribed Piece of Parchment, or Paper. Having pricked off and copied the several Maps on any Kind of Paper, unite them by cutting with scissors along the Edge of one Mearing which is adjoining the other, but not cutting by the Edge of both, and throw aside the Parts cut off; then lay these together on a large Table, or on the Floor, and where the Mearings agree, they will fit in with each other as Indentures do; and after this Manner they are easily connected: Measure then the Length and Breadth of the entire connected Maps, and the Length and Breadth of the Parchment or Paper you are confined to; if the former be three four, or five Times greater, (that is longer and broader) than the latter, reduce each copied Map severally to a Scale that is three, or four, or five Times less, as before; and the same Parts of the Mearings you cut by in the large Maps, by the same you must also cut in small ones, and unite the small as the large ones were united; cementing them together with white Water: Thus will your Map be reduced to the assigned Size, which copy over fair, on the Parchment, or Paper you were confined to. 