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 Obfervations of Liutloso, ard ande eS 
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 CO M:ith Books of heir fet, eam, Ty Pie fle 
 
 
 
 
 _ The New Lmproved Theodolte. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The Double Level. 
 
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 = Practitioners of Wathematical 
 net thee Tountuh my Sran.fondone 
 
 Vath erratic 
 
 
 
 
 
 
 

 
 
 
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 ress 
 
 or He 
 
 PRACTICAL SURVEYOR: 
 
 | eee CONTAINING | 
 The moft approved Methods 
 
 . FOR i 
 "Surveying of Lanps and Wate BA 
 
 By the feveral 
 INSTRUMENTS NOW IN USE: 
 Particularly exemplified with 
 ‘The Common and New Theodolites, 
 AND ALSO 
 
 | How to plot and caft up fuch Surveys, wee the 
 
 Manner of adorning the Maps thereof. 
 
 To which ate added, 
 Some ufes of the new Theodolite, viz. 
 In drawing the perfpective Appearance of Buildings, €s’c. 
 In levelling, for, the conducting of Water, and 
 In taking the Dimenfions of ftanding Timber. 
 
 Together with the Defcription and Ufe of 
 An improved Sliding-Rule for Timber, ee, 
 An Loker) Dial, 
 ' A Meafuring Wheel, and 
 The Pantographer, for copying of Drawings. 
 
 
 
 Firft publifhed in part, 
 By JOHN HAMMOND; 
 Since enlarged, 
 By SAMUEL WARNER; 
 
 And now revifed, correfted, and greatly augmented. 
 
 
 
 Ry me a a RET RE UN am 
 
 “The THIRD EDITION. 
 
 
 
 
 
 
 
 ie 0 aN DO Vv . ; 
 Printed for T. Heatu, Mathematical-Inftrument-Maker, at the 
 Hercules and Globe, near Exeter-Exchange in the Strand. 
 
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 PREFACE 
 
 N the following treatife is coritained the whole 
 bufinefs of land furveying, in the manner.as 
 1S NOW practifed by the moft experienced artifts ; 
 together with fuch problems and obfervations as 
 
 are ‘really neceflary :, And herein the fubject is treated 
 of in fuch a plain, tho’ concife manner, that the moft 
 common Capacity, with a very little refleGtion, will 
 readily conceive the whole ;, efpecially if hie has 
 thie inftruments before him while he reads of their 
 ufe: And although a great part of this work may 
 be like what has been delivered by other writers, yet’ 
 there is not one article relative to ptactice, but. what 
 the authors have drawn from their own experience. 
 
 The reader will hére find, after fome few intro- 
 ductory problems, a very par ticular and exact deferip- 
 tion of the feveral inftruments ufed in furveying, and’ 
 a jut comparifon of them together ; ‘particularly the 
 various forts of Theodolires: With due directions 
 and cautions in their management, according to their 
 feveral kinds; in order to prevent errors and mi- 
 ftakes, as well in the taking obfervations, and core 
 recting them on the fpot, as in plotting and laying 
 them down in the draught. 
 
 Alfo two very large examples, being parts of ac- 
 tual furveys, containing moit of hers varieties that, 
 can happen in the pradtife of this arc; the one per- 
 formed by the common Théodolite, the other by the 
 
 a new 
 
 
 

 
 4i Th PREFACE. 
 
 new improved Theodolite: The manner of keeping 
 the field-book in a diftinct and clear method is here 
 
 fhewn; how the obfervations and meafures are to © 
 
 be plotted, and the contents of the feveral inclofures 
 
 _ and pieces caft up: Alfo in the courfe of thefe two 
 
 examples, and other parts of the work, there will be 
 met with, every caution and direction that can any 
 way contribute towards the ready difpatch and ac- 
 curacy of the practitioner, not only with regard to 
 the field work and plotting, but alfo in the drawing, 
 colouring, and ornamenting of the map. 
 
 The new improved Theodolite is herein explained — 
 
 in its parts and ufe ; alfo its application to water level- 
 ling, taking of heights, and drawing in per/pective, 
 are diftinctly and clearly treated of, 
 In the account of the Meafuring-wheel, Univer- 
 fal-dial, and Pantographer, the reader will fee fome 
 particulars very ufeful and interefting; but, as there 
 is annexed a copious table of contents, it will be 
 necdlef$ in this place to infift further on any of the 
 
 atticles contained therein. | 
 The major part of this work was originally com- 
 pofed by that ingenious artift Mr. Samuel Cunn ; but 
 for fome reafons he let it appear under the name of 
 Fobn Hammond, who was a clerk to his friend Mr. 
 Charles Brent. ‘The fecond edition of this book was 
 under the care of Mr. Samuel Warner, a perfon well 
 known for. his fkill in the bufinefs of furveying; he 
 added an appendix, containing a more particular de- 
 feription of the Improved Theodolite, with a new 
 method of ufing it in taking obfervations in the field ; 
 whereby an error may be more readily difcovered 
 and prevented than by any other way hitherto ufed ; 
 with an example of the field-book of part of an ac- 
 tual furvey taken thereby. Likewife a full explana- 
 tion of the manner of laying down thofe obfervations 
 from one center, fo as to avoid the faults which arife 
 from protracting angle by angle. As alfo how to 
 reduce 
 
 ~ ae 
 
 
 
The- P. R: E- FACE; iit 
 reduce irregular figures to triangles, with the appli- 
 cation thereof in the cafting up the contents of the 
 forementioned example. This appendix is now put 
 into the body of the work, part being in Seétion I, and 
 
 of the reft is compofed the VIIIth SeGion. | In the 
 
 prefent edition, the former order of the fubjects are 
 varied, the revifer thinking the order they now ap- 
 pear in to be better: But befides this change, there 
 are a very confiderable yariety of corrections, alter- 
 ations, and additions; for the X1Vth and XVith 
 Sections are not only added, but there ate introduced 
 into the work, many articles not in the former edi- 
 
 tions, and which were now thought very necellary 
 
 to be communicated: Notwith{tanding which, the 
 bulk of this book is not increafed above the former ; 
 tho’ the prefent contains near three fheets of matter 
 more than was in the laft ; \which has been effected by: 
 making the page both broader andlonger. Alfo the 
 figures which in the former impreffions were in four 
 fmal] plates, indifferently defigned, and as ill refer- 
 red to, are in this brought into one plate, and ren- 
 
 ‘dered more ufeful. 
 
 It may be proper to obferve, that fome of the no- 
 tions in Section XIV were drawn from a little book 
 of Martin Mafter, publifhed in 1661: And part of 
 
 the XVIth Section, is a tranflation from a French 
 
 piece publifhed by C. Langicis, an engineer to the 
 French King, who pretends to no more than to have 
 perfected an inftrument of this kind already known ; 
 and, indeed, among the inftruments of Sir ‘fonas 
 Moore, fuch a one was found, but fomewhat more 
 antique and inconvenient than that which is now pro- 
 pofed: But M. Langlois not having given a tab'e of 
 the. lengths of the feveral divifions from their refpec- 
 tive centers, nor how they are to be found, it was 
 thought proper to add thefe articles to compleat th¢ 
 
 account of the Pantographer. 
 Feb. 18, FOR 
 1749-50. is 
 
 3 2 Note, 
 
 
 

 
 iv Th PREFAC E: : 
 Note. The enfuing directions having been jae 
 
 in their proper places, it was thought convenient to 
 
 annex them in this place. 
 
 in the beginning of the field-book it will be pro- | 
 
 per to write ore ach title as the following~ 
 The field-book, containing obfervations and di- 
 menfions taken in the furvey’ of the manor of. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 in the parifh of-——in the county of. ; belong- 
 ing to Surveyed in the months af in 
 the year-———by———-and the following affiftants, wiz. 
 A. B. of the parifh of. labourer. 
 
 Cp: mae 
 
 &e. 
 
 Specifying their names, places of abode and occu- 
 
 pation 5 and at the beginning of each day, write the_ 
 
 day’s name, day of the month and hour; alfo at the 
 end of each day’s work write the hour ; and, if there 
 fhould be occafion to change any of the aMiftants, 
 or have new ones, let this be alfo inferted, with the 
 day: For fuch obfervations may be of fervice, in 
 cafe the furveyor fhould, on any account relating to 
 the premifes, be called on to give his teftimony. 
 
 In drawing out the Terrier “of a furvey, a difpo- 
 fition, fomewhat like the following, may be found 
 convenient. In fix columns, titled N°, Kind, Names, 
 Proprietors, “Tenants, Quantity ; write 
 
 1ft, The number refered to in the map, if the fe- 
 veral pieces therein are numbered. 
 
 2d, ‘Che kind, whether arable, pafture, meadow, 
 wood, garden, Hautes! yards, water, EFe, 
 
 gd, The name that the piece is known by. 
 
 4th, The name of the lord of the manor, or other 
 
 perfon, to whom the piece belongs, whether in fee- 
 
 fimple or copy-hold, 
 
 5th, The name of the tenant who rents, or oc- 
 cupies the piece, 
 
 6th, The quantity that piece contains, in acres, 
 rods, ent poles, 
 
 eth ANE ALIEN I, 
 
 
 

 
 
 
 op si dig: 8 085 
 
 4 SE. C yee B 
 
 " F menfuration in general, with the moft necef- 
 
 - O° fary geometrical problems. page 1 
 Viz. To draw perpendicular lines. at 
 
 To bifeét lines. 4 
 Io make equal angles. | 5 
 To draw parallel lines. 5, 6 
 _ Lo divide right lines into many equal parts. 6 
 _ To make equal right lined figures. 7 
 To reduce irregular figures to triangles, 8 
 
 i Sy Ovo vir: 
 Of bir uments ure in iH ieee of land. If 
 Bee Peony. 
 To obferve the ne tion of a line by any of the pre- 
 ceding infiruments. 14 
 Pirft, By the circumferentor. . ibid. 
 To try.if a needle plays well. 1s 
 . Lo protratt any line, whofe bearing is taken | 
 by the circumferentor, 17 
 Rerondlys To obferve with a Theodolite, both by the 
 limb, and by the box and needle. 18 
 To corrett the angles and bearings, before 
 the infrrument is removed, ~\19 
 
 T 0 plot, and therein to difcover and cor- 
 
 \ rett an error before it is communicated 
 to the following part of the work 25 
 Traverfe tables, ufeful in furveying. 28 
 
 Thirdly, To obferve with a femitircle, that has a 
 box and needle. 30 
 Fourthly, Of the peraétor. ibid. 
 Fifthly, 
 
 
 
Th CONTENTS. 
 
 F ifthly,. Of the plain table, a 
 = © Totake a plan by the plain table. 32 
 Sixthly, Of working with the chain. 35 
 Of the off-fet faff. ibid. and 52 
 Of the arrows. | ibid. 
 ' Lo take the pofition of lines by tbe chain. 38 
 To plot uch pofitions. - 40 
 To find the pofition of a meridian line. 4t 
 SlE iG. Bay, | 
 To caft up the contents of land; with the method 
 of reducing irregular curves to ftrait lines, 43 
 S. E.G Desi 
 Of the laying out, or dividing of land 46 
 Firft, By a line parallel to one fide. v4 49 
 Secondly, By a line drawn frow one angle. 50 
 Thirdly, By lines drawn from any point within, 51 
 S: BE Gta VAR 
 
 The ufe of the common Theodolite, exemplified in fur- 
 veying of feveral parcels of land lying together ; 
 with the form of a field-book. 52 
 
 How off-fets are to be taken. 3 54 
 
 To difcover errors caufed by the lofs of arrows. 56 
 
 To correct the obfervations of pofition. : 
 
 Van 
 To mark a flation, fo as to find it again, 61 
 Of the allowance for afcents and defcents, 65 
 Neceffary cautions, Pi 60 
 The field- book, 68 
 S.E.C: Ty. Vik 
 
 To protrad the obfervations contained in the pre- 
 ceding field- book: 87 
 To prevent errors in plotting. go 
 
 What articles foould be inferted in plans. 
 To make a fair plan from the rough draught. 94 
 SE Gabe 
 Of a ncw, certain, and expeditious method of jur- 
 veying and plotting by the Theodolite, as now 
 improved. ) Os 
 Caujes of the lines of a draught not clofing. ibid. 
 | The 
 
 
 

 
 oa aaa 5 ite - 
 
 The GON-HEM TS St 
 
 The improved Theodolite decribed, | 97 
 i boot with this Theodolite, : 
 Pe book of part of an actual her pey performed 
 a Oy this infirument. 102 
 ee the obfervations and meafures in this jfield- 
 book are protratted. 112 
 The cafting up the contents of this furvey in fe- 
 parate pieces, and in one, piece. | 116 
 RC We TR 
 Of furveying of shoals and fands by help oF the 
 new Theodeliie. 119, 
 Soe A, Oe a> 
 Of water levelling, or the condutting of water, 122 
 To adjuft the level. ibid. 
 To ufe the level. . vig NBOe 
 Neceffary obfervations. “4 226 
 Table of allowances for the curvature of the earth 128 
 Pil, Dyk 
 Of colours and pencils. 130 
 S.E.C.T. -XIL 
 
 A further ufe of the Theodolite (as now improved) ; 
 conjointly with ibe ufe of a fliding-rule aptly 
 divided; to meafure timber either round or 
 hewn to a fquare, or unequally [quared: Alfa 
 how to allow for afcents and defcents, by find- 
 
 ing the horizontal lines. ¥23 
 Of the notation of the fiding rule. ibid. 
 Io meafure planks. 133 
 To meafure round timber. 139 
 Lo meafure fquare timber. Se 
 
 _ Lo meafure parallelopipeds. 
 
 To meafure the height of ftanding timber by the 
 Theodolite. 150 
 
 To find the horizontal lines in floping ground, 151 
 
 ShcG Te RI. 
 
 The ufe of the Theodolite in drawing ihe per- 
 fpcéiive appearance of any building without 
 meafuring one fingle line. 152 
 b Firft, 
 
 
 
 
 

 
 vill Fhe* C‘O-N* TE ON’ Ts: 
 
 Virft, When the pitture is parallel to one of the 
 fronts. yn os 
 Neceffary theorems in pir oceans r55 
 Secondly, When the picture flands againf{ an 
 | angle of the building, oblique to two - 
 adjoining fronts. TS7. 
 5S aA ty | 
 
 The defcription and ufe of the Perambulator, or 
 
 Mea/uring-wheel, 159 
 
 To find the diftance run by the wheel, ‘160 — 
 
 How this inftrument may be made to do the bufi- 
 nels of furveying ee with its advan-— 
 
 tages. 16 I/ 
 $-B:C-T. ae , 
 The defcription and ufe of the Univerfal Dial, hid 
 of the variation of the compafs; 164 
 Of the pedeftal of the dial. , 165 
 Of tbe meridian, equinotital and bridge. 166 
 Ina known latitude, on a given day of the month, 
 to find, Firft, The hour of the day. Lae se 
 Secondly, The pofition of the meridian, 168 
 Thirdly, The pofition of the pole. | ibid, 
 Fourthly, The variation of the needle. ibid, 
 Fifthly, The Sun’s azimuth. ibid. 
 sixthly, The Sun’s altitude. — ibid, 
 Ta find the declination of a wall. ibid. 
 To apply this dial to a Theadolite, gibt ys 
 To find the latitude of a place by the common Theo- 
 doliie. 171 
 
 Sof hee T. Sev 1 
 Lhe defcription and ufe of the Panera or 
 
 Imitater, 173 
 — Toufe the Pantographer — 174 
 Of the different parts of the inftrument. 196 
 
 To compute the difiances of the div fe ons from their — 
 
 relpeftive centres. 180 
 
 Eight plates. 
 
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 Of Mensur ation in general, with the moft 
 necefjary GEOMETRICAL PROBLEMS. 
 
 Geometricians ufe the word, is, to 
 Wi? aflume any certain Quantity, and ex- 
 WZ prefs the proportion which other fi- 
 NW milar Quantities bear thereto: But 
 IWeLA® in the common acceptation, to Mea- 
 irc, is, to apply fome certain known quantity pitched 
 upon for a ftandard, and thereby to determine the 
 precife extent, quantity ot capacity of any thing of 
 
 the fame kind. Thus: 
 The meafure of a line is found by applying the 
 lineal Inch, Foot, Yard, Pole, &@c. to that line, in 
 ; B o.der 
 
 
 
 
 
 

 
 | CHYy | 
 order to difcover its length ; the doing of which is 
 called Lougimetry. rs 
 
 The Meafure of a fuperficies is obtained by the 
 application of the fuperficial or fquare Inch, Foot, 
 Yard, Pole, Acre, &%c. thereby to determine its 
 Areaor Content; the method of doing which is called | 
 Planimetry, whereof Surveying of land is a part ; 
 and of this the following pages chiefly treat. ~~ ~ 
 
 The Meafure of a Solid is had by comparing it 
 with the folid or cubic Inch, Foot, Yard, Gallon, — 
 €%c. thereby to find its capacity or folid content, ~ 
 which is called Stereometry, and comprehends the 
 meafuring of Timber, Stone, &c. 
 
 Now, though it cannot be fuppofed that any Per- 
 fon, who is wholly ignorant of the firft principles of 
 Geometry, fhould expect to become a compleat Sur- 
 veyor by barely reading this Book, whence it might. 
 feem altogether unneceffary to infert the common 
 Definitions and Problems ; yet, in order to refrefh 
 the reader’s memory, when other books are not 
 at hand, it was thought not improper to lay down 
 
 fome few of the moft popular Problems ; and fuch | 
 are thofe that follow., | ] 
 
 PROB. 
 
 
 
‘ 
 
 Pen Bn 
 
 Upon a given right line, to eet? another right line, 
 which feall be perpendicular to the right line given, 
 
 MTHE right line given is AB (Fig. 1.) upon 
 ™ which, from the point E it is required to erect 
 _ the Perpendicular EH. 
 _ Opening your Compafies at pleafure to any cons 
 ‘venient diftance, place one foot in the afligned 
 point EB, and with the other make the marks C and 
 D, equi-diftant on’ each fide the given point E, . 
 Then opening your Compafies again to any other 
 convenient diftance, wider than the former, place 
 | one foot in C, and with the other defcribe the Arch 
 GG; alfo (the Compaffes remaining at the fame di- 
 ftance) place one Foot in the point D, and with the 
 - other defcribe the Arch FF: Then from the point 
 H, where thefe two Arches interfect or cut each o- 
 ther, draw the right line HE, and it will bea Per- 
 pendicular to the given ,right line AB; which was 
 the thing required ‘to be done. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 : 
 
 
 
 
 
 
 
 po GA oni! otro: P BiG B,, Tt. - ie 
 To erect a Perpendicular upon the End of a right Line 
 | “| given. alti . 
 
 LE T. AB (Fig.2.) be a right Line 
 = from the End. thereof, at B,: let ite 
 to erect the Perpendicular BF. 
 Firft, Your compafies being opened at 
 - venient Diftance, place one foot in B, a1 
 other make the mark C ; the Compafs poi 
 in C, with the other foot make the mark | 
 - given line AB; lay a Ruler fro 
 draw the line DE, making CE equalt 
 from B, through E, draw the line B 
 
 be the Perpendicular required, 
 
 B2 
 
 SO ee ne ne ne on ne nee ee ee eS 
 
: | wey : Se 
 PROB. III. 
 Lo divide a given right Line into Two er Parts. 
 
 LE T CB ( Fig. 3.) be a right the given, to be 
 divided into two equal Parts. | 
 
 From the extremes B and C, with ‘an SB Gance 
 greater than half the given line, defcribe the arches 
 above and below, cutting one another in the points 
 
 _D and F: Draw DF, and it will divide AB into 
 two equal parts in H, as required. 
 
 . | , PROB Iv. 
 Fo let fall a Perpendicular from any Point aff Fond, 
 ee upon a right line given. 
 
 rs T the point given (Fig. 4.) be C; from which 
 point it is required to draw a right line, which 
 fh] be : perpendicular to the given right line AB. | 
 
 
 
 
 
 
 
 
 
 “ft, From the given point C, tothe line AB, 
 an occult line at pleafure, as CE, which divide 
 ual parts in the point D: Then placing 
 t of the compafies on the point D, with the 
 
 DC, deferibe the Semicircle CFE, cutting © 
 line AB in the point FY Lafily, From 
 C, draw the right Line CF, andit fhall be 
 
 PROB. 
 
 
 

 
 
 
 (5) 
 
 : P.R O-B.. ¥. 
 To makean Angle equal to om Angle given. 
 
 TET the Angle given be ACB (Fig. 5.) and let 
 it be required to make another Angle equal 
 thereunto. 
 
  Firft, Draw the line EF at pleafure ; then on 
 the angular point C, as a center, with any conve-. 
 nient diftance defcribe the arc AB, between the 
 
 legs of the angle given; alfo upon the point F, 
 
 with the fame diftance defcribe the are DE: Then 
 
 take with your compaffes the diftance AB, and fet. 
 the fame diftance from Eto D. Laftly, Draw the 
 
 line FD, fo fhall the angle DFE be equal to the 
 
 given angle ACB. | 
 
 PROB. VI. 
 
 i Aba given Diftance, to draw a right Line parallel to 
 he a right Line given. ss 
 
 TE T the line given be AB, (Fig. 6.) unto which 
 — it is required to draw another right line parallel, - 
 at the diftance MN, | 
 
 Firft, Open your compafies to the diftance MN, 
 then placing one foot in A, with the other defcribe. 
 the arc C; alfo place one foot in B, and with the 
 other defcribe the arc D. Lajfly, Draw the line 
 CD, fo that it may only touch the arcs C and D ; 
 _ fo fhall the line CD be parallel to the line AB, 
 and at the diftance MN, as was required. | 
 
 
 

 
 (6) 
 
 PROBS VIB ) 
 
 ‘A right line being given, to draw another right line 
 parallel thereunto, which fhall alfo pafs through a 
 point affigned, | 
 
 Tt AB (Fig.7.) be a line given, and let it be 
 
 required to draw another line parallel thereunto 
 which fhall pafs through the given point C. ¥ 
 _Firft; Take with your compaffes the diftanc 
 
 from A to C, and placing: one foot thereof in B, 
 
 with the other defcribe the Arc DE; then take in 
 
 your compaffes the diftance AB, and placing one 
 foot in the point C, with the other defcribe the Arc | 
 
 FH, croffing the former Arc DE in the point H. 
 
 Lofily, Draw the line CH, and it fhall be parallel ~ 
 
 to AB. 
 
 Thefe two laff Prostems may be more eafily per- 
 formed by a parallel Ruler. : 
 
 PUR O88 VIE: 
 To divide a given right line into any number of equal 
 parts. 
 
 L= T AB (fig. 8.) be a right line given, and let 
 it be required to divide the fame into five equal . 
 arts. | 
 if Firft, From the end A of the given line, draw 
 the line AC, making any angle; then from the 
 other end B of the given line, draw the line BD 
 parallel to AC, (or make the angle ABD equal to 
 the angle CAB) then upon the lines AC and BD, 
 fet off any four equal parts (which is one lefs than 
 the number of parts into which the line is to be di- 
 vided) on each line, as1, 2, 3,4 then draw lines 
 from 1 to 4, from 2 to 3, from 3 to 2, and from 4 
 - ta1, which lines, croffing the given line AB, fhall 
 divide it into five equal parts, as was required. 
 
 PROB, 
 
 
 

 
 
 
 (7) 
 
 P R..O Bai FX. 
 
 Any three right lines being given, provided the two 
 foorteft taken together be longer than the third, to 
 make age @ Triangle. 
 
 peri it i required to make a Triangle of the 
 
 three lines C, B, and A, (Fig.g.) the two 
 fhorteft whereof, wiz, C and B taken together, are 
 longer than the third line A. 
 
 Firft, Draw the line DE equal to the given line 
 B, then take with your compafies the line A, and 
 fetting one foot in "E, with the other defcribe the 
 Arch HG; alfo take the given line C in your 
 compafies, and placing one foot in D, with the 
 other defcribe the Arch KF, cutting the former Arch 
 HG in the point O: Lajily, If from the point O, 
 you draw the lines OE and OD, there will be 
 formed the Triangle ODE, whofe fides fhall be e- 
 qual to the three given fiaes Ay B,C; 
 
 In like manner, a Triangle /mm may be made equal 
 to another given Triangle LMN. See Fig. 10. 
 
 Alfo any rectilineal figure abcdefg, is made equal 
 to any other rectilineal Figure ABCDEFG, by mak- 
 ing the Triangles adg, bef, bfe, bce, ced, refpectively 
 equal to theT riangles ABG, BGF, BFE, BCE, CED, 
 See fig. 11. 
 
 B 4 PROB, 
 
 
 

 
 Ce) 
 
 P-RO-B. ae 
 ‘To reduce any irregular Figure into aT. rriangla, 
 
 By he Problem the content of any pees piece of 
 land may be caft up much fooner and more accurately 
 than by the common method of dividing it palo “he ra- 
 pezia and T riangles. | 
 
 oF HE practice hereof bi via on sat re, 
 
 Prop. of the 1{t Book of Euchd, where it is de- 
 monftrated, that Triangles ftanding on the fame 
 bafe, and being between the fame parallels are peu 
 ene to the other, | ny | 
 
 EXAMPLE. I. 
 
 Let itbe required to reduce‘the Trapezium ABCD, 
 Fig. 12. into-a Triangle, ngviie its Vertex at 
 Angle A, 
 
 Produce the bafe BC, and draw the diagonal AG 
 thro’ D craw DE parallet'to AC, tllit meet BC in 
 E, join AK and ABE will be the Triangle required. © 
 
 fig. 13. thews how in- like manner. to reduce a 
 Trapezium having a re- entian angle, 
 
 EXAMPLE. Hf: 
 
 Let it be required’ to reduce the Trapezium. 
 ABCD, Fig. 14. to a Triangle whofe vertex fhall be 
 at the point E in one of the fides AD.’ 
 
 Join BE and CE, draw AF parallel to BE, and 
 DG paralicl to CE, till they meet the bafe BC pro- 
 duced in F and G, draw the lines EF ‘and EG, 
 
 and the triangle FEG will be equal to the Trapezium 
 given, 
 
 -.* This Problem and itg Examples, are a Part of Mr. 
 
 : Warner’ s Appindix to the laft Imprefiion of this Work. 
 
 E X- 
 
 ~ 
 
 
 

 
 
 
 Pe 
 wee EX AMP I.E. -Il 
 
 ~ Let it be required to reduce the Pentagon ABCDE, | 
 fig. 15. to a Triangle, having its vertex at the © 
 Angle A. 
 * ~ Produce the bafe CD both ways, and draw the . 
 _ Diagonals AC, AD: Through B draw BF parallel 
 
 to AC to cut CD in F, and through E draw EG pa- 
 rallel to AD to cut CD in G, join AF and AG, and 
 
 AFG will be the Triangle fought. " 
 
 EXAMPLE IV. 
 
 Let it be required to make a Triangle equal to the 
 
 irregular Hexagon ABCDEF, and let the fide AB 
 be one fide of the triangle Fig. 16. 
 _ Produce tie fide DE, join AF, and parallel thereto 
 thro’ F draw FH to mect DE in H ; join BD, and 
 parallel thereto draw CG to meet DE in G; by B 
 and G draw outa right Line ; join AG, and parallel 
 thereto thro’ H draw HI tomeet BG produced in I, 
 draw Al, and ABI will be the triangle required. 
 
 | cig he 9 4 Oe ag Wg a EA 
 
 To reduce any right-lined Figure given into a 
 Triangle ; as  fuppofe the. feven-fided Figure 
 ABCDENVG, Fig, 17. 
 
 Firft draw BD, and its parallel CK ; then if BK 
 be drawn, it will cut off from the Figure the triangle 
 DKS, and will take in the triangle BCS equal thereto, 
 and the fide BK will fupply the ufe of the two fides 
 BCand CD. Alfo, draw GE, and its parallel FL ; 
 then if GL be drawn, it will cut off from the figure 
 the triangle LRE, and take in the triangle GRE 
 equal thereto, and the Side GL will fupply the ufe 
 of the other two fides GF and FE, and the whole 
 Plot ABCDEFG confifting of feven fides, is re- 
 
 2 duced 
 
 on on oe oe ee yy yey rt 
 
 ae a ce a a a ae 
 
 
 
 
 
 ot 
 

 
 ( TO 
 duced to the five-fided figure ABKLG, yet aan Tome 
 taining the fame quantity. Now to reduce this plot’ 
 into a triangle, work in all refpects as in the Third 
 
 Example, Firft, produce the Bafe both ways, then 
 
 draw the lines AK and AL ; and parallel to them 
 the lines BH and GM, cutting DE extended inH 
 and M.  Laftly, draw the lines AH, AM, and - 
 they will conftitute the triangle AHM equal to the 
 right-lined figure given, 
 
 In like manner may any other irregular figure of 
 ever fo many fides be reduced toa triangle, and that 
 very readily by ufing a parallel Ruler, whereby we 
 avoid drawing the unneceffary lines, only marking 
 their interfections on the bafe. Thus in Fig.18. lay the 
 edge of a parallel Ruler to the points B and D, then 
 open the Ruler till the fame edge cuts the point C, 
 and mark where it interfects the bafe DE at k ; lay 
 the Ruler again to the points k and A, transfer i it to 
 B, and ail its interfection on the ne ath; then 
 draw Ah, which will be one fide of the Triangle 
 fought.. Again, laying the Ruler to E and G, tranf- 
 fer it to F, and mark the interfection on the bafe at 
 ], lay the Ruler to | and A, and mark where its pa- 
 rallel edge by G interfects the bafe prolonged at m. 
 Laftly, draw A m, and the Triangle A hm will be 
 equal to the feven-fided figure as was required, 
 
 a gh 
 
 SECA, 
 
 
 

 
 ae A VE © blir 8 , 
 Of InstRUMENTS ued 17 Surveying Land: 
 
 
 
 NSTRUMENTS ufed in Surveying are, ei- 
 
 ther to meafure, or lay down the lengths of 
 
 lines, or their pofitions. ‘ 
 
 The moft proper inftruments for meafuring ‘ 
 lengths, in Towns, Streets, or any other Buildings, | 
 are 5 Foot and 10 Foot Rods, and a Chain of 50 
 Foot long ; for Fields and Woods, a Chain, which 
 from its contriver is ufually called Gunter’s Chain, 
 and is in length 66 Foot or 4 Poles, confifting of 
 100 Links, each containing 7 Inches and +o 5 
 and a Rod, called an Offset-Staff, whole length is 
 equal to <1, part of the Chain, that is, 10 Links, or’ 
 6 Foot 7 Inches and 2,, tho’ fometimes this Rod is 
 15 Links in length, or 9 Foot 10 Inches and +>. 
 
 The Wheel is ufed with moft advantage in mea- 
 furing of Roads. 
 
 The Inftruments ufed for taking the Pofitions of 
 lines are of two kinds, 
 
 With fome we take the Pofition of a line, by 
 the Angle which that line makes with the Meridian, 
 ufing a Box and Needle ; as with the Z. heodolite, the 
 
 Semi-Circle, the Circumferentor, the Plain-Table, the 
 Perambulator, the Perador, 8c. and this is ufually 
 called the Bearing of the Line. 
 
 With others we take the pofition by the angle 
 that the line makes with any other given line in po- 
 fition; as with the limb of the Tbeodolite, the ae 
 
 o 
 
 SS ee ae nears : : : re B= Re eS. ee ee oe 
 ie a ome - a pe a noes = aera new eeoS— = <5 = cs - = = = Saree as < = ¢ 
 
 is ie ae ols oe es = 
 oT x z . Lr. 
 o el lg l glel Paty yy gr Leet 
 
 rt 
 ~— 
 
 Seite 
 
 Stee oe swore 
 rer rs 
 
 
 
 ba 
 
 — 
 
 
 
 
 

 
 (12 ) 
 
 of the Semicircle, the frame of the Plain-Table, the 
 
 Bevel, the Chain, or Rods. 
 
 All other inftruments either aed from thefe only 
 in their names, or elfe are contained i in them. = 
 
 But with fome of thefe inftruments, very conve-~ 
 niently we take the pofition in both cafes, at one 
 obfervation ; as with the Theodolite, the Os 
 or i.e Plain Table, 
 
 With fome of thefe inftruments we take the ans” 
 gle itfelf, as with the Bevel, or with the Plain Table 
 
 cover'd with a fheet of paper ; and with others, we 
 
 exprefs the relative quantity of that angle by num- 
 
 bers. So when we ufe the chain, we exprefs the 
 
 angle by Sextants, Links, and tenth parts of a 
 Link ; when we ufe Rods, we exprefs it by Sextants, 
 and centefimal parts of a rod; and when we ufe 
 
 other inftruments, we exprefs the angles by de-s 
 
 erees and minutes, 
 
 We may alfo obferve, that of Theodolites and Semi=. 
 circles there are various kinds ; in fome the Box and 
 Needle is fix’d to the Plate, in others to the Indexes © 
 
 And the working with each of thefe varies according 
 to the manner of their Numbering, 
 
 As for Roads, the Wheel with its Indices, fhew-' 
 
 ing the diftance, and its box and needle with fights 
 
 ni 
 
 {hewing its bearing or pofition in refpect of the Me-) 
 
 ridian, is an inftrument fpeedy and fufficiently exact : 
 
 provided we reject the breadth of the road, and’ 
 
 only regard the bearing and lengthy © me 
 
 Lali 
 
 
 

 
 
 
 (32 ) 
 
 Laftly, Inftruments for plotting, are a feale deci- 
 mally divided the whole length, clofe to both the 
 edges ; and at every tenth divifion numbered 
 0, 1, 25 3, 4, &c. denoting Chains ; the. Number- 
 
 ing fo ordered that we may counc either from the 
 
 Right to the Left, or from the Left to the Right ; 
 and a Protraétor always to be divided, numbered, 
 and fitced according to your inftrument, 
 
 Thus, all Circumferentors (either abfolutely fuch, or 
 only ufed as fuch, wz, when contained in the Theo- 
 dolite, Semicircle, or Plain Table) \et the numbers in 
 the Protraéor increafe contrary to thofe in the box; 
 but when the box and needle takes the bearing, as 
 the Peraéior or Perambulator doth, the nurnbers of 
 the Protraéor mutt increafe as thofe in the box. 
 
 ind for khblimbs of all 7. heodolites, Semicireles, and 
 
 Pilin Toblés. “if ‘the. citcuit be made eet te 
 
 contrary 
 
 ‘the numbers on the limb, thenumbers of the Pro- 
 
 traffor moft conveniently increafe the) Tne 
 
 way with the numbers on the limb of the inftru- » 
 ‘ment, and this fuppofing the eye in the center. 
 
 
 
 SECT. 
 
 ie 
 uc 
 i H 
 Hi 
 4 la 
 i tae 
 | ae 
 
 
 
eee 
 
 
 
 SHE SAN Gis EN” > 
 
 To obferve the Pofition of a Line by any of the preceding 
 Inftruments. ‘ 
 
 I. By the Circumferentor. 
 
 HE Box of the Circumferentor is divided into 
 360 degrees, and numbered in 4 quarters, 
 from the North and South both to the Eaft and 
 - Weft, by the figures 10, 20, 30, 40, 50, 60, 70, ._ 
 x 80, 90; but thefe divifions are alfo numbered from 
 the North towards the Eaft or Welt, ali round, till 
 they end at the North again ; by the figures ro, 20, 
 30, 40, 50, 60, 70, 80, 90, 100, and fo onto 360. 
 _ Of thefe two ways of numbering, the latter is pro-. 
 perly the Circumferentor, and the former the tra-— 
 verfing Quadrants or Quarters. | 
 
 Now, if it be required to obferve the bearing of 
 the line AB (#7g. 19.) the Inftrument ftanding at 
 A; the Flower-de-luce in the Box being towards 
 you, direct the Sights to B ; and the South end of 
 the Needle will point at 207 Degrees in the Circum- 
 ferentor, and at S. W. 27, in the traverfing Qua- 
 drants, 
 
 And if you were going round the Field, and fo 
 next to obferve the bearing of the Line BC; at B 
 turn the Index about, the Flower-de-luce being to- 
 
 wards you, till thro’ the Sights you fee the hair cut 
 “€: Then will the South end of the Needle point at 
 Illy 
 
 
 

 
 311, in the Circumferentor, (which is the bearing al- 
 ways counted from the North, and in thefe Examples 
 from the North to the Eaftward) and at S:; E, 69 in 
 the traverfing Quadrants, which is the bearing al- 
 ways counted trom the North or South towards the 
 Eaft or Weft. Here we may note, that the bear- 
 ing taken with the Circum/ferentor may be any nume 
 ber of degrees not exceeding 360, but that with 
 the traverfing Quadrants never exceeds ninety de- 
 grees. apt be 
 When you fufpect the Needle does not play well ; 
 direct the Index to your mark, and note, ina wafte 
 ‘piece of paper, the degrees pointed at by the 
 Needle ; then with a clean Knife, or a Key, or any 
 other polifhed bit of Steel, which has touched a 
 Loadftone, move the Needle, by applying it to the 
 Box, and when it hath fettled again, examine what 
 degree it then points at, your Index being ftill di- 
 rected to the preceding mark ; and if the decrees 
 -are the fame, they may be entered into the Field- 
 Book ; but if not, the Cap and Pin mutt be cleanfed 
 ‘with fome brown paper and a little Puttey or Whit- 
 ing, and thereby freed of fuch duft or dampnefs as 
 ‘hath gotten to it; if, after all, the Needle doth not 
 play freely, fcrew in a new Pin, or ufe another 
 Needle, or do both. Thefe Neceffaries every Sur- 
 veyor ought to have in his pocket while he is in the 
 Field. | 
 If you fufpect an error in the bearing of any 
 line already taken, arifing from the Needle’s being 
 acted on by fome hidden Magnetic power, or from 
 your own miftake in obferving the degrees pointed 
 at; the doubt may be cleared, and the error cor- 
 rected at the next ftation ; thus, 
 
 Having come to B (fg. 19.) the Flower-de-luce 
 being from you, look back to A, and then will the’ 
 South end of the Needle point at 207 degrees in 
 : : the 
 
 
 

 
 ( 16 s 
 the Céeuailedvur me at S. W. 27 degrées in: the 
 traverfing quadrants; juft as it did at A. | 
 
 Laftly, if you have no reafon to fufpect ‘hie 
 Needle, and it is moft convenient to plot by it, the 
 fpeedictt way is to place the inftrument only at every 
 other Angle, and there to take the ae: of the 
 
 two lines which form that angle. 
 
 So, if you would obferve the bearings of the 
 lines of Fig. 19. firft place the inflrument at B, and 
 with the Flower-de-luce from you, direct the ‘fights 
 back to A, fo the South end of the Needle will 
 point at 207 degrees in the Circumferentor, and at 
 S. W. 27 degrees in the traverfing quadrants, 
 which is the bearing of AB; then with the Flower- 
 de-luce next you, direct the fights to C, fo the ° 
 South end of the Needle will point at 121 degrees 
 in the Circumferentor, and at S, E. 69 degrees in 
 the traverfing quadrants, which is the bearing of 
 BC. 
 
 Now place the Inftrument at D, the F losbiule 
 luce being from you, direct the fights back to C, fo 
 the South end of the Needle will point at 44 deg. 
 30 Min. in the Circumferentor, and atN. E. 44 deg. 
 30 Min, in the traverfing quadrants, which is the 
 bearing of CD; and dire¢ting the fights to E, the 
 Flower-de-luce being towards you, the South end 
 of the Needle will point at 102 Degrees 15 Minutes 
 in the Circumferentor, and at S. E. 47 Degrees 45 
 Minutes in the traverfing Quadrants. 
 
 In like manner work at F, €e. always keeping: 
 the Flower-de-luce from you when you look back- 
 wards, and towards you when you look forwards; 
 fo will the South end of the Needle point at . the 
 Degrees of the Bearing in both Cafes, | 
 
 To: 
 
 
 

 
 
 
 
 Be pe a whofe ae is takers » te 
 a © 4 Circumferentor. 
 
 : iR ST, draw lines parallel to one another quite 
 tl ro" the pon ag draught, at diftances not ex- 
 
 pa tof tieioreisctor on A, the bint given reprefent- 
 d ing the ftation A in the field, and, by help of 
 divifions continued beyond the ends of the di- 
 ster of the Protraéior, lay the diameter parallel 
 to thofe north and fouth lines; and if the Pro- 
 tractor be only a Semicircle, lay the beginning of the 
 numbering northwards, when the degrees are 
 fewer than 180, but Recarts when ‘more: The 
 Protratior being thus placed, make a mark clofe ta 
 the limb againft 207, the degrees of the bearing, 
 and thro’ it draw the line AB; and fo will AB have 
 
 a bearing like to that, which you obferved the line 
 | ABto have inthe field. In like manner you may 
 lay down the bearing of any other line, as BC; if 
 you obferve to lay the beginning of the numbering 
 northwards, when the degrees are lefs than 180, 
 and fouthwards when more: Butif the Protraéor be 
 a whole circle, there will be no ,occafion for turning 
 
 the beginning of the numbers, which may always be 
 _ northwards, 
 
 And if you would lay down the bearing of any 
 line AB, Fig. 19. from any affigned point A, with 
 the traverfing quadrants ; after you have drawn 
 north and fouth lines as before, the north being 
 upwards, write eaft onthe right hand fide of the 
 map, and weft on the left, Now lay the center 
 wf the Protraéor and diameter as before fhewn ; 
 fave that inftead of obferving the number of the 
 degrees, you turn the limb ‘of the Protraffor catt- 
 
 C ward, 
 
 
 
 
 
 
 

 
 Il. To obferve with a Vheodolite, both by Be Linb, 3 4 
 
 “wards you when the fixed fi ights are directed, and 
 
 
 
 oe ay 18 )- a 
 ward, when the bearing is N. Re or S, E. and wel ae 
 ward, when it is N. W. or S.-W § 3 (a 
 
 The Protractor being thus placed, “aha. S.W. 3 
 27. make a mark, and thro’ it draw the line AB, — 
 and {o will AB have a bearing like to that which ~ 
 AB was obferved to havein the field. In like man- 
 ner you may lay down the bearing of any ac a 
 line. c. 
 
 oy : 
 ee ee een 
 . nite oa 
 
 and by the Box and Needle. 
 
 BEFORE you engage in a furvey, you ought to 
 confider the numbering of your inftrument ; 
 thus, when the eye is conceived to be placed in the 
 center, confider whether the numbers increafe from. 
 the left to the right ; or from the right to the 
 left; or, according to the farmer’s familiar phrafe, 
 whether the numbers increafe with or againtt the 
 fun’s motion, a 
 And then obferve, that with a 7, beodolite, shot 
 box is fixed to the plate, the circuit-is moft con- 
 veniently made with the increafing of the numbers; 
 and the fixed fights fhall always be direéted to. the 
 next ftation, and the index to the laft. But 
 when the box is fixed to the index, ’tis beft to go — 
 round contrary to the order of the numbers; and ~ 
 then the fixed fights are to be direéted to the laft 
 ftation, and the index to the next, 
 And if the beginning of the degrees are kept to- 
 
 the Flower-de-luce towards you when the index is 
 direcicd ; the degres cut by the end of the index 
 which is next you, are thofe which meafure the an- 
 gle ; and the degrees pointed at in the box. by the 
 fouth end of the needle, give the bearing of the 
 next length. And this bearing will be, in all re- 
 fpects, the fame with that taken by the Circumferene 
 
 tors 
 

 
 ee, 7 eat de tg 5 
 | ; tor i shoved that the box be divided and ere 
 : e that - of the Circumferentor, x 
 This double obfervation is of great ute to the 
 urve eyor ; for hereby he may either plot by the an- 
 gle, or the bearing, or by both, as he fhall find 
 ~ moft convenient ; and alfo, may prove his obfervae 
 tion before he moves the inftrument. For, of the 
 _ numbers expreffing the bearing of the lines form- 
 ‘ing any angle, if the leffer be fubtracted from the 
 greater, and the remainder be increafed by 180 de- 
 E43 _ grees when lefs than 180, or, if greater than 180, 
 _ is diminifhed by 180; the refult in either cafe will 
 _ Sive the angle itfelf, or its fupplement to 360 de- 
 ee erees: 
 as When a Theedolite 1s aed with a box fixed to the 
 plate, and the numbersin the box increafe the fame _ 
 way with the numbers on the plate; or, ° which 
 comes to the fame, with the box fixed to the index, 
 and the numbers therein increafe the contrary way 
 with the numbers on. the plate (moft Theodolites be- 
 ing made one of thefe ways, or fhould be fo to be 
 moft convenient) ; then a Protractor being numbered 
 contrary to the numbers in the box, will be fitted 
 to lay down the plan, either according tothe angles. 
 taken by the limb, or by the bearing taken with 
 the needle, or by both together, in order to prove 
 the truth of éach other: And then alfo may the 
 truth of the angle or bearing be proved, before 
 the inftrument is moved from the ftation by either 
 of the two following rules. 
 
 If to the prefent bearing be added 180 ene? 
 and from the fum you fubtraét the laft bearing 
 then the remainder will be the prefent angle. 
 
 And if to the prefent angle you add the laft bear | 
 ing, and fromthe fum fabtrack 180; then will the 
 
 remainder will be the prefent bearing. 
 
 
 
 
 Bl 
 
 ae 
 a 
 
 
 
 
 
 
 C2 But 
 
 
 

 
 | (20) a 
 But if the degrees to be fubtraéted are more than 
 thofe from which they are to be fubtra&ted ; the lat- 
 ter muft be increafed by 360, and then fubtract. — 4 
 And if the remainder be more than 360, then — 
 abate 360, and the refult gives the degrees re- 
 quired. ih eae 
 So, with a Theodolite that hath the box fixed to — 
 the index, and the eye being conceived inthe cen- — 
 ter, the numbers on the plate increafe from the left _ 
 to the right, but thofe in the box the contrary way, 
 and fo moft proper'to work againft the fun: If you 
 would take the bearings of the lines of Fig, 19. be- 
 ginning from any affigned angle, fuppofe A; then — 
 your inftrument being planted at A, direct theindex 
 to the next ftation at B, and the fouth end of the 
 needle will point at 207 degrees in the Circum- 
 ferentor, And for the following angles and bearings, 
 when the | 
 
 B i ie Al 
 
 Be ts [B 
 
 inftrument is} D{ direét the fix’d JC 
 planted at } E fightsta )Df¢ 
 
 F E 
 G F J. 
 C+ 
 
 2; ; D 
 
 and there {crew the inftrument faft; } E 
 a then direct the index to nN : 
 
 A 
 
 ‘ 
 o & 
 $4. 00 
 
 and the end of the index next your | 113. 30 
 ~ eye will cut on the limb the J237- 45 
 
 ig PRM te rea, SPARS 49» 35 
 | angles ae es = meeps 102, 40 
 
 
 

 
 
 
 
 
 
 
 asin the Circumferentor, point at 
 oo. es 
 
 
 
 oh. ae 308. 30 
 
 And with a Theodolite, that hath the box feed to 
 the index, and the numbers of the plate contrary to 
  thofe of the box, while the eye is conceived placed 
 _ in the center, increafe from the right to the left, 
 and fo moft proper to work according to the fun’s 
 _ motion ; if you would takethe angles and the bear- 
 be: sl of the lines of Fig. 19. and begin from any 
 __affigned angle, fuppofe A; then your inftrument 
 being planted at A, direct the index to the next fta- 
 tion G, and the fouth end of the needle will point 
 at 231° 30 in the Circumferentor. And for all the 
 following angles and bearings, when the 
 
 ak AG A 
 
 ; , 23 oe eae G 
 
 inftrument is} E { direct the fix’d JF 
 
 ; planted at ) D fights to E 
 
 { é C D 
 B Cr 
 
 F 
 
 : E 
 
 and there fcrew the inftrument faft ; } D 
 
 then direct the index to : 
 
 A 
 
 and the End of the index next the} 1°2- 40 
 eye will cut on the limb the an-2 49> 35 
 gle = 64 = = = ~ = =a a 2.37- 4S 
 
 a = is 4 Il3. 30 
 
 Cz and 
 
 
 
Tag ee: 
 
 ( 22) 
 
 3B 
 30 +, ‘ Pe 
 Silo ae 
 450 
 30 
 eg 
 
 and the fouth end of the needle, as in} 
 the Circumferentor, will point to the a 
 bearing - + - 2 See 
 
 
 
 
 
 But with a Theodolite that hath the soak fixed to. ‘ 
 the plate, and the numbers on the plate as well as | 
 thofe in the box (the eye being placed in the center) 
 
 ‘increafe from the right to the left; and therefore 
 moft proper to work contrary to the fun’s motion ; 
 if you would take the angles and the bearings of 
 the lines of Fig. 19. and begin at an affigned angle 
 A; then your inftrument being planted at A, di-— 
 rect the fixed fights to B, and the fouth end of the. 
 needle will point at 207° 00, as in the Circumferen- 
 tor, and as in the firft example. And for all the’ 
 following angles and bearings, when the inftru- 
 
 B meky oo ©: 
 
 C fdireé&t the — 2 
 
 ment is planted at fixed fights? F 
 F to 
 G 
 
 G 
 A 
 Ax 
 3 aiee 
 then {crew the inftrument faft, and direét the }C 
 
 Index to = a e a Sil it 
 | F 
 
 = 
 
 84. 00 
 
 113. 30] 
 
 fo will the end of the index next the} 237. 45 { 
 eye cut on the limb the angle 49+ 35 
 } 102. 40 
 234, 00 
 
Le} 
 
 | : eae III. 
 eas ae of the needle, 2 44. 
 he Circumferentor, will point at.71°?: 
 
 — i) queen 331. 
 | | 25 4. 
 - 308. 
 
 
 
 
 
 
 
 
 
 -: the sp ae the numbers on the plate, as well as 
 hofe n the box, the eye placed in the center, 
 ncreafe from the left to the right, and therefore 
 sf moft | proper to work according to the fun’s motion ; 
 if you would take the angles and the bearings of 
 | the lines Fig, 19. and begin at an affigned angle 
 vat A, direct the fixed fights to G, and the fouth 
 end ‘of the needle will point at 231° 30 as in the fe- 
 cond example, And for all the following angles 
 _and bearings, when 
 
 Bf 
 . 
 : 
 
 tay 
 
 ee Suh er te: 4 
 yes’: the inftrument is 
 planted at 
 
 _direét the fixed 
 fights to 
 
 wWOUnZMA 
 
 then fcrew the inftrument faft, and teas 
 me the index to... - ie 2 : 2 
 
 _ —_ 
 
 QuMAOarrway 
 
 and fo will the end of the index next ) 49. 356 
 | the eye cut on the limb, the angle 237+ 45 
 
 os C4 and 
 
 
 

 
 
 
 
 
 ( 24) | 
 
 
 
 
 and the fouth end of the needle, as in\2 
 © the Circumferentor, will point at the 
 bearings = - - - Ba 
 
 both as in the fecond example. be 
 
 With either of thefe four ‘a(traknaHes ‘the angles — 
 and the bearings of the Lines are taken, at once fet- 
 ting the index, as eafily and expeditioufly as the 
 angle itfelf only ; which evidently appears from the 
 four preceding examples. And. the truth of thefe © 
 obfervations may be readily proved, by either of ae 
 rules already laid down. 
 
 For, the inftrument being planted at B in fe 
 firft and third examples, if to 111°00' the bearing 
 there taken, you add. 180° oo’ and from the fum > 
 291° O0', take the laft bearing 207° oo, there will 
 remain 84° oo, which gives the angle taken at Bee 
 exactly as there obferved ; and proves the angle and 
 thefe two bearings to have been truly obferved. 
 
 In like manner, the inftrument being planted at 
 C, in the fame examples; if to the bearing there 
 taken, 44° 30’, you add 180° oo’, and from the fum 
 224° 30, you fubtract 111° 00, the bearing taken 
 at the Jaft ftation ; the remainder 113° 30! gives the 
 angle at C exactly as it was there obferved ;, which 
 proves that the angle, and alfo the laft and prefent 
 bearings are truly obferved. 
 
 Alfo the inftrument being planted at D ; if to the 
 bearing. there taken 102°15,, youadd 180° oo’, and 
 from. the fum 282° 15°, take 44° 30! the laft bear- 
 ing; ‘the remainder 23%7° 45! gives the angle at D, | 
 as there obferved; . 
 
 But the inftrument being planted at BE, if to the © 
 bearing there taken, 331° 50 you add 180° 00" 
 and from the fum 511? sa! you fubtract 102° 15, 
 
 - the 
 

 
 
 
 
 
 
 
 
 
 
 ue. FES | 
 bearing ; the remainder 409° 35’ leffen’d by 
 pecaufe greater than 360, gives 49° 35’, the 
 {, And fo of all the reft. | 
 
 in like manner may the angles and bearings 
 ompared in the fecond and fourth examples. | 
 ir the angles and bearings may be compared by 
 the fecond rule thus: The Inftrument being planted 
 at B, if to 84° oo’, the prefent angle, youadd 207° 
 30", the laft bearing, and from the fum 291° 00’ you 
 take 480° 00’, the remainder 111° Oo, gives the 
 prefent bearing, as obferved. 
 _ The angles and bearings being truly taken, it 
 remains to fhew how ~ 
 
 _ Lo plott, and therein to difcover and correé an error 
 | before it is communicated to the following part of tbe 
 eS ead) 
 Havre provided yourfelf with a Protractor, whofe 
 “ numbers increafe contrary to thofe in the box, 
 draw acrofs your defigned draught parallel lines, as 
 in plotting obfervations taken with the Circumfe- 
 venior. , 
 Then having chofe a convenient point to repre- 
 fent the firft flation, as at A, from thence, working 
 by the firft or third examples, lay down the bear- 
 ing 207° 00’, and draw AB, as fhewn in plotting 
 from the Circumferentor. On the point B lay the 
 center of the Protractor, and its diameter on the 
 line AB produced both ways, if neceffary, fo that 
 the beginning of the degrees may be towards the 
 laft ftation, if the angle be lefs than 180°, but the 
 contrary way, if greater ; and clofe to the edge of 
 the Protractor make a mark againft 84° oo’, the 
 degrees of the angle B, and draw BC, ‘Turn the 
 Protractor about on its center, till the diameter be 
 parallel} to the meridians, the beginning of the de- 
 grees being towards the north, when the abitads : 
 2 efs 
 
 
 

 
 
 
 
 
 
 
 
 
 (au om 
 lefs than 180° ; but contrarywife when more $ ah 
 if the line BC ras the bearing 111° -oo' on the ed 
 of the Protractor, that line is ‘truly laid down ; b 
 not fo, ifit cutany where elfe, 
 
 But working according to the fecond Bnd fourth 
 examples, lay down the bearing 231° 30’, and draw 
 AG: On the point G lay the center of the Protrac« 
 tor, as before fhewn, its diameter coinciding, with 
 the line AG, and mark off the angle G, 234°0, — 
 
 draw GF: Turn the Protractor, as before: andtie we 
 
 FG cut 285° 30’ on the Protracior’s edge, the line a 
 is truly laid down. oe 
 Inlike manner, may any other angle be eased om 
 and if found erroneous, the error may be corrected, 
 before it is communicated to the following yoke of ; 
 the work. . 
 
 And we may obferve, that, if the plot be laid 
 down by the bearings of the lines, thofe bearings 
 may be examined by meafuring the angles as foon 
 as plotted. . 
 
 Though this method fufficiently recommends — 
 itfelf, both in refpect of difpatch as well as accuracy 5 _ 
 I do not expect it will be practifed by any but the — 
 unprejudiced. For he who hath furveyed much 
 land with a Circumferentor alone, or with a Semicircle 
 or Theodolite, without a needles or with any other 
 inftrument, that doth not aftord a double obferva- 
 tion; he I fay, hath not provided a check to his 
 frailty, and will fcarce forfake his old way, becaufe’ 
 he will not accufe himfelf. 
 
 There are two other ways to ufe thefe Theodolites, 
 each equally exact with the former, but not fo ex- 
 peditious. One way is to take the bearing with the 
 traverfing quadrants ; the other is to take the bear- 
 ing with “the degrees on the limb, But the angle i 1S 
 always taken as above. 
 
 If you would ufe the traverfing quadrants, thier 
 the obferving, the plotting, and the proof in plot 
 
 anes 
 

 
 
 
 
 
 Es (67) 
 ting, are all as eafily, fpeedily, and exactly done as 
 by the | irft method ; but the proof of the obferva- 
 
 im ner, is neither fo eafily performed, nor fo eafily 
 
 reduced to one fingle rule. But the perfon who is 
 lve to plot by the traverfing quadrants, had » 
 
 9 ft take the obfervation both by the Quadrants and 
 
 Be Pioting by the eine eae 
 __- Laftly, Vf you would take the direction or bearing 
 * Be the divifions on the limb with a Theodolite, whole 
 _ Box is fixed to the plate; then (having taken the 
 angle as before fhewn) turn the inftrument about till 
 the north end of the needle point .at 360 degrees in 
 the box, and fcrew it faft ; direct the teed to the 
 next ftation, and the end next you will give on the 
 limb the direétion in sisal and minutes, as in the 
 _ fermer examples. 
 But with a Theodolite, whofe box is fixed to the 
 index, if you would take the direction by the di- 
 _ vifions on the limb ; then (after the angle is taken, 
 as before fhewn) direét the fixed fights to the next 
 
 ftation, fcrew the inftrument faft, and turn the in- - 
 
 dex about till the north end of the needle point at 
 360 degrees in the box; and then will the end of 
 the index neareft to the fouth end of the needle cut 
 on the limb the direction in degrees and minutes. 
 
 ~ 
 
 But .the Protractor to lay this bearing down, mutt) 
 
 be numbred contrary to the limb on the inftru- 
 TMB 024° 
 
 ae field, though equally true with the. 
 
 hw 
 
 The great advantage ufually propofed by this laft . 
 
 method, is, that the degrees on the limb are larger 
 and more diftinétly cut, and confequently more 
 nearly eftimated than thofe in the box. But con- 
 fider that you can no better bring the needle to polit 
 at any one degree, than you can eftimate its pofition 
 
 in pany other degree ; and that fince we ufe the piss 
 a 
 
 + nat nom 
 —_ —o a 
 
 ie, 
 ital 
 ie 
 Ff 
 
 yt 
 
 
 
( 28 ) | 
 all the objections made in one method are incident to 
 the other ; and then you may eafily conclude, that 
 the advaniage 1s only imaginary. | 
 
 Befides, here we are obliged to take two obferva- 
 tions, either of which take up as much time as the : 
 obfervation ufed in the former method ; seiidh rene | 
 
 . ders it not fo fit for a practitioner. 3 ‘a 
 
 Of the ufe of thefe Theodolites, I have one thing 
 more to advertife, viz. To meafure and caft up the. 
 content of one ‘large fingle Wood or Common, 
 where there are fome fcores of angles to be takens 
 the fafeft way is to caft, without plotting, by help 
 of the needle. And in this cafe I would take the 
 direCtions both with the Civcumferentor and the tra- 
 verfing Quadrants ; andin the field prove the direc- 
 tions taken with the Circumferentor by the angles 
 taken by the limb ; and then, {till in the field, prove 
 both lengths and directions, in calculating a traverfe, 
 by help of a Traverfe Table ; and laftly, from this  ~ 
 traverfe (at leifure) deduce the true content. . 
 
 But the Traverfe Tables that are naw extant, are’ 
 but fpecimens of thofe which are fit for ufe; inftru- 
 ments are not fufficiently exact, and trigonometrical 
 operations too laborious, and therefore this way of | 
 computation muft be deferred, till fome perfon who 
 hath leifture and patience to ferve the world, imcalculat- 
 ing fuch a table, is refolved to do it *. 
 
 Of any one of the four 7 beodolites, which have 
 the numbers in the box contrary to thofe Theedolites: 
 before defcribed, one or more inconvenience will al- 
 ways arife, ufe which of the three forementioned 
 methods you pleafe. 
 
 It is true, the angle taken by the limb is per-: 
 formed as fhewn in the preceding rules but fince: 
 
 
 
 * Here the author promifes if he can procure fuch a 
 table, as he hoped to do, to publifh it with its ufes in Prae- 
 tical Surveying and Navigation: But he being long fince 
 dead, that defign has dropped. 
 
 1} : it 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 ee ees 
 not fafe to work by the limb only, if you ufe the 
 ircumferentor, as fhewn in the firft rule, you mutt 
 ner fubtract the direction from 360 degrees, and 
 the remainder inftead. of the direction pointed 
 by the needle ; or elfe ufe two Protractors, which 
 be troublefome, and alfo apt to caufe miftakes 
 ufing the one for the other. 
 
 Dead: eee" x 
 ‘IF youufe the ¢raverfing Quadrants only, then in- 
 _ deed the ufe is in all refpects the fame with the pre- 
 _ ceding ones; but thefe, as I have already thewn, 
 are not fo expeditious as, nor more exact than, the 
 method firft laid down. | 
 
 _ If you will take the direétion by the limb, and ftill 
 make one Protractor plot both obfervations, you 
 muft direct your inftrument twice, whereas by the 
 firft method laid down, it might be done at ance. 
 
 : 
 
 | Lafily, Of Theodolites thofe are beft which have 
 telefcopes with plain fights on them, and fo con- 
 trived that the furveyor may at any time adjuft any 
 {mall accident, without coming to a workman; and 
 that both of them may be elevated or deprefied at 
 leaft ten degrees ; one of thefe telefcopes inftead of 
 the fixed fights, the other inftead of the moveable 
 ones, and as long a needle as will play well, with 
 other the like conveniences, fufficiently known to a 
 Akilful inftrument-maker. 
 
 HI. 
 
 
 

 
 ( 30) 
 
 Ill. To obferve with a Sevnivircll ‘that bath a Bas 
 
 and Needle, ee, i 
 
 Semicircle is juft half the TZ, Geodtlite a ibannicl ing 
 of juft as many varieties ; it is numbred on the 4 
 
 limb to 180 degrees, and in an arch concentric to 
 this is denominated by the numbers 190, 200, 2403. 
 &c. to 360 ftanding under the former numbers 10, 
 20, 80; Coro 1s ule, in all refpeéts (both to the 
 plate and box) is the fame with the Theodolite ; fave 
 
 in this, that when the end of the index next the eye, _ q 
 
 falls off the plate, the degrees cut on the limb are to 
 be taken from the further part of the index reckoned 
 
 among the divifions of the inner circle, and will be oe 
 
 always more than 180 degrees. 
 
 There are other ways of numbering and dividing 
 (and perhaps without a box and needle) ufed in thefe 
 
 inftruments ; but they are not worth notice. 
 / 
 
 IV. Of the Peratior. 
 
 TH FE, Peractor is the fame with part of that 7 heo- 
 
 dolite, whofe box is fixed to the plate; and the 
 directions given for the Theodolite in page 27, will 
 ferve for this, 
 
 
 
 
 ere 
 
 “a 
 

 
 
 
 
 SHE E Bivihions’« on ah limb bP the Plain Table, 
 with its box and needle, being like thofe of the 
 eodolite, or modern Circumferentor ; ; if the 360 de- 
 rees on the limb be upwards, and the box and 
 needle ferewed to the fide of the table; it performs, 
 in all refpeéts, the ufe of the Theodolite, whofe box 
 is fixed to the plate, For lay the edge of the index 
 on the divifion numbered 360, and to that numbered 
 _ 180; and turn the whole inftrument about, till 
 [. 
 
 
 
 “through the’ fights you fee the next ftation (the 360 
 
 being: “towards: you, as fhewn with the Tbeodolite) 
 
 and ‘there ferew it faft; ‘then turn the index about 
 
 upon the center, till you fee the laft ftation, and fo 
  ewill the end of theindex next you cut the degrees of 
 _ ‘the angle, and the fouth end of the needle will give - 
 ee ioe direétion or bearing. 
 
 ~ But if the box be fcréwed to the nde, it in like 
 manner becomes a Theodolite, with a box fixed to 
 the index. 
 
 _ If the box and needle be {crewed to the ftaff, it is 
 a Circumferentor, 
 
 _ If the box be fcrewed to the table, and that fide 
 of the frame be upwards, which is divided into four 
 nineties, it is the Perambulator. 
 
 If that fide of the frame is upwards, which hath 
 only the 180 degrees of the femicircle numbered on 
 it, then it is a femicircle, either with the box to the 
 plate or not, according as the box is fixed to the 
 table or to the index. 
 
 And what hath been already faid of thefe inftru- 
 Mments may ferve for directions, to ufe the plain table 
 thefe feveral ways, and need not be again repeated 
 here, | 
 And 
 
 
 
(32) 
 
 properly be called Panorganon, or the tinlyetlall ins: - 
 {trument, in refpect of land furveying, Poa 
 
 There are two fmall holes towards the middle one . 
 the board, which ferve as centres to the divifions on 4 
 the limb ; the one for thofe when the table is ufed as 
 a femicircle, the other for the degrees numbered as 
 in a Theodolite: In thefe holes the protracting pin is 
 to be fet while the floped edge of the index flides 
 againft it, and cuts the divifions on the frame. 
 Now if thefe holes were conical, and were the con=- _ 
 tinuations of a conical hole in the index, {fo that the 
 index could be fixed to them by a conical pin paffing 
 
 thro? its hole, and the central one, into which the 
 pin icrewed, the fiducial or floped edge of the index 
 being made to correfpond with the center of the pin ; 
 alfo if the divifions on the frame be cut as accurately 
 as on the limb of a Zheodolite ; and the wood would 
 neither fhrink nor {well any more than brafs; and a 
 telefcope mounted on the fights ; and the back fide 
 of the index brought alfo to a fiducial edge; then 
 the plain table would be a very compleat ins 
 ment. 
 
 It remains to fhew, how to take angles when we 
 ufe the plain table covered with a fheet of paper ; 
 but this hath been fufficiently handled by Mr. Ley- 
 bourn, and almoft all the common writers on Sur- 
 veying ; therefore I fhall content myfelf with laying 
 down a method to correct an error committed be- | 
 fore it is communicated to the following partsof the 
 work, Though I do not any ways doubt but the 
 reader may, by what follows, learn the ufe of this 
 plain inftrument. 
 
 Suppofe you were to draw the plan of the field 
 ALMNQR: (fig. 20.) Draw on the table a line 
 to reprefent AL in the field, and by the fcale lay 
 cown on the plan the length AL was found to be 
 in ‘the field, when you meafured it with a chain, 
 
 Then 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 ( ideale 
 Then p inting the table at EB, lay the index on AL} 
 and oe the whole inftrument about till you feea 
 _ mark fet at A, then {crew it faft, and turn the in- 
 dex : about on Las a centre, till through the fights 
 you fee M, draw LM, and by the fale, give it on 
 the table the fame length you found it to have in 
 
 | dae, by meafuring with the chain, 
 
 Yow in order to examine the length of LM; and 
 fo its pofition in refpect of AL; “plant the inftru- 
 jent at M, lay the index on LM, and by turning 
 
 
 
 
 
 Po he inftrument, direct the fights to L, and dices 
 {crew it faft ; chen direct the index répned about on 
 
 M, towards A in the field, and if the edge does not 
 
 cut the point A in the table, the line LM is falfe, 
 
 either in pofition or length, and therefore muft be 
 
 examined and corrected before you proceed. 
 
 The line LM being truly laid down, plant the 
 inftrument at M, lay the index on LM, and direct 
 the fights to L, by turning round the table, and 
 fcrew the inftrument faft : Now turn the index a- 
 bout on M, till through the fights you fee the hair 
 cut N, by the edge of the index draw a ftrait liney 
 ‘and by your fcale, from M lay the length NM e- 
 
 ~ qual to what you meafured it in the field. 
 
 But to prove whether the line NM is truly laid 
 
 _ down both in pofition and length ; having planted 
 the inftrument at N, and direéted the index laid oa 
 
 _ NM to M, and there fcrewed ‘the inftrument falt.; 
 
 - from N direé&t the index to either of the marks L or 
 _ Ain the field; and if the index then does not acs 
 oniely cut L or A on the table, the line MN is 
 _ falfe, and muft be corrected before you proceed. 
 
 And in like manner through the whole furvey, 
 you may proceed to lay down every line, and ex- 
 
 amine it before you leave it, (provided that you 
 leave all your marks ftanding at the ftations,) by 
 
 ays the index on the latt line, and turning 
 the inftrument about till thro’ the fights you fee the 
 D hair 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 | G4, i 
 hair cut the laft mark ; and then fcrewing the ‘nick 4 
 ‘ment faft ; if you turn the index about on the point — 
 reprefenting the ftation where the inftrument ftands, — 
 till you fee any one of the marks paffed by, except — 
 the laft of all; and if the edge of the index does not — 
 cut on the table: the reprefentative of that point, the. i 
 laft line is not truly laidddown. 
 - But when frem any ftation, fuppofe N, you can- 
 not fee any other mark but M, fet up fome mark Aya 
 from whence you may fee fome of the preceding 
 marks, fuppofe L, as well as M and N; and from — 
 this point a examine the truth of the pofition of Ps . 
 line MN. : 
 Or thus; you may fet up a ia a, any where in — 
 the field, from whence all, or feveral of the angles © 
 may be feen ; then the inftrument being at A, and © 
 the index on AL, fcrew the inftrument faft; and 
 turn the index on A, till youfee a4, and draw Aa, 
 The inftrument being at L, the index on LA, © 
 and the index direéted to A; lec the inftrument be 
 {crewed faft ; turn the index about on L, till thro’ 
 the fights you fee a, draw by the edge of the index - 
 La ; and fo will the point a be determined. a 
 Then the inftrument being at M, the index on © 
 LM, the fights directed to L, and the inftru- 
 ment {crewed faft ; turn the index about on M, till 
 thro’ the fights you fee the mark a in the field: 
 Then if the edge of the index does not cut ain the _ 
 table, the line ‘LM is falfe either in pofition or 
 lencth. Py 
 inililee manners eae being at N, the index om : 
 NM, the fights directed to M, and the inftru- 
 ment fcrewed faft ; turn the index about on N, and 
 direct the fights to the mark a ; and if the edge of 
 the index doth not cut a, on the table, then MN is 
 falfe either in pofition or length. ha 
 Laftly, inftead of a mark fet up as 4, you may 
 afe any remarkable tree, fteeple, &¢. not at too | 
 
 ( 
 it 
 
 erea 
 
 
 

 
 j | (35) 
 ‘great a diftance from you, whether it be in the land | 
 “you are then furveying, or not. 
 
 And when the mark you have laft ufed is at too 
 Fe fo diftance from you, or lies almoft in the fame 
 trait line with that which you are about to lay down ; 
 en ule fome other mark in its ftead. 
 
 
 
 
 
 
 evi Of working with ihe CHAIN, 
 
 G Fe ST, provide a ftaff juft 6 foot 7 hes and 
 = two tenths long, which divide into 10 equal 
 - parts ; and fo will the whole be the length of 10 
 links, and each part the length of one, and 10 times 
 the length of this ftaf, the length “of the whole 
 ~ chain. | 
 ~ With this ftaff examine the length of the chain, 
 and alfo of every 10 links; ftretching it on level 
 ground, to fuch a degree as you defign to ftretch it, 
 in the field work. 
 Before you meafure with it, provide 1o arrowsor =“ 
 final fticks, each about two foot long» and of fuch 
 _ thicknefs, that a man may conveniently grafp 10 of 
 them in one hand; alfo two ftrait ftaves about 5 foot _ 
 long each: The arrows may be made of Ground 
 > Af, a.tough wood and not aptto break ; let them 
 be thod with fharp-pointed iron ferrils ar one end, 
 and have pieces of red rag tied at the other ead, 
 whereby they will be very readily diftinguifhed and 
 _ difcovered when fet down in long grafs or corn. 
 When you are about to meafure with the chain, 
 Jet him that leads it take the 10 arrows and one of 
 the ftaves ; and he that follows it the other ftaff. 
 Then the follower ftanding at the ftation, let him 
 by motions with his hand to the right or to the left, 
 _ as they have before fettled it, direct the leader to 
 a Ee his 5 foot ftaff at the chain’s end in the fame 
 ight line with the ‘lations ; and then let the leader 
 D 2 take 
 
 
 

 
 
 
 
 
 ( 36 Ye : ¥ 
 take up the ftaff, and in its place flicking down one — 
 of the arrows, go on. . 
 
 Now the follower being come to the arrow, take 
 it up, fets his {taff in the hole, and directs the leader 
 to place his flaff as before. 
 
 And then let the leader, ftanding at his fae 
 look back towards the laft ftation, and he will fee ‘ 
 the ftaves and the {tation inone right line, if they _ 
 have directed right. But if they are not inone right 
 
 line, the leader muft direct the follower to place his: : 
 
 ftaff at the chain’s end, in the fame right line with 
 the ftation, and the teaser s ftaff, 
 
 And fo, let each direct the other, till ee two 
 flaves and the two ftations are in one right line ; 
 and then muft the leader put down an arrow inthe ~ 
 place of his ftaff, and go on: And the follower take — 
 up his ftaff and the arrow where he laft ftood, and 
 go after him. 7 
 
 And let them thus proceed till they have meafured 
 to the ftation, or till the leader is nearer the ftation 
 than one chain’s length ; and then will the number 
 of the whole chains meafured, be exprefied by the — 
 number of the arrows pricked down by the leader, 
 and taken up by the follower, which fuppofe 8. ¥ 
 
 Now let the leader go on to the ftation, and there 
 hold the end of the chain, and let the follower ftretch 
 the chain as ufual, and then fee how many links are — 
 contained between the laft arrow and the ftation ; 
 which may be readily counted by help of different. 
 bits of brafs, or curtain rings, or other marks fixed 
 at the end of every tenth link, which links fuppofe 
 to be 47. 
 
 Then enter in your field-book the chains and — 
 finks without any diftin€tion between them, and — 
 they will be 847 ; which imply either 847 links, or 
 -8 chains 47 links. 
 
 But here we are to obferve that the links muft BD 
 ways pofiefs two places 5 as 8 chains and 4 links 
 
 muft 
 
 
 

 
 up 
 
 €3>.) 
 
 | mutt be written ie ; that is 8 chains and 4. links, 
 
 804 links and 8 chains without any links, muft be 
 
 * written 800, implying 8 chains, or 800 links, 
 
 Te is neceflary that the furveyor fhould enquire of — 
 his affiftants at the end of every meafured length, 
 how many arrows each hath; and if the fum of the 
 
 - arrows are not ten, it is evident they have dropt or 
 
 deft behind, thofe that are wanting; and confe- 
 quently the laft length meafured is doubtful, and 
 muft be re-meafured before you proceed, 
 
 _ When you are come to the ftation, if it be con- 
 _ venient to continue the length, let the “follower ftand 
 
 at the laft arrow, and let the leader go on with the 
 
 ‘chain, and fo place his ftaff, that it and the two fta- 
 
 tions are in one right line ; then in the place of the 
 fiaff put down an arrow, and goon; always direét- 
 ing himfelf to place his flaff, and confequently his 
 arrow, by the two ftations, 
 
 When you have continued your length, till you 
 
 have nearly loft fight of the fartheft ftation, fet up 
 
 another ftation-ftaff in the place of the laft arrow, © 
 
 and continue the length by the two neareft ftations. 
 
 But withal take this caution, that it is not fafe to 
 continue lengths very long, when the flations are 
 near one another, 
 
 When your length is very great, having mea-~ 
 fured ten chains, let the leader go on and fet his 
 ‘ftaff down at the eleventh ; ; now let the follower put 
 his ftaff in the place of the leader’s, and give the 
 Jeader nine arrows, and then goon. But obferve 
 “to enter in the field-book thefe ten chains, and 
 never truft to your memory. And if the length 
 confifts of ten chains more, work as before, and en- 
 ter 20 chains, and fo on. 
 
 For a fhife, the furveyor may perform many 
 works with the chain ; but this at beft is both Jabo- 
 rious and tedious, the only inftruments for furveying 
 
 ~ all manner of lands both great and {mall in all cafes, 
 
 D.3 being 
 
 
 

 
 ( 38 ) om 
 being the Theodolites before mentioned; yet left there 
 fhould fometimes be an abfolute neceflity for taking 
 the pofition of a line by the chain when other inftru- — 
 ments are wanting, we have here added the method ~ 
 of taking an angle therewith. . 
 In ordex to do this, provide three round fticks, — 
 very ftrait, and about four or five foot long. And 
 if you were to take any angle as DBC (Fig. 21.) fir 
 place one ftick upright in B, and there hold one end — 
 of the chain, and let your affiftant carry the other — 
 end and another ftick towards C, and direct him to — 
 move fideways, till the ftick held upright at E, be © 
 exactly in the right line BC, at the chain’s end, — 
 where let him leave it. 
 Then let him take the end of the chain and move — 
 towards D, and, as before, direét him to plant the ~ 
 third {tick at the chain’s end upright in the line BD 
 
 at Pe. | : 
 Then meafure the diftance EF in links and deci- — 
 mal parts of a link, if lefs than one chain, and enter 
 them in the field-book : So if the diflance EF were — 
 94 links and 7 tenths of alink, they might be enter’d — 
 thus, o° 947s. denoting o Sextants, 947 Parts ; 
 the fextant ftanding for the chord of fixty degrees, 
 
 In this work great care ought to be taken, that — 
 the fticks be as ftrait as a workman can fhoot them — 
 with a long plane ; and that they are planted either 
 exactly perpendicular, or at Jeaft fo that the fticks 
 planted at B and E, and the mark C may be exaétly 
 in the fame plane, and alfo the fticks B and Fy, and 
 the mark Din another plane. | 
 
 But becaufe it is very difficult to ereét a ftick ex- 
 actly perpendicular, it will be cafier to perform the — 
 Jatter thus; plant the ftick as nearly perpendicular 
 as you can; then move yourfelf backwards towards 
 G, the farther the better, till your eye, the ftick at 
 B, and the mark at C, are all in one ftrait line, — 
 there ftand and direct your affiftant to plant his ftick, 
 
 fo 
 
 salt ey 
 
 oe 
 
 oat 
 
 
 
 
 

 
 veo ) 
 fe that the ftick at B exaétly cover it from the top 
 ~to the bottom. 
 
 But if it fo happen, that you cannot move back-. 
 wards at all towards G; then having planted the 
 flick at B, as upright as you can, let your fecond . 
 _affiftant move forwards towards C, and let him there 
 direct your firft afliftant to plant the ftick at 1a fe 
 _ that it exactly cover the ftick at B, while you direét 
 _ him to place it in a right line with the ftick B and the 
 ~ mark at C; and the like caution mult be ufed in 
 planting the flick F. Neverthelefs it will often hap- 
 pen fo that the mark at D may be a little fhifted, 
 and in this cafe, time and trouble may be a little 
 leffened ; for having planted the ftick at F nearly 
 in a true pofition, move forwards towardsD, and 
 - direct your affiftant to incline the ftick at F, fo that 
 it exaétly cover the ftick at ‘ then returning to By. 
 direct your affiftant at D to place the mark in a right 
 line with the fticks Band F. 
 
 ‘But, fecendly, if the angle DBC is fo great that 
 the line EF be longer than-the chain (as in Fig.-22.) 
 lay out a fextant ; thus while the chain was Jaid 
 from Bto E, fet down an arrow at H 50 links; then 
 let your affittants hold the chain’s ends at H and B, 
 while you with the middle in your hand, move to- 
 wards I and lay both halves ferait ; fet down an ar- 
 row at I, which conftitutes the equilateral triangle 
 HBI; and thereby gives the angle HBI a fex- 
 tant. Now the chain’s end {till held at B,  ftretch 
 it through the point [| to K, whiere alfo fet down an. 
 atrow ; then meafure KF in links and decimal 
 parts of links, which fuppofe to be 76 links and 4 
 tenths; and then fhall be entered. in the field-book 
 2° 764, implying one fextant and 764 parts. 
 
 Tn like manner, if the angle were more than two 
 fextants (as in Fig.23); then n having laid off the fex- 
 tant FBI, let your affiftants hold the ends of the 
 chain at B and I, while you with the middle of the 
 D 4 chain 
 
 
 

 
 
 
 
 
 
 
 
 
 . ° 
 
 ( 40 ) 
 
 chain in your hand fet down an arrow at L, confti- 
 
 tuting the fextant IBL ; and then as before, the 
 chain being ftill held at B, Jay it through L, and at ~ 
 the other end K, fet down an arrow; then mea- ~ 
 fure FK, which fuppofe to be 43 links and 5 tenths, 
 
 and enter in the field-book 2°435, that is, 2 fex- ~~ 
 
 tants and 435 parts. 
 
 If you would continue a ftrait line, fignify it by 
 
 entering in the book 3000 3; that is, 3 fextants. 
 
 If an angle be external, and fo contain more than 
 three fextants (as in Fig, 24); let one affiftant hold 
 one end of the chain at B, and let the other affiftant 
 ftand with the other end of the chain at E, and there 
 hold a ftick, fo that E, B and C, are in the fame © 
 plane as before fhewn ; and let him alfo plant a ftick 
 atF’, fo that the fticks B and F, and the mark Dbe 
 alfo in the fame plane. Then meafure the angle 
 EBF as before, and to it add three fextants, and fo 
 will the fum be the meafure of the external angle 
 CBD. So if the angle GBD be o8 947, then will 
 the external angle CBD be 3° 947. But if the angle 
 GBD be 1° 764, then the external angele CBD will 
 4°764, And ifthe angle GBD be 2° 435, then the 
 external angle CBD will be 5° 485. 
 
 Now to plot any of thefe angles thus taken (fup- 
 pofe that in Fg. 21); chufe fome line divided into 
 4000 equal parts, and with this line as a radius from 
 the center B defcribe an arch ER, and lay thereon 
 from E to F 947 equal parts and draw BD, 
 
 And if youwould plot the angle taken in Fig, 22 3 
 from B with the length of the divided line, defcribe 
 an arch EF’, and lay thereon the length of the divided 
 line from EF, to K, and afterwards 764 parts from K 
 to F, draw the line BFD, and you will conftruct 
 the angle required. | . 
 
 Again, 
 

 
 i 
 7 
 
 (41) 
 
 Again, if you would plot the angle of Fig. 23; 
 then as before, with the length of the divided line, 
 from B defcribe the arch EF, and thereon lay EP, 
 
 _ PK, each equal’ to the radius ; and afterwards lay 
 435 equal parts from K to F, draw BF’; and you 
 _have the angle required, 
 _ And if you would protract an angle greater than 
 - three fextants (as the external angle CBD in Fig. 24); 
 _ firft continue the line CB, then from the angle fub- 
 tract three fextants and make the angle GBD equal 
 to the remainder. 
 
 Angles about gardens or buildings may be taken 
 with rods of 5 and zo foot, and laid down in all re- 
 fpects as with the chain, but are no ways fitting for 
 large plans. _ | 
 
 Ifthe furveyor has only a chain, and having” 
 drawn his plan, would draw thereon a meridian line ; 
 he may do it thus; exaétly at twelve aclock, mark 
 the fhadow of fome upright object, as the corner of 
 a houfe, or fome ftrait tree, or your ftaff fet up- 
 right ; then plot this line on your plan, and it is a 
 meridian line, : 
 
 Or thus; in a night when the Pole-fiar is to be 
 feen, place yourfelf fo, that your eye, the Pole-ftar, 
 and fome upright object, as the corner of a houfe, or 
 the fide of a ftrait tree, be in one {ftrait line; then 
 plot the line from your feet to the upright object, 
 and it will be a meridian line, 
 
 Indeed the Pole-/far moves round the real pole ; 
 but at fo fmall a diftance from it, that in this cafe 
 the variation may be rejected. 
 
 How- 
 
 
 

 
 
 
 
 
 ~ 
 
 (42). 
 
 However, you may obferve that the Pole-ftar is 
 ¢ March and September at 12,) 
 | April and Offober at 2, 
 full north about ! AZayand November at 4, | 
 
 ‘the 20th day of | Fune and December at 6, 
 
 | Fuly and Fanuary at 8, | 
 L Augujft and February at1o J 
 
 a clock either morning or evening ; always increafing ~ 
 
 nearly 2 hours for every month. 
 
 Therefore if the obfervation is made about thefe 
 
 times, the variation will be very inconfiderable. 
 
 Alfo obferve, that 5, 6, or 7 hours before or after 
 thefe times, if the pointers are to the eaftward of the 
 pole, then the variation of the ftar is about 3 
 degrees and a half weftward ; and is then the 
 oreatett. 
 
 But if to the weftward of the pole, the variation ~ 
 
 is about 31 eaftward, and then at the greateft, 
 
 Note, The pointers are the two hinder wheels of 
 the conftellation called Charles’s Wain, which are 
 gbferved to be always in a direct line with the 
 Pole-fiar. 
 
 
 
 Speer. 
 
 
 
 x 
 oa 
 ¥ 
 ae 
 5 
 \ 
 \ 
 A 
 ie 
 
 Se oe at 
 

 
 To cat up the Contents of LAND, with the 
 Method of reducing lrregular Curves ¢o Strait 
 Lines, 
 
 HE contents of any field may be readily caft 
 
 up thus: Take each bafe and perpendicular 
 of every triangle, and each diagonal of every Tra- 
 pexium, in links, efteeming every chain 100 ; inevery 
 Trapezium multiply the fum of the perpendiculars 
 by the diagonal ; and in every fingle triangle, the 
 bafe by the perpendicular; then add the feveral pro- 
 ducts together: Put a point between the fourth and 
 fifth places, and another between the fifth and fixth, 
 reckoning from the right hand; then halve the figures 
 to the left hand of the points, and fo will this half 
 be acres; if an unit remain, that unit is an half 
 acre or two roods; and if the figure between the 
 points be five or more, take five from it and ac- 
 count it another rood. Then, multiply the remain- 
 ing figure o between the points, by 8, and-to the 
 product add the tens to be carried from the fourth 
 figure, and you have the perches. If any perfon is 
 fo curious, as to efteem the decimal parts of the 
 perches, they will be the product made by multi- 
 ~ plying the figures to the right hand of the point by 8. 
 So in figure 25 the operation will be thus. 
 
 313 
 
 
 

 
 
 
 
 
 ( 44 
 
 313=AC; 214=KL; FG=418_ 
 612=DE; 396=HI; ie Pa 
 
 
 
 
 
 
 
 
 
 
 
 925 610 2am 6200 
 725 = BF 500=FM as 
 4625 305000 
 1850 7 
 6475 670625 
 a! 305000 — 
 670625 | 376200 
 
 
 
 13]5|1825 
 AVRYT. 
 Anfwer, 6:3:31 
 
 Here half of 12 gives 6 the acres, and one re- 
 maining is 2 bras ee ; then the 5 between the points 
 gives another rood ; and fo the whole is 6 acres and 
 three roods ; and becaufe there is but one ten to be 
 _ carried from the fourth place, and that after the 5 is 
 taken out of the fifth, there remains nothing, there 
 is but one perch, 
 
 In like manner, if the whole fum of all the 
 
 A. Rie 
 
 171415304 8.2.36 
 
 Products }11]9|2765 (the con-} 5.3. 34 
 be 10/5/4321 ( tent is )5.1.03 
 81413764 4.40.35 
 
 So if the fum of the products be 4117|6354, the 
 content is 20. 3.. 2110832. But this method muft 
 be only ufed when the figure is reduced to triangles 
 and trapeziums, 
 
 It may not be improper, to add in this place, the 
 manner of cafting up fuch fields as confift of many 
 
 {mal} 
 
 
 
 ot - 4 » ee ea, TP eo ae pe = aa - fe 
 x. 5 ae pes Ni a Re oF A a eV ae { “ 
 
 af ERA Bie Rae “> Po aC pear Oe Aen i see ee ee a tinnrces P 
 > o ~ a ae 2 A ei 7 < ss 
 
‘ 
 
 
 
 | — (45) 
 {mall breaks in the hedges ; without reducing them 
 to a multitude of triangles ; thus. 
 Let Fig. 26, be fuch a field; produce NM, one 
 of the longeft fides; then lay the edge of a ftrait 
 : _ tuler from M, one of the angles at the end of NM, | 
 to G the next angle but one ;_ holding the ruler thus 
  faft, take with a pair of compafies the diftance from 
 L to the edge of the ruler, and with this diftance let » 
 one point of the compaffes move gently clofe to the 
 ruler, while the other point traces out a line parallel 
 to it, and croffles NM in Q. Now draw GQ, and 
 it will reduce that fide of the figure, which was 
 ‘bounded by the two lines ML LG, to another 
 bounded by GQ, one fingle line only. 
 
 In like manner QG being produced, and a ruler 
 Jaid from G to BE, carry the diftance of F from the 
 ruler parallel to it, till you crofsQGin K. Then 
 lay a ruler from K to the next point D, and carry 
 the diftance of E from the ruler parallel to it, till 
 you crofs QGin H. Now lay a ruler from H to- 
 the next point C, and carry the diftance of D, the 
 
 ~Jaft point from it, parallel, till you crofs QG in I. 
 Laftly, draw IC, and the fide GC which confifted 
 of the four lines GF, FE, ED, DC, will be reduced 
 to the fide IC, confifting of one line only. And in 
 like manner we might proceed if the lines were never 
 fo many. | 
 - And thus laying a ruler from C to P, draw PO, 
 and in likemanner AQ. So will the ten-fided figure 
 be reduced to a four-fided one, and fo may be caft 
 up by one multiplication only. The practice of 
 this will be rendered vaftly eafy by help of a parallel 
 ruler, | 
 
 Provide a plate of thin brafs in form of an arch of 
 a circle ; near whofe ends let there be drilled fmall 
 holes, through which ftring it with a very fine hair 
 or wire.. Being thus provided ; when a hedge at 
 GC bends in and out in feveral places, and thofe 
 
 4 | bends 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 SSS SS 
 
 \ 
 
 ( 46 ) : 
 bends contain very fmall fpaces, lay the hair over it 
 lengthwife, fo that the quantities thereby cut off 
 from the figure may be equal to thofe added to it; 
 and with your protracting pin, near the ends of the 
 hair, make two marks, through which draw a {trait 
 line ; and fo will this irregular fide be reduced to a 
 reoular one. And here we may obferve that in very 
 {mall bends, we judge better by the eye than we can 
 by the compafies of the equality of the parts taken 
 in and left out. 
 
 But, if hedges confift of large curvatures, chufe 
 
 out fuch points, and fo many of them, that right 
 lines drawn from: point to point, may vary the 
 quantity by fuch parts only as may be rejected. 
 And herein your hair will be a ready affift- 
 ance, 
 
 \ 
 
 SSPE RR bee Lot o4 S 20S SEO ESO Le LOBOS ORIGOLO LUST OOPS TOG OL ORS J 
 oe Cubeeys 
 Of the Laying out, or Dividing of LAND. 
 
 (4 7 HEN any number of acres, roods and 
 ¥ ¥ perches are to be laid out, or meafured off 
 from another field, it is convenient to reduce them 
 to iquare links, which may be done thus: 
 
 
 
 I 40 
 If the roods are? 2$ add 2 80% to the perches, 
 3 120 
 
 and to the fum annex 4 cyphers. Divide this laft by 
 16, or by 4 and 4, and write the quotient figures, 
 if they confift of 5 places, after the acres, 
 
 But when the number of quotient figures are but 
 
 S ‘ ; write a oe ners pater the acres, and then 
 
 the quotient hgures ; ana fo will you have the fquare 
 links required. 
 
 Ex, 
 
 
 
 Fr. 
 \ 
 F 
 i. 
 - a 
 a 
 ‘ a? 
 ite 
 A, | 
 
== 
 
 
 
 A 
 
 alee “A PROP. 
 Ex.I. Reduce 7 2 24 to _[quare links. 
 bay to 24. perches, 
 | mere. Add 80, becaufe 2 roods 
 E ae '16)1040000(65000 _ 
 ie | 80000 © 
 
 : Anfwer 76 thes 
 me | AR, oP. 
 
 
 
 Fr? Ex. JI. Reduce 7 Oo 11 ¢to fquare links. 
 b3 | Me ies perches 
 ¥ fda o becaufe o roods, 
 4)110000 i 
 4) )_ 27500 
 
 Ghioliine Base 6875 bas four places: 
 3 Anfwer 706875. 
 
 A REOR. 
 Ex. III, Reduce 7 0 on to fquare links. 
 
 to o1 perches, 
 Add o becaufe o roods, 
 
 16)10000(625 three places 
 40 : 
 80 
 _ Anfwer 700625. 
 
 we 
 
 A K,: PB, 
 _Ex. IV. sib ine 13 3 37 40 square links. 
 "perches, 
 Ma 120 = becaufe 3 roods, 
 4.)1570000 
 4)392500 
 uotient 98125 bas 5 places. 
 = Anfwer 1398125 /quare links, 
 
 In 
 
 
 

 
 
 
 (as : 
 
 Tn the ope out of lands, there ate three Be 3, 
 or Problems, which arife in practice, 
 
 For, citer the partition line is required to be pa- 
 rallel to fome other line affigned, or is to pafs thro’ 
 _ fome point affigned in the fence, or to pafs through 
 fome point afiened within the land. 
 
 In the folution of each of thefe cafes, I chufe an- 
 arithmetical approximation rather than a geometrical 
 conftruction ; for reafons fufficiently known to thofe | 
 who have practifed. 
 
 Note, When a quantity of land is to be laid out, 
 or taken off from a field ; itis neceffary to have an 
 exact plan of the place, or field; and this is aps 3 
 one in the following problems. . 
 
 
 
 
 Oo v6 
 ms % Rae ROR 
 ao 4% 5e0% 
 
 
 
 PROB. 
 

 
 
 =_ 
 = 
 
 t it be required to cut off towards AB, 8 Acres; 
 3 Roods, 18 Perches, by a line drawn parallel to 
 
 
 
 
 
 
 _* near the place where tis imagined the partition 
 Tine fhould be; and then caft up the content of the 
 figure CDHG, which fuppofe to be 772575 fquare 
 Tinks, which is. lefs than 84: 38 18P-, or 886250 
 -fquare links, by 113675 fquare links ; which fhews, 
 that the partition line fhould be more towards K, 
 
 _ Now divide the excefs 113675, by 965, the 
 Tength of CD in links, and at the diftance of 118 
 links, the quotient, draw EF parallel toCD, and is 
 will be fufficiently near the partition line required. — 
 
 But if by curiofity you are led to correct the va- 
 ration; you may conceive CD to be a line given in 
 pofition, and 113675 fquare links, to be the quan- 
 tity to be cut off, and EF the line drawn by guefs. 
 
 But if the line CD had cut off the quantity CDHG 
 greater than that required; then the partition line 
 had been more towards GH, whofe diftance fromi 
 CD would be found as before, by dividing the dif= _ 
 ference by the length of CD. 7 
 
 ea PROB, 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 From the Field LMPQRSTW, Fig. 28. zi 4 
 
 To cut off 5% ih 35°: towards the corner Ly by. a ie ne 
 . drawn from the point Vere ™“ 
 
 Re ite given quantity 54: oR 3 SP. to ‘quare 
 links, and they will be 521875. ae 
 Then draw LV, forming the triangle VLW, 
 
 which being caft up, amounts to 30800 fquare linkem 
 which is too little. a 
 
 To the next angle draw VM, ining sid tril 
 angle VLLM, which being caft up will be “found to” 
 amount to 294632 fquare links, which added to the 
 triangle VLW, you have 328432 fquare links, the 
 content of the Trapezium VWLM, which is fell t too 
 little. i} 
 
 To the next angle draw VP Saha 3 another nl 
 32843 the content of the BB ‘figure, gives | 
 732282 {quare links; which is more than the re- 
 
 quired quantity, by 210407 {quare links ; therefore i 
 the partition line muft pafs between P and M. 
 
 Divide the excefs by 497, half the length of vO | 
 the perpendicular in links, and lay 423 the none | 
 from P to N, and fo fhall VN be the true line om 
 
 Partition. . 
 
Seer oe an rae att 
 
 
 
 
 
 Sara pee te Ae 
 mae ae pee ae tee 
 GE: ( Su) 
 ca 
 ra 'p ROB. Tih 
 te, 3 
 By 
 
 
 
 io) Seat this with one fie: : Confider ‘ieouck 
 which two fides of the field the partition line 
 will pafs. Reduce the figure to a Trapezium, full 
 retaining thofe fides, as fhewn in page 45. Which 
 | divide by a line through the affigned point A. 
 bm But, becaufe this weed is ie eg and depends 
 “on the concourfe of many lines ; and though we 
 — fhould ufe numbers, we fhould fide mend the mat- 
 ter, and indeed is often impoffible to be performed — 
 by one fingle line ; it may not be amils to thew how 
 to do it by: two lines. 
 
 From A to any two angles H and B, draw the 
 lines AH, AB, forming the triangle ABB, this be- 
 _ ing caft up, amounts to 338000 iquare links, which 
 is lefs than the quantity required. 
 
 To the next angle C, draw AC forming the tris 
 ~ angle ABC, which being cat up, amounts to 
 » 322500 fquare links ; which added to the triangle 
 
 AHB, gives 660500 fquare links ; which are fil 
 lefs than the quantiry required. | 
 _ Tothe next angle F draw AF, forming the tri- 
 argie ACF, whole content 280800 fquare links, 
 added to the preceding triangles AIWB, ABC, gives 
 9413003 which exceeds the quantity required by 
 158175 iquare links ;: now divide this excefs 158175 
 by 292, half the length. of the perpendicular EA, 
 lay the quotient 541 ‘from F to D, and draw AD; 
 and fo will the lines AH, AD, be the partition ines 
 required ; and the figure AHBCD wiil contain the 
 given quantity which was to be laid out. 
 * E 2 SEC ith 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x PSS 
 
 Stud h se 
 
 SE. Cush oa. 
 
 The ufe of the Theodolite exemplified in Surveying eve , 
 ral parcels of land lying together, with the form of ] 
 
 a Field-Book. 
 
 Ae TER a general defcription of inftruments q 
 
 
 
 and their ufes, fome practical examples are ne- 
 
 cefiary to illuftrate and explain the particular varieties 4 
 
 which often occur. 
 
 The following example is ‘ielivicell lin Gey Ee s 
 
 method which at this time is commonly practifed. 
 
 - The inftrument ufed in this furvey is a Theodolite q : 
 numbered on the limb from the left to the right, and 
 in the box (which is fixed to the index) the fame way ; — 
 
 the eye being fuppofed in the center. 
 
 The Chain, the Off-/et-Staff, the Arrows, &c, are 
 as defcribed in the third Section. 
 
 In one end of the Off-/et-Staff, it will be conve- 
 nient to ferew in a piece of iron, having at the end a 
 kind of fork, whoie legs fhall be juft “long enough 
 to embrace the hand-ring of the chain, which being 
 put in the fork, the end of the chain may be thruft 
 through a hedge by the means of the Off-fet-Staff, 
 
 to dive leader oh the chain on the other fide of the 
 
 hedge. °° 
 The field-book may be divided into three columns. 
 The middle one contains the feveral lengths taken 
 
 % 
 

 
 
 
 
 
 
 
 
 
 Ptlich are to be met.with in the furvey. 
 mark © is denoted a ftation; by Z an 
 le; and by 7 an outfide angle: by (B) is 
 bearings by Jn. the cutting a hedge by 
 hain ; by ag. fome remarkable objeét on the 
 her fide of the hedge. Thefe Aa are ufed 
 
 cat, exprefs e bree. 
 ing thus provided, in the firft sane of the field- 
 ok, near the top, enter the title of your furvey : 
 hen having fixed the in{trument in fome convenient 
 place, as A to begin at, l enter in the middle co- 
 ep the | mark © 1. denoting the firft ftation. 
 Here obferve, that I always chufe to work in a 
 Pate as often as opportunity prefents, 
 _ © The inftrument being planted at A, I fend a fta- 
 tion ftaff forwards in the lane as far asI can fee di- 
 a — ftinGly, the farther the better, fuppofe to (B 3.) and 
 x when I work in the land, I fend a ftation-{taff to the 
 next eminent bend in the hedge, or even to the far- 
 ther end of it, if the line font the inftrument to the 
 ftaff be not at too great a diftance from the hedge, 
 fo as to caufe off-fets greater than achain, or a chain 
 anda half, or thereabouts. For off-fets sen too 
 great, produce fome uncertainties, | 
 | Then I obferve the bearing of the line AB, 
 thus; the flower-de-luce in the box being towards 
 me, I direét the fights to B 3, and then find the 
 needle cut 327°, which I enter in the middle column 
 under © mutous, 6 327°. 
 
 Note, By the inftrument ufed in this example, the 
 bearing is accounted from the north, weftward quite 
 round to 360°, 
 
 . The obfervation being made of the line’s pofition, 
 which I am about to meafure, the next thing is to lay 
 3 the 
 
 Py 
 
 et, ee 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 (54). 
 the chain from this ftation A in a right line ~~ 
 the next ftation B 3 3 which being done, Tet it | 
 
 length ; ; viz. I areal the dittances Bi the chain 
 from the brow of each ditch, which I enter in the - 
 outfide columns, that on the right hand of the chain 
 in the right hand column, that on the left in the left 
 hand column 5 and Alp the names of the a 
 fome of thofe which I am sane to furvey, | ie enter 
 the names of them ; .and in all sae aspects to wich 
 land the hedge belongs. Be 
 
 Thefe precepts will not be renedtestt ‘tho? I hall 4 
 ever make ufe of them 3 but if any other are ufed, : : 
 they will be laid’ down the viel ene they occur. in 4 
 this example, but not afterwards, 
 
 Now Ienter -o in the middle column, ade 20 a 
 in the right hand one; and 20 in the left; de- ~ 
 noting, that at ‘no qiteaters or at the ‘efitomeAe \ 
 the ditch on the right hand is 20 links from the . 
 chain, and that on the left alfo 20, In the right — 
 hand column I write William Wayy’s land, bedve to 
 Wary; and in the left, Lord Title’s land, hedge to 
 Lord , becaufe the land and hedge on the right is © 
 Weary’s, and that onthe left my Lord’s. 
 
 Being: now come to a, | am right againft the — 
 fouth hedge of Hazle Spring, and alfo of Woodfield, — 
 and there find the diftance from the ditch on the 
 right hand to be 25, and on the left to be 20, and 
 that afterwards the hedge on the right hand belongs — 
 to Hazle Spring, and on the left to Woodfield. There- 
 fore I enter in the middle column 65, and in the 
 right hand column 25, ag. hedge to Hazle Spring, 
 hedge to Spring ; and in the left 20, ag, hedge on 
 Woodfield, hedge to Field. 
 
 Here it may be obferved, that thefe off-fets, or 
 diftances of the chain from the hedge, are meafured 
 (with my ten-link ftaff, which I therefore call my 
 
 Off fet 
 
 =i 
 ma 
 a) 
 i” 
 P, 
 as Vs 
 + 
 a 
 ‘i 
 Se 
 Wi i 
 aah 
 re 
 *, 
 aa 
 7 
 d 
 ) = 
 oY 
 * 
 ns? 
 - 
 
 Bo ee ee 
 
yous 
 
 
 
 oe igen) 
 
 of. fet-S aff) perpendicular to the chain, and fo far 
 till I come to that brow of the ditch, bicliis fartheft 
 from ‘the ftem of the hedge: And that here by the 
 brow of i ditch, I mean Bers determined diftance of 
 
 ‘ 4 0 Ta lay thi 
 
 be oo to have two pieces at one end of it at 
 
 
 
 
 | iy. ee, may be made to fall into the ftaff, by {prings 
 is Tike a clafp- knife. 
 * Having entered thefe obfervations in the firft 
 t length of the chain, I obferve what place of the 
 ground is exactly under the center of the inftrument, 
 b by dropping a mufquet-ball, or plumbing it with a 
  ftring and weight ; then I remove the inftrument, 
 and in that place fix, as upright as can be, a ftation- 
 ftaff, and then proceed with the chain. 
 
 And becaufe in the fecond and third lengths of 
 the chain I meet with no fenfible turns in the hedge, 
 nor other material occurrences, I go on to lay ita 
 fourth time, and there againft 4¢ links I find a bend 
 in each hedge ; where on the right hand the brow 
 
 _ of the ditch is 50 links diftant from the chain, and 
 on the left 40; therefore in the middle column [ 
 enter 345 (denoting 3 chains 45 links) and in the 
 right hand column 50, and in the left 40. 
 
 And here it may be obferved, that I take off-fets | 
 
 only at each end of fuch parts of a hedge, as run 
 very nearly ftrait, omitting the intermediate parts ; 
 fince when the extremes of a right line are given, 
 that right line itfelf is alfo given: So here, though 
 the diftance of the hedges from the chain between a 
 and @ continually vary, yet I only take the off-fets at 
 aand Bb, fince thefe are fufficient. But when the 
 hedge runs on with a continued but irregular cur- 
 vature, I take off-fets at every chain or half chain’s 
 length, or perhaps oftner, as the thing requires, But 
 
 BK 4 when 
 
 
 
 yy yr eT 
 
 = 
 
 ox 
 
 =< 
 
 r 
 
 
 
( 56 vey ae + a a 
 when the curvature is regular, I take its extremities 
 by off-fets, and exprefs its nature by a fketch, in 1 the : 
 outfide columns. E 
 
 In going on from 4 towards B, when I am come a 
 toc, the chain touches the brow of the left- nang Ry 
 ditch, againft 20 ; then] afk the hindmoft man, or 
 the follower of the ‘chain, how many arrows he hath? a 
 he anfwers 5; then Lenterinthe middle column 520 _ 
 (denoting 5 chains 20:links) and in the left hand co- 
 lumn oo, denoting that the brow of the ditch isat 
 no diftance from the chain. ‘The chain full lying, — 
 again{t 40 links, I find a bend inthe right hand — 
 hedge, where the ditch 1s diftant from the chain 50% 
 links. 4 
 Now it may be obierved. that I frequently afk 
 the follower of the chain, ane alfo the leader, how 
 many arrows they have? efpecially when I am about 
 the off-fet or other occurrence, partly to know the 
 number of the chains, and partly to prevent the lofs 
 of an arrow ; for this always raifes a doubt of the — 
 length, and mutt be removed before we proceed ; 
 and leit when a ftick is dropped, another may be 
 picked up in its room, I always give my arrows 
 fome marks of diftinétion. 
 
 If the fum of the arrows in both my affiftants 
 hands are lefs than ten, then the laft length muft 
 either be re-meafured, fince it is doubtful, or elfe 
 the furveyor muft ftep it, and thereby difcover which of 
 them dropt it: And this, with a little practice, he will 
 eafily do by counting his fteps, and ufing himfelf to 
 ftride about the fame diftance each ftep ; and by 
 
  Joofing a button of his coat when he hath gone as 
 many fteps as (by experience he knows) carry him 
 the length of a chain. And hence he may know 
 ewactly the number of the chains, though he cannot 
 perhaps. find exactly the odd m eafure, But. the 
 number of chains 1s fufficient, becaufe the error by 
 dropping arrows always falls in whole chains, 
 
 
 
 
 
 
 
 
 
 In 
 
 
 
 
 
 
 

 
 
 
 (57) 
 
 Tn like. manner, at the length of juft 800, be- 
 ufe the chain touches the right hand ditch, and is 
 int f from the bend in the Teft hand 40 links, I 
 er in the middle column 800, in the night hand 
 lumn oo, and in the left 40. 
 
 Then I continue on to my ftation-ftaf at B’, 
 
 
 
 
 
 
 i tate, I find to be at the length of 825, where, be- 
 —caufe there is no bend in the hedge, nor other ma- 
 - terial occurrence, I enter 825 in the middle column, 
 and under it I draw a line, denoting that this length, 
 
 and all the occurrences therein, are obferved and 
 entered in the field- book. 
 
 ~ Since [have endeavoured to be a and eafy in 
 this firft length ; fo fhall I, in the following part of 
 this example, be as concife as may be, sree where 
 fomething arifes not before fpoken of ; referring the 
 reader rather to the field-book and explanations, 
 than tiring him with repetitions. 
 
 Being come to B’, I there fo plant the inftrument: 
 by help of the plummet, that its center is direétly 
 over the hole, which the ftation-ftaff ftood in ; and 
 I fend my ftation-ftaff forwards, as far as I can con- 
 yeniently fee it as toC. 
 
 Now with the beginning of the degrees towards 
 me, I direct the fixed fights back to the ftaff at A, 
 and fcrew the inftrument fatt: And then with the 
 Flower-de-luce towards me, I direct the index to 
 the ftaffat C; and there find, that the end of the 
 index next me, cuts 202° 457, and the fouth end of 
 the needle points at 304° 15’. Therefore I enter in 
 the middle column of my field-book, © 2, and un- 
 der it Z 202° 45’, and next under this B 304° 14°; 
 denoting, that at the fecond ftation, the angle made, 
 is 202° ae: and the bearing of the gFCOnG length is 
 304° 
 | But beta I proceed, I examine thete numbers 
 
 thus: To the bearing of the laft ftation 327°, I add 
 
 the conftant number 180, and from the ire G07. 
 fubtragt 
 
 
 

 
 | ( 58 » 
 
 fubtract the prefent bearing 304° 15'; and find ect a 
 remainder 202°45', exactly equal to the angle, aa y 
 Or elfe, to the angle 202° 45, I add the prefent 
 bearing 304° 15°; and from the fum | 507° fubtract 
 the conftant number 180, fo fhall the remainder 
 327° be the bearing of the laft length exactly, as” { 
 taken at the laft ftation., 4 
 And this operation I place in the outfide Pe 
 againft the fame angle and bearing, to fignify, ne 4 
 the angle and bearing have been compared, and do 4 
 agree, ae 
 But if thefe numbers thus compared, do not a- 
 gree, the prefent angle and bearing muft be ex- 
 amined and corrected 5 and if, after fuch examina-. 
 tion, they do not agree, there is an error in the laft. 
 bearing, which may be taken again ; thus, 4 
 The inftrument ftanding in the fame place, I ac, a 
 rect the index, the Flower-de-luce being from me,. 
 to the laft ftation-ftaff at A ; ; and then will the fouth 
 end of the needle point at the fame degrees which it 
 did when the inftrument-ftood at A, and the index, 
 was directed to B+. . 
 
 Having thus taken, entered and examined the 
 angle and bearing, I proceed with my chain, and 
 find the lengths a and occurrences to be as you fee them 
 in the field- book, i 
 Then fixing the inftrament at C, as before fhewn, 
 obferving always to fet the plate horizontal by the 
 help of a fpirit-level, or otherwife ; I fend a ftation- 
 ftaff forward to D, and obferve, enter, and prove 
 the bearing and angle atC; and then ftretching the 
 chain towards D, | find at the length of 250, a gate 
 on my right hand, and at 260, at the diftance of 10 
 links, the corner of Hazle-Spring. Therefore in the 
 middle column # enter 250, and right againft it, in 
 the right hand column, I write Ga/e; again, in the 
 middle column, I enter 260, and right againft it, 
 in 
 
 
 
 
 
eh PAS hl ee ia a ee 
 
 
 
 
 
 
 
 at ithe curd ation D, I do not go up the 
 ards E, but turn off towards [,; in order 
 in Hazle dls and. ee Bee ; sek ob- 
 
 nd f facil as Pole 
 ‘Therefore having fenta ftaff to L; Tobferve, en- 
 er and prove the angle and bearing at D. 
 Here it maybe oblerved, that when I came to K 
 inthe firkt length, the. hedge on the left hand be- 
 | es Pisa to Woodfield, and not to the lane; and there- 
 fore I enteredin the lefthand column, Hedge to Field ; 
 and fince this note, the hedge on the left hand hath 
 continued to belong to the pine Woodfield ; theréfore 
 J have not repeated that occurrence. But in going 
 from DtoL, atthe lengthof 15 links, I am againit . 
 the corner of Long Mead, and 10 links diftant from 
 it, and then the hedge belongs to Long Mead. 
 
 Ga Therefore after © 4. 7 259° 20, B 261° 10, I en- 
 ter in the middle column 15, and on the left hand 
 
 10 Corner, then on Long Mead, then Hedge to Long 
 
 Mead. 
 
 But becaufe on the right hand we have ftill Haze 
 Spring, and the hedge 1s 5 fill to the Spring, and be- 
 -caufe thefe have been always on the right hand fince 
 I firft entered them; I go on without any farther 
 remark, till 1 meet with a different occurrence. 
 
 Being come to L, I obferve, enter and prove the 
 bearing and angle, and then proceed to M. AtM 
 I obferve and proceed j in like mannertoN., But at 
 N, the feventh flation, inftead of going on in the 
 line, I proceed to clofe in Hazle Spring, and there- 
 fore fend a ftation-ftaff to O in Spring Clofe. 
 Therefore at the feventh ftation N in the lane, 
 having obferved, entered and eS oved the Angle 
 MNO, 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 MNO, and the bearing of the line NO, “and atther Ye 
 the chain from N towards O; I find the chain cuts 
 the brow of the ditch at 10 fink ‘diftant from N 
 therefore in the middle column I enter 10 /ut. denot 
 ing the chain’s interfecting the hedge, and then] 
 write Jn Spring Clofé, denoting that the land we are 
 in is called Spring Clofe; and in the right hand CO ba 
 lumn, but the next line, I write Hazle Spring, and — 
 under this, Hedge io Spring, denoting that the land | 
 on our right hand is Hazle Spring, and that the ~ 
 hedge belongs tothe fame. Then I proceed toob- 
 ferve, meafure and enter thofe occurrences as they 
 are found in the field-book, till I come to O. : 
 At O, I obferve, enter and prove, and proceed as 
 ufual towards Q ; noting that at the length 720 the 
 chain did cut the hedge i in the very corner of the _ 
 fence ; and therefore enter in the middle column 
 720 Int. and in the right hand column oo Corner, 
 and then in the middle column IJ write, Jz William 
 Weary’s Land; and {fo proceed to Q. 
 Being come toQ, the ninth ftation, I fend a fta- 
 tion-{taff towards A ; and then obferve, enter and 
 prove my angle and bearing ; and fo proceed with 
 the chain, entering all occurrences, as in the field- 
 book ; till coming to the length 830, I find myfelf 
 right againft the corner of Hazle Spring, and 43 di- 
 {tant from it; which being entered as you fee in the 
 field-book, I write in the middle celumn * Clofe 
 -Hazle-Spring, denoting that the extremity of this 
 off-fet coincides with the firft off-fet taken to Hazle 
 Spring. 
 Having thus compleated Hazle Spring, 1 return ~ 
 
 to N, my ftation in the lane, according to that ge- 
 neral rule I always obferve, of working in a lane, 
 and according to that rule of clofing as often as pof- 
 fible. 
 Now, turning back the leaves of my field-book, 
 
 I find the. ftation, immediately before my coming ‘ 
 into 
 

 
 
 
 
 
 was by number the Guanie 
 field-book, I enter © yf 
 
 on 9 return to the fame flation: before I leave it, I 
 t <a from the hole where: the ftaff ftood, or’ 
 re fome other mark, whereby I may exactly find 
 again readily; and in the field-book to the mark 
 ), I prefix the letter R, or write the word Return: 
 by which, and the other concomitant notes, I rea- 
 dily difcover the number of the ftation. 
 
 But when the © to be returned to, falls in a way 
 where many carriages, €&c. pafs; or when it may 
 be thought proper, as a cheque on the foregoing 
 ~~ work, to direét a line from fome convenient © to 
 a former ©, feveral days after you departed from 
 _ that former © ; in fuch cafes, it will be beft to drive 
 
 
 
 a plug, cut from a hedge-ftake, and pare the ground 
 
 away, or leave a few ftones, about this plug; or 
 make fome mark in the hedge oppofite to this plug, 
 whereby it may be readily found again ; obferving 
 __ toconceal thefe plugs or marks from the country- 
 people, who in general, hating the practice of tak- 
 ing furveys of their grounds, will frequently remove 
 the furveyor’s marks, either to give him trouble, or 
 divert themfelves. 
 | And for the convenience of the ready cutting and 
 driving of thefe plugs, one of the affiftants fhould 
 | have a fmall hatchet ftuck in his girdle ; befides, 
 fuch an inftrument is often wanted to cut away the 
 {mall ftuff in a hedge, in order to open a proper 
 view to the ftation-ftaff. 
 
 Having now planted my inftrument a fecond 
 
 : time at N, and fent a ftaff forward to R, I obferve 
 : the angle MNR, made by the line NR, I am next 
 about to meafure, and the line MN, that which I 
 : meafured immediately before I came to N the firft 
 |e time, 
 
 
 
 And 
 
 
 

 
 
 
 owe the angle with that Tine whieh: was a ie 
 immediately before I came to the ftation, where I 
 took the angle the firft time. So here I obferve the — 
 
 angle made with MN, and not with any other as 
 ON, and therefore in proving the angle MNR, ba ‘« 
 ufe the bearing of MN taken at M. 
 
 Now having taken, entered and proved: the 2m 
 MNR, and the bearing of NR, Igo on with 'the 
 chain towards R, entering the feveral occurrences as 
 you find them in the field- “book. 
 
 Being come to R, the tenth flation, tho’ my , 
 fion is to inclofe Spring Clofe, yet becaufe the laft 
 length, continued ftrait forwards, will take the fouth 
 hedge of Long-Mead ;, in the middle column I enter 
 © 10, < 180, B. 274, 45. and then direct the 
 leader of my chain to lay it right forwards by help of 
 the {tations R and N ; and accordingly I enter the 
 -occurrences of that length, as you fee in the field- 
 book. 
 
 This finifhed, I return to R, and fending a ftation-_ 
 ftaff to S, I enter again @ 10, and the angle and 
 bearing at R, and fo proceed to S. 
 
 And then from S to T, and fo from T the 12th 
 {lation to P, inclofing Spring Clofe, 
 
 Spring Clofe being finifhed, I return to my ‘fourth 
 fiation at D; and fend a ftation-fiaff forwards to 
 E, and then under © 4, obferve and enter the 
 bearing of DE, and the angle CDE ; and then by. 
 the bearing: of CD, taken at the ftation C, 1mme2 
 diately before I came to D, prove the angle CDE, 
 and proceed with the chain, entering all occurrences 
 as ufual. 
 
 Being come toE; I fend a flation- fat toF, inor- (am 
 der to clofe in Woodfield. Now, after I ‘have ob- | 
 ferved and entered the angle and bearing at the thir- 
 teenth flation EF, when Icometo prove them, [find 
 by adding 180° to 353°15, the bearing of the line 
 
 4 which 
 
 
 
 
 

 
 
 
 € (63 ) 
 
 h b ought me to this ftation ; and when from 
 7 e fum 533°15, I have fabtracted 82°, the Hees 
 bearing, A”: find the remainder to be Ae Une 
 
 - number greater than the 360, Now as oft as this 
 yyy rappens, I leffen this number by 360 degrees, and 
 fo will the remainder be, asin this example, 91° 15’, 
 | ee “the prefent angle exadlly, 
 
 
 
 
 
 
 iy 
 
 Ee 74 ‘Then entering the occurrences, I proceed to F, 
 and in like manner from F to G, from Gto H, 
 ee - from H to IJ, and then from J, the feventeenth fta- 
 tion, to K, thereby inclofing Woodfield. 
 _-. This done, I return to F, and there becaufe] can 
 : continue my length DE, right forwards conveniently, 
 la enter © 13, Z180° 00; , B. 353. 15. and then go 
 : on to V. 
 And then entering angles, bearings, and other oc- 
 currences, I proceed from V toW, and from W to 
 X, the 2oth ftation. 
 Being come to X, and having entered 7 234° 
 20', and B 307° 40’, then after 1 have added 180° 
 _oo'to the lait Bearings 2° 00, | find the fum 182° 
 oo is lefs than 307° 40’ the parigne bearing: In fuch 
 ‘cafes I always add 360 tothe fum 182, and then 
 from the refult, taking the prefent bearing 307° 40’, 
 the remainder will be, as in this example, 234° 20, 
 the prefent angle, 
 
 Then I proceed to Y, and from Y to Z. 
 
 Being come to Z, the 22d ftation, in order to en- 
 clofe Long Mead, | go off to a, from eto f, from 
 B toy; where, becaufe the feveral bends of the 
 iver cannot fo commodioufly be taken without ic, 
 from y I go off to d ; and then from ¥ to ¢, from ¢ 
 to g, from % to 4, and from :y the 28th ftation, toé; 
 thereby inclofing Long Mead. Amd then return to 
 Z. But obferve that at ftation 23 where the river 
 falls in, the breadth fhould be taken, and wrote in 
 the field. book; and in  coafting the river, its 
 breadth fhould be taken in feveral places, and 
 
 marked 
 
 
 

 
 oe Gye 
 marked in the field- book ; alfo at flation 28 Gide. 
 the river ceafes to be the fence, it muft be noted, 
 
 together with its breadth; the courfe of the rivers Ne 
 or the way it runs muft be likewife entered’in the - 
 
 book. 
 Being come to Z, I find it convenient to con- 
 
 tinue my length ftrait forwards; and therefore under 
 © 22, I write < 180, and fo go on to x, from x to 
 A, from A to ; and then in order to inclofe Butts 
 
 Choe, I go off from z, the 31ft ftation, to p, and 
 
 p toc, 
 
 Then returning to z, I go on to A* the 33d fta- 
 tion, and then, in order to clofe the Flome Clofe, 1 
 go of to B*, and fo then to C*, and D*. 
 
 Returning then to A*, Igo onto E’, from E? to 
 F*, from Fe fon. and G* to a a the 3gth fta- 
 tion. 
 
 Being come to H’, in order to clofe in Mottle 
 Mead, 1 go off to I’, froml’ to K*, from K*to L*, 
 the 42 polition, and from L? to Me, ‘and fo is Moitle 
 Mead finifhed. 
 
 Then in order to inclofe Hazle Wood, I 20 from 
 
 L” to N*, from N* tothe angle at F, and fo is 
 
 Hazle Wood finifhed. 
 ~ Then Ireturn to H’ the 39th ftation, and thence 
 go to O*, and from O% to P*, the 45th ftation. 
 
 And now, in order to clofe in Hazle Field, I go 
 from P* to Q’, and from Q* to T*, 
 
 Which being done, I go from P* to R*, and 
 from R* to S?; “and fo the whole is finithed as you 
 find it in the field-book ; and as far as relates to the 
 field work. 
 
 It remains to fhew, how this work may be plotted | 
 
 without any regard to the memory; nay, though it 
 were furvey’d by one perfon how it may be plotted 
 by another who never faw the land; provided that 
 the perfon who furvey’d it, hath ftritly obferved 
 the rules here laid down. And I do affirm, that 
 
 any 
 
 
 
 
 r eel *. bee oat dine in yt ee 
 si Nea Ba ee . er iat ” PF . a a a le aa. See ici? “~ ot a ~ 
 > Ce RE DTP TE Santee ee REN a Kaew Gey eee ee Pacer aie te Se se eae SA mae 
 = , 5 ons re ee a ety oe 
 
 St era 
 
Tare yer oh gees aes 
 
 
 
 
 | pat Gas) : 
 any method of keeping a Geld-book, which lays a° & 
 burthen on the memory, or by hich a perfon re- 
 mote from the land, cannot plot it, is imperfect, 
 and ought not to be practifed, | 
 Burt it may not be improper, to ae arate the 
 rade that thereis one thing abfolutely neceMary to 
 be taken notice of, in obferving with any of the 
 foregoing inftruments, viz. that the plate muft lie 
 always parallel, or very near paralle] co the plan of 
 the, horizon. 
 
 Likewife, he ought to allow for the difference 
 Bectiéen afeending and defcending lengths, when 
 Be “compared with the horizontal length. 
 
 For it is evident, that the length meafured up an 
  afcent, or down a defcent, will be always greater 
 4 than the horizontal lengths, which only are the mea- 
  fures that ought to be entered, either for cafling or 
 ' for drawing the plans of any parcel of Jand wh hatfo- 
 ever; fince thefe afcending meafures, if laid down, 
 _ would crowd the adjacent ones out of their places. 
 And fince thefe things are required very frequent! Ys 
 many times in going upon one afcent, and confe- 
 quently ought to be ‘performed 3 in the field, in order 
 to make a proper entry in the book; I would have 
 the practitioner be provided with fuch a T. becdolite, 
 as will perform without compafies, rulers, fectors, 
 ‘tables, €%c. thefe ufeful practices, or without any 
 ‘further obfervations than what is required to take the 
 angle only. Such Theodsdites may be made, not 
 Only to perform thefe, but alfo to thew by inipec- 
 tion, the height of any ftanding ftick of timber, 
 without any calculation, tho” the - ftick food on level, 
 _ fifing, or falling ground: Or the length of any arm 
 out of reach; or height of any ftceple or hill: Or 
 | by it a level proper for the conducting of water ; 
 very ufeful for all furveyors in general. | 
 
 Tho’ I do defign to’ give a {pecimen of this 
 improved inftrument, hereafter, in all its 
 i con- 
 
 
 
 
 
‘conveniencies, I could not pafs it by in this place, 
 
 (66 ony, 
 
 = 
 
 left the reader fhould over-look it. 
 
 _ Jn this place it will be proper to obferve fome pat- 
 ticulars which experienced furveyors have found ne- 
 
 ceflary. 
 
 In taking the Theodolite thro’ a hedge, it fome- 
 times happens, that a thorn or fprig catching the 
 
 horfe-hairs in the fights, breaks them ; therefore the © 
 
 furveyor fhou'd have fpare horfe-hairs ready, and a 
 
 piece of dry ftick to cut to a fharp point, to fix frefh 
 
 horfe-hairs to the fights. 
 
 In running the chain along a field where are many 
 furze-bufhes, thorns, or other fhort ftuff, (or by 
 
 other accidents). the links will be frequently bent, | 
 
 and the rings opened, whereby the chain parts ; in 
 
 fuch cafe, a fmall hand-vife, and a pair of nippers 
 
 Ds; 
 
 fhould be ready, that the chain may be put together 
 
 again, the rings clofed, and the links. ftraitened: 
 
 
 
 And. left fome of the links fhould be broke, or the 
 
 rings loft, there fhould’be fpare links and rings at © 
 hand. One of the chain-men may eafily carry.thefe 7 
 articles in his pockets: And it will be properthat 
 one of them fhould every evening, or the morning — 
 
 before he goes into the field, examine the chain from 
 end to end, and rectify what may be found amifs, 
 
 In cloudy dark weather, or towards the even- 
 ing, the ftation-ftaves cannot be eafily feen, unlefs 
 at fhort diftances ; and as it is much better on all 
 accounts, to have them at long diftances when that 
 
 can be had, andisa lofs of time to fet intermediate 
 ‘ftaves ; therefore if pieces of tin, or other white 
 
 marks were ready to fix to the top of the ftaves, the 
 furveyor would find his account by fuch precau- 
 tions, 
 
 It 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 apper 
 et sd a rain, mift, dews, or ‘your breath ; 
 ng this off to fee the needle, the glafs by 
 bed becomes electrified, and thereby ats) 
 
 t by touching the glafs with his Anger wetted, 
 the place to which the point of the. needle ad- 
 4 it will be releafed from the electrical attrac- 
 
 cd 
 
 AR Pautitious farveyor will not leave the fe 1d 
 
 for a finall, mizling rain ; and altho’ he cannot then 
 write in his book with ink, yet his obfervations may 
 be entered with a black:lead pencil, and thefe wrote 
 over with ink when he returns to his abode. 
 
 There are “feveral things that occur in a furvey, 
 -which cannot with convenience be entered in the 
 f ield- book by the foregoing directions, fuch as, 
 “places where are many ~ buthes, pits, or other ob» 
 itions where the inftrument and chain cannot be 
 eadily directed ; alfo the fite of houfes, barns, 
 ards, aoe ee Such things fhould be en ares 
 
 4 pofite page, and fuch lines meafured with the chain 
 or off-fet-ftaff, as are neceflary to furnifh the means 
 of pakiie a true pen thereof, 
 
 
 
 ey 
 
 ; 
 
 shige NON «ch Sore _ Obfervations 
 
 
 
 ne needle, prevents its free. motion: It rh ay 
 
( 68 ) 
 
 
 
 4 
 | 
 ~ 
 
 a 
 
 HOR: CLLRS ELSE 
 
 -Obfervations and Dimenfions of Lands lying in hon ¢ 
 Parifh of —-—-— in the County of - Part t¢ 
 the Eflate of 
 
 
 
 
 
 
 
 February the 2d, 1725. ; 
 
 Beginning at the lane leading from¥ardly to Roughton. 
 
 ‘ On Lord Title 20 O 
 
 
 
 © I 
 
 B 327, fefo) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Hedge to Lord Hedge to Wary 
 ag, Hedge 201 65 ' |25 ag. Hedge 
 On Woodjield On Hazle-/pring 
 Hedge to Field ; Hedge to Spring 
 
 490) 345 {5° | 
 OO} Azo 
 540 
 40 00 
 825 F 
 3). Bir, 
 327, 00 | 
 180. 00 iz 
 507. OO 7 202.45 
 304. 15 B 304.15 
 202. 45 
 15}. 240 
 250. 2g 
 
 
 
 
 
 20 On Will. Wary > | 
 
 304. 
 
 \ 
 ERE BILE GE TTP 
 
 
 
¢ Ge )- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ee if 03 
 _ 304. 15 
 ; 108 ° ’ 
 eee ie £.143-45 
 484. 15 : 
 340. 30 B ot eka be 
 143. 45 250 Gate 
 le “ihe 260 10 Corner 
 : ZO ZIPS). 
 ae ee 
 r 180 all K 4 
 520," 30 
 be “7 259. 20 
 tes B 261, io 
 259. 20 
 Corner 10 15 
 
 
 
 - On Leoaz Mead 
 Hedge to Long Mead 
 
 
 
 261. 10 
 180 
 
 441, 10 
 284,-20 
 
 156. 50 
 
 
 
 284: 20 
 ' 180 
 
 464. 20 : 
 Spr: 3° B 2572 30 
 206. 50 : 
 
 \ 
 
 
 
 
 
 lro againft Hedge 
 
 On Spring Clofe” 
 
 | Hedge to Spring Clofe 
 | : 
 
 10] 230 
 
 
 
 240 
 
 
 
 Hg 257 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ( 70 ) 
 he RO7 
 Sey. 30 
 Ph Orns 
 437> 30 “7 264. 30) | 
 173 B 173.00 
 264, 30 40 Int. 4 \ 
 In Spring {Clofe 
 On Hazle Spring 
 Hedge to Spring 
 195° 289 3 
 | 245 |15 
 173, 00 © 8: “fh 
 180 Y 202,15 
 253.000 4B 150.45 
 150. 45 
 202. 05 sl 54 < ied 
 335 ge 
 BOO tues 3 
 720 Intioo Corner 
 InWilliam\| Wary’s \Land 
 $e Fs 
 150. 45 oD 
 180 “7 24.0. OO 
 330. 45 B 99. 45 
 99:1 45 oo ee 
 ) 510 ~ [05 
 enc hnA 640 |70 
 155° Pagg 
 830 |43 Corner 
 * Clofe| Hazle  \Spring 
 
 
 
 
 
 
 
 
 
 Taken 
 
 
 
x 
 
 Land 
 |Hedge to Spring 
 Clofe 
 
 300 + ={100 
 
 340 |10 
 
 370 We 
 
 
 
 Se 
 i ye q Bs 
 a 
 mS F 4 208 
 iis j aes 
 aoe hea a - 
 s) : fi 
 
 
 

 
 ‘1. a ue 
 eee a Cb me nn SNS ba am LL 
 fe hs 2 ay pan a8 JEN ya a 
 : Tea hah eh 
 ‘ 
 
 | 
 | 
 | 
 | 
 
 
 
 
 
 
 
 j 340. 30 
 180 
 
 520. 30 
 LOD G |B 353.15 
 
 
 
 
 
 > 
 On Woodfield 10 10 Corner ie a : 
 _ Hedge to Woodfield \Long Medd - >. 
 forse Hedge to Fs Mead 
 Gate 20} 440 loo 
 
 bg 
 
 “ er 
 tem am nene s 
 
 
 
 
 
 { 
 r 
 

 
 
 
 
 
 e 1 
 353-15 
 180 
 533. 15 
 $2. 00 
 451. 15 
 360 
 QI. 15 
 
 82. 00 
 180 
 262 
 163 
 
 99 
 163. 00 
 180 
 343 
 
 93-15 
 
 249. 45 
 
 orc Rae 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Rt 013 
 he. gt. 45 
 |B 82. oo! 
 20 Int, rs 
 In Woodfield 
 20 15 Corner of Hazel- 
 (Wood 
 Hedge to Wood 
 550 15 
 © 14 
 Z. 99. 00 
 {B 163.00 
 tt -@0-- J10 Gate 
 On We aod-Clofe 
 Hedge to Woodfield 
 ee GO 
 O15 
 7 249-45 
 B93. 15 
 35 00 Corner 
 430 130 
 600 WO ete 
 610 = 150 againjt Hedge and 
 Corner of Woodfield. 
 On Lord Title’s Land 
 Fledge to Title 
 835 10 Corner 
 
 
 
 
 
 95 
 
 
 

 
 againfi Hedse 
 On Hazle Wood 
 Fiedge to Wood 
 
 
 
 20 
 
 TS vais ee 
 \t5 Corner — 
 
 
 
 
 
 @ 904 
 Z.180,00 
 B 353-+15|Oa Long Mead 
 
 
 
 
 
 
 
 [Clef Weofita 
 
 20 Hedge to ditte * 
 140 loo Set kik 
 O18 ‘ " 
 
 7 182.45 . 
 Bi 220; 30) 
 360 © a6 
 445 [20 
 350. 
 

 
 
 m B07. 40. 
 
 oh. 
 
 ROO 
  nensnns 
 182. 00 
 
 360 
 
 
 
 
 
 
 
 
 
 py eed Bee 
 
 . Gate. 75, . bo 
 
 if “A Saat 4190 
 againft Hedge 201 215  |o0 
 On Butts Chfe © | a 
 Hedge to Clofe 
 
 
 
 “oo] 450. |20 
 
 SD 
 
 
 
 ey” - qth Be 
 Vs t 
 
 } 
 
 
 
 
 
 
 & 
 
 Z°7 
 
 
 

 
 
 
 
 
 ——— 
 
 Cees Aa atone 
 
 
 
 
 
 
 
 
 
 
 
 Se © 21 
 307. 40 
 180 | 7 200. a 
 487. 40 B 287. 00 
 287, OO 
 200. 40 | 
 20] 50 
 20| 260 
 FAN PFS 
 1 380, |Gate 
 70] 490 E ; 
 |00 againft Hedge and — 
 \Corner of Long Mead 
 OnWalter’s Meadow 
 9 5 sho 
 287. 00 R © 22 
 180 “7 280. 40 
 467. 00 B 186. 20 
 186. 20 | 10 {nt 
 280. 40 In Walter’ Meadows 
 ; 24 110 Corner 
 On Long Mead 
 | Hedge to Long Mead 
 360 15 | 
 540 190 
 735 10 
 | 
 
 186, 
 
 
 
 
 

 
 ° ! 
 186. 20 
 180 
 366. 20 
 166. 15 
 200. OF 
 Corner 10 
 On Trout Beck 
 Common Mead 06 
 10 
 10 
 River 40 
 166. 15 
 180 
 340. 15 
 IIr- 
 235. 15 
 10 
 ) 20 
 River 50 00 
 - 9 5 
 River 40 
 III, 0O 
 180 
 291 
 229. 20 
 61. 40 30 
 30 
 25 
 10 
 
 
 
 105 
 
 In Long Mead 
 Flere Trout Beck 
 River becomes the 
 
 
 
 
 

 
 
 
 
 
 
 251. 20 ate : Ley ae 
 180 3 
 431. 30 ; ZALT ook. 
 
 290. 30 — B 290. 30 
 141. 00 a on 
 
 
 
 oe River 30 70 
 
 
 
 River goes off at, \this place 
 
 i 
 pie ‘he 
 ' ‘ ‘ he 
 es ‘ yt oe 
 Mie P t 4 i ean 
 H ‘ © ra 
 om " 4 
 mis ; : 4 
 vA ‘ iw) 
 bya) wre. 
 ie 2) 
 ¥ - 5 rae 
 . ¥ TE 
 | f p See Pete 
 ; < “ eee ras 4 
 4 cS 
 me, | 
 ‘ 
 : 4 , 
 y ¥ 
 i 
 "; 
 
 rr eo ES FOES 
 
 
 
 299. 
 
 
 
‘sien 
 On But’s Clofe 
 Hedge toChfe 86) 230 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ( 80) 
 e £ O 30 
 2.10 ae 
 180 Z. 89.00 
 182. 10 B 93-10 
 93. 10 oe 65 Int. 
 “T9. 00° In\ But’s Clofe : 
 On Roughton Com. 
 100 | 65 Hedge to Clof 
 : 350 100 | 
 750 ° |100 
 835 15 
 93. 10 Rl © 31 
 180 Z_106, 00 
 273. 10 B 167. 10 , 
 167. 10 o {20 Ou Home-Clofe 
 et Hedge to Home-Clofe 
 . 590 15 
 167. 10 © 32 
 180 | £126.40 
 Bi ie B 220. 30 
 220. 30 © pee : 
 = 85 10 againft Hedge 
 120. 40 On Hazle Wood 
 Hedge to Wood 
 AIS {oO 
 clofe But’s Clofe 
 3r 
 Z.180, 00 
 8 93. 10 
 20 Int. \Gate 
 | In Home \Clofe 
 On Roughton Com. 
 195°) 1g 3 
 195. 175 
 7 BOT tre 
 
 
 
 
 
 
 
 93° 
 
 
 
  egeseh sill 
 
 
 

 
 
 
 3 ra ne Oe ca 
 
 
 
 wal 410 
 a 
 O73. 10 
 he 180. 30 
 
 
 
 "92. 40 
 
 180. 30 
 
 180 
 
 
 
 360. 30. 
 
 238. 20 
 122. 10 
 
 238.20 
 
 180 3 
 418. 20 
 308. 30 
 
 —————— 
 109, 50 | 
 
 (81) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ri 9 33 
 a 
 ts 92. 4 
 B 180. On Mattle Mead 
 oo = | Hedge to Home clofe 
 625 15 againft Hedge 
 | On Hazle-Wood 
 | {Hedge to Wood 
 7350 ee 
 © 34 
 Z.122. 10 
 B 238.20 | 
 oO 10 
 310 = {10 
 © 35 
 Z.109. 50 
 B 308.30 
 00° LO 
 ‘ ASar IG 
 | clofe Home-Clofe 
 Taken from © 311 © 33. yea 
 ZATI. 10 
 B 102.00 
 20 Int, 
 In Mottle | Mead 
 300 «= |Oz Roughton Com- 
 315 25 (mon 
 
 
 
 — 
 — 
 
 
 
 G 102. 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 On La. Titles ‘Land 
 Hedge to Lord — 
 255 [50 | 
 
 
 
 co ©6130 On Hazle Field | 
 Hedge to Mottle 
 
 295 135° (Mead 
 605 | \15 Corner a 
 620 ; 
 

 
 
 
 
 
 
 
 ies 
 
 2914 56 
 180 
 
 
 
 451. 50 
 
 183. 00 
 
 268. 50 In 
 On Hazle Wood 
 Hedge to Wood 
 
 
 
 25 
 Corner 10 
 
 799 
 
 
 
 
 
 
 
 
 
 © 42 
 7 268. 50 
 B 183.00 
 
 15 Int. 
 
 Hazle 
 
 375 
 760 
 
 
 
 
 
 
 
 
 
 15 againft Hedge 
 On Hazle Wood 
 ledge to HazleW ood 
 
 
 
 HS 
 clofe Mottle Mead 
 
 ee 
 
 
 
 
 
 Field 
 
 183, 
 
 
 

 
 
 
 
 
 
 
 ee 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ( 84 ) 
 aa © 434 
 183. 00 exe 
 180 Z.153. 30 
 363. B 209. 30 
 209. 30 efi Sole 
 553+ 3° 
 Corner o0| 445 Int. 
 In| Wood |\Chfe 
 25 650 
 Corner of 30 ~ 860 
 Hazle Wood | 
 ana Woodfield ! 
 Taken from © 38} ©39 
 201. 50 7 196. 35 
 180. 'B 185.405 oN 
 381. 50 i ev ree 
 “186.15 I sal Field 
 Sen n AZlé 1é 
 193+ 35 On Ld. Title’s Land 
 Hedge to Lord 
 400 165 
 365. {100 
 1100 10 
 © 44 
 Oy we ary ‘7193-45 
 165.15 IB ra. 30| 
 4180 200 {ITO 
 305. 15 345 30 
 Li Lorao 4.40 7Q 
 193.45 BE ey 
 
 3, 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 785 
 a i 
 © 45 
 apts 30 ° j 
 180, jz. 81.00 
 351. 30 279+ 3° 
 270. 30 
 $1 15. 45 On Wood Clofe 
 Hedge to Wood Clofe 
 100 = 65 ¥ 
 3405) 19 
 ; 650. 75 
 740 {80 
 999 8413 
 270. 30 | 
 +80 | Fis 46 | 
 ee 412,90 
 450. 30 | 
 338. CO {3 33408 3 
 112. 30 Soles 
 . z 200 1164 ag. Hedge 
 clofe Hazle Field On Hazle Wood 
 O45 |. 
 “7 180. 00 
 B 171.30 | 
 1 «5  |10 Corner 
 35 Int, \On Ld. Title's Land 
 Hedge to Lord 
 In} Wood \Clofe 
 255 3° 
 | 300 
 
 
 
 
 
 
 
 G 3. 171. 
 
 
 

 
 DONA Ne Bi wach. 
 20 againft Hedge 
 Woodfield = — 
 
 afer” 2; 
 
 
 
 
 
 
 
 
 
 

 
 
 SECT. VI, 
 
 % 0 To protrast the obfervations contained in the preceding 
 Field- Book. 
 
 IRST, draw parallel right lines, as thofe in 
 
 Plate I]. marked NS, reprefenting meridians 
 er north and fouth lines, at a diftance from one an- 
 other, not exceeding the breadth of the Gameiricn 
 part of the Protracor. | 
 
 Then picking out fome convenient Bees to repre- 
 fent the firft ftation, as A ; the field-book being 
 open before me, I lay the center of the Protractor 
 on the point A, and the diameter parallel to the 
 lines NS, and the beginning of the degrees down- 
 wards, becaufe the bearing is more than 180 ; ; then 
 againit 227 degrees, I make a mark with my Pro- 
 tratling Pin, to which J draw an obfcure line from 
 A, reprefenting the chain-line from the {tation A to 
 che {tation B. 
 
 Then to this obfcure line, I lay the ode of my 
 Plotting Scale, the beginning of the divifions co- 
 inciding with A, and “increafing towards the next 
 {tation B, and eae the off-fets, inthe firft leneth, 
 are taken at the diftances 65, 345, 520, 540, 800, 
 825 ; therefore, again{t thefe numbers on the {cale, 
 
 I make marks in the obfcure line clofe to the edge of 
 the fcale. 
 
 This done I turn my fcale perpendicular to the 
 obfcure line, and apply it fucceffively to thefe feve- 
 ral points, and there prick off the lengths of the fe- 
 
 G 4 veral 
 
 See 
 
 
 

 
 
 
 
 
 
 
 " 1 tee 
 
 ( 88 } | 
 ral offfets on their refpective fides of the obfcure line, 
 fo at A, I prick off 20 on the right hand, and 20 
 on the left; at the length 65, which is the next 
 
 point, I prick off 2g on the right hand, and 20 on . 
 
 the left ; and at the next point, which is at the di- 
 ftance 345, I prick off 50 on the right hand, and 40 
 
 on the left ; at the fourth point, which is at the di- | 
 
 ftance 520, I prick off oo to the left hand ; at the 
 
 fifth point, which is at the diftance 540, I prick off | 
 
 50 tothe right hand; at the-next point, which is at 
 the diftance 800, I prick off oo to the right hand, 
 and 40 to the left; at the laft point, becaufe no 
 off-fet was taken, I lay none down. 
 
 And now, if lines are drawn from point to point 
 on each fide of the obfcure line, they will reprefent 
 the fences as was required. But when the off-fet is 
 oo, as in the fourth and fixth diftances, thofe points, 
 to prevent being over-looked, fhould be marked 
 with a black-lead pencil, or fomething elfe, which 
 may be eafily rubbed out again. 
 
 At the fecond diftance, where we were againft the 
 fouth fences of Woodfield and Hazle Spring, with a 
 black-lead pencil draw two fhort lines, cutting the 
 Jane, to denote that the fouth fences come up to the 
 lane, and will hereafter be of ufe in clofing thefe 
 
 lots. , 
 2 Having thus finifhed my firft length, J produce 
 
 it, if occafion require from B, both ways, till it is as 
 
 
 
 Jong each way as the Radius of the Protraéior. Then — 
 
 _ I place the center of the Protraéor on B, and thereon 
 
 turn it about, becaufe the degrees of the next angle 
 are more than 180, till the begnning of the degrees 
 of the Protraéfor are contrary to the laft flation A, 
 
 and the diameter coincident with AB. Then clofe 
 
 to the edge of the Protraéfor, right again{t 202° 45', 
 I make a mark with my Protraéting Pin, and to it 
 from B draw an obicure Jine reprefenting the chain- 
 line from B taC, | 
 
 Tnen. 
 
 B 
 

 
 ¢ 89) 
 
 Then T ‘turn the Protraffor about, the center ail! 
 coinciding with B, and becaufe the bearing i is more 
 than 180, fet the beginning of the degrees towards S, | 
 and the diameter parallel to the meridians ; ; and 
 then, if you have truly wrought, the line BC before 
 drawn, will meet the limb of the Protrattor again{t 
 304° 15), the bearing of the line BC. 
 
 
 
 ie But if it doth not, the line BC is not in its true 
 
 F. ~ pofition, and mutt be corrected before you pro- 
 
 ceed. 
 
 Or thus; the center of the Protraffor colficiding 
 with B, I turn it about till the beginning of the de- 
 grees is towards S, becaufe the bearing i is greater than 
 180, and till the diameter lies parallel to the me- 
 ridians ; and then clofe to the edge of the Protraéor, 
 with my Protracting Pin, I make a mark againft 
 304° 15, the bearing ofthe line DC, and toit, from 
 B, draw a ftrait line reprefenting the ftrait line BC. 
 Then turning the Protraéfor about on the center C, 
 and becaufe the angle there taken was 202° 45', or 
 more than 180, I turn the beginning of the degrees 
 of the Protragfor contrary to the laft ftation A, and 
 the diameter to agree with AB; and then will BC 
 meet the limb of the Protraéfor againft 202% 46 sit 
 the bearing is truly down. 
 
 And thus the plot may be laid down by the bear- 
 ings, and examined by the angles. 
 
 ‘Then to this obfcure line, 1 apply the end of my 
 Plotting Scale, the beginning of the divifions co- 
 inciding with the prefent ftation B, and the num- 
 bers increafing towards the next C ; and then clofe 
 to the edge thereof, againft 240, 250, the lengths 
 where the off-fets were taken, I make marks with 
 my Protrating Pin. ‘This done, I turn my {cale 
 perpendicular to the obfcure line, and at 240, I 
 prick off 15 tothe left hand, and againft 250, which 
 gives the point C, J prick off ro the right hand, as 
 the field-book directs, Now continuing the fences 
 
 to 
 
 
 

 
 ' | (90 7 : 
 to thefe off-fets, I fhall have finifhed the fecond 
 length from B to C. 
 
 The fecond length thus finifhed, I produce it, + 
 otcafion require, from C both ways, till the length. 
 each way be at leaft equal to the Radius of the Prow 
 itrvaéior, Then I place the center of the Protragfor. 
 on C, and becaufe the degrees of the angle at C are 
 Jefs than 180, I lay the beginning of the degrees of > 
 the Protraétor towards B, the laft ftation, and the 
 diameter on BC. ‘Then clofe to the edge of the, 
 Protraétior, with my Protraéing Pin, 1 make a mark 
 againft 143° 45', the quantity of the angle at C, and 
 
 -toit draw an obfcure right line from C, reprefenting 
 the line from C to D. 
 
 Then turn the Protrafor etine its center ftill co- 
 inciding with C, becaufe the bearing is more than 
 180, the beginning of the degrees towards S, and 
 the diameter parallel to the meridians, and then if 
 you have worked truly, the line CD before drawn; 
 will meet with the limb of the Protracfor againft 
 340° 30', the bearing of the line CD. 4 
 
 But if not, the line CD is not in its true poles | 
 and mutt be corre@ted before you proceed. 
 
 From the laying down thefe two angles and baie 
 ings, it appears how errors often happening in prac- 
 tice, may be prevented. 2 
 
 The general rules I obferve herein are three, viz. 
 
 
 
 
 
 1. I lay the diameter of the Protraéfor on that ~~ 
 line which brought me to the prefent ftation, where ¢ 
 the angle, about to be laid down, was taken. 
 
 2. I Jay the beginning of the degrees of the Pro- 
 traéior towards the Jaft ftation, when the angle is 
 lefs than 180 degrees ; but the contrary way, when 
 the angle 1s more. 
 
 ri 
 
 nD 
 
 
 
e : 
 
 ie | gr ) i 
 ! igs ogc arte gia v 
 i, Mr laying down or examining the bearing, 1 
 ‘a the beginning of the degrees of the Protrafor 
 northwards, . when they are fewer than 180; but 
 fouthwards, when more. — 
 “Yn like manner I lay down and examine the angles. 
 | snd bearings taken at D, LL, M, N, O, Q, the 4th, 
 sth, 6th, 7th, 8th, gth Batons: and ‘alo the cor- 
 refponding lengths and occurrences. But in the laft 
 length QA, having at the length 830 laid off an 
 off-fet of 42, it gives exactly that corner of Hazile- 
 f ring, which was noted down in the firft length in 
 
 e Jane; which proves that the angles and lengths 
 fnclofing Hazle-{pring, are truly laid down, But if 
 the extremity of the laft off-fet in the length QA 
 doth not coincide with the extremity of the fecond 
 
 off-fet AB, both denoting the fouth weft corner of 
 
 Hazle-fpring, the lengths and angles defigned to in- 
 
 clofe the fame Hazie-fpring, are not truly laid down, 
 
 and therefore muft be examined and corrected be- 
 _ fore you proceed. 
 
 Now © 7, being marked with 7, anumber not 
 greater than 9, ‘the number of the lafl ftation, be- 
 ing the next work noted in my field-book ; I retura 
 to © 7 1n my. draught, and there with MN, the 
 line which I meafured immediately before I came to 
 N, Imake the angle MNR 162° 45,, and the bear- 
 ing NR 274° 45, as noted in the field-book, and 
 then proceed to lay down the off-fets and other oc- 
 Currences, at their proper lengths and diftances. 
 
 Having finifhed NR, I find next following in my 
 field-book .© 10, which becaufe it is greater’ ‘than 8, 
 the number which immediately follows 7, the num- 
 ber of the laft ftation; and becaufe I find no ftation 
 already laid down, marked with a number fo great 
 as 10, therefore I eencliles that the ftation R, vier 
 I now am, is to be durabred 10; and from thence 
 
 proceed 
 
 
 
 
 
 
 

 
 proceed to lay down 
 
 
 
 ( 92 ) 
 
 bearing at R, as ufual. 
 The rules I obferve in thefe cafes are, 
 
 1. To erates with black lead all the ftations I | 
 
 have already laid down in my draught, and alfo to 
 exprefs thofe numbers fucceffively after one another, 
 in a piece of wafle paper, which I examine as often 
 as J pleafe. | | 
 
 {a 
 
 2. If I come to a ftation whofe number doth not 
 jmmediately fucceed the number of the laft ftation, 
 but is greater than the greateft of thofe numbers 
 noted in my wafte paper by an unit; then at the fta- 
 tion now. arrived at, I lay down and examine the 
 bearing and angle with the line I meafured imme- 
 
 diately before I came to this ftation. And this fta- 
 
 tion I number as denoted in my field-book. 
 
 3. If lcome to a ftation, whofe number doth not 
 immediately fucceed the number of the laft ftation, 
 but is greater than the greateft of thofe numbers 
 noted in my wafte paper by more than an unit, 
 
 and examine the angleand 
 . Ns ae 
 
 
 
 then fome omiflion hath arofe in my wafte paper, 
 
 and mutt be rectified before I proceed. 
 
 4. And laftly, if I come to a ftation whofe num- 
 ber is already entered in my wafte paper, then I re- 
 turn to that ftation in my draught, and there lay 
 
 down and examine the bearing and angle with the . | 
 
 line, meafured immediately before I came to this 
 ftation, the firft time, 
 
 Now the next obfervation I meet with in my field- 
 book, is again © 10; therefore again at © 10, I 
 
 lay down and examine an angle and bearing, as 
 
 noted in the field-book, and then proceed to lay 
 
 ~dowa » 
 
( 93 ) 
 7. the lengths and off-fets of the line RS, as I oy 
 find in my field-book. 
 
 Being come to S, I proceed to T, a from T to ° 
 P, there clofing with the extremity of the off-fet at 
 _P, coinciding with the fouth-weft corner of Spring- 
 clofe, and the fouth-eaft corner of Haz/e-/pring. 
 
 This done, I find next in my field-book © 4; 
 therefore I return to © 4, and there proceed as my 
 field-book direéts, till I come to ftation 13; and be- 
 -caufe this is a number greater, by an unit, than 12, 
 the number noted in my wafte paper, I number it 
 
 13, and then proceed, as my field-book directs, to 
 F, G, H, I, and K, there clofing in Woodfield by 
 the extremity of the off-fets there laid down. 
 
 This done, I next find © 13, and therefore, be- 
 caufe already entered in my wafte paper, I retusn to 
 © 13 in my draught ; and then proceed as before 
 
 _ fhewn, till I have plotted all the occurrences men- 
 tioned in my field-book: But the remaining part 
 hereof I leave for the exercife of the reader. 
 
 All houfes, barns, mills, or other buildings; alfo. 
 kilns, ftone-pits, gravel-pits, ponds, watercuts, hills, 
 hollow-ways, land-marks, bridges, roads, bridle- 
 ways, foot-ways, ftiles, remarkable old trees, and 
 any other particular which the furveyor may mect 
 with on the eftate he is working in, fhould be noted 
 in the field-book ; and fuch meafures, and {ketches 
 of them taken, as that they may be inferted in the 
 plan: For fuch particulars being frequently referred 
 to in old terriers of eftates, their being accurately 
 
 _ delineated in a map, would afcertain their pofition 
 and diftance from other places; and thereby pre- 
 vent fome of the fatal contefts that arife ae 
 neighbouring families. 
 
 When all the particulars contained in the field- 
 book are delineated or mapped, caft up the contents 
 of each inclofure, road, lane, wafte, €Sc. by the me- 
 thods before fhewn; and.-write the contents, together 
 
 4. with 
 
 
 

 
 
 
 ee: 
 
 [ee ’ 
 ue vi ‘ ; 
 a7 
 
 ( 94 ) 
 
 with the name in each piece: Let the plans of build 7 
 ings be fhaded by lines drawn acrofs; and’write the 
 names of the neighbouring eftates or parifhes on the 
 outfide, near the places where they bound the lands 
 
 in your map ; alfo at the ends of roads and_ lanes, 
 write where they lead to and from; and thus will 
 
 the foul draught of the furvey be finithed, This 7 
 
 foul draught may be transferred to your clean paper, 
 
 parchment or vellom, many ways ; among which ~ 
 
 the following one is eafily practifed, 
 
 ANG Laie the i fcrapings of red chalk and black lead, in| 
 equal quantities, mixed together ; rub the back of . 
 
 the map with this powder, and then wipe off as 
 
 much as will come away with gently rubbing a cloth — | 
 over it: Lay this coloured part downwards on the _ 
 
 paper or vellom, faftening them together with 
 weights, pins, és¢. Then with a fharp-pointed bod- 
 deli or tracer, trace all the lines of the furvey, and 
 the impreffion of them will be marked on the vellom : 
 Take the foul draught off, and go over all the co- 
 Joured lines with a fine pen and ‘Indian ink; and fo 
 will the draught be transferred. 
 
 Annex a fcale of polesand yards; with acompafs, 
 allowing for the variation of the needle ; alfo infert 
 the latitude of the church, manor-houfe, or fome 
 other noted mark ; and embellifh the map with fuch 
 
 other ornaments as are commonly introduced in ~ 
 
 works of this kind. 
 
 Obferve that the reprefentation of the hedges ought 
 
 to be laid down onthe fame fides of the fences, that 
 they are inthe land; and to be broke off where 
 there are to be the reprefentations of gates, Ec. 
 There ought to be imaginary lines, both vertical 
 and horizontal, denoted by letters placed at the top 
 and bottom, and alfo on the fides, to be referred to 
 by the table of references ; for the ready finding any 
 field, or parcel of land therein contained. 
 Laftly, 
 
 
 
C95) 
 
 ~Laftly, I fhall, in this place, only add, that in 
 all.performances of this kind, errors, for the moft 
 part, arife from the defects of inftruments, in the 
 framing, dividing, and contriving. 
 
 
 
 ; PEC rT Vil 
 
 Of a new, certain, and expeditious Method of Survey- : 
 _ ing and Plotting by the Theodolite, as now im 
 proved. 
 
 
 
 N the practice of furveying, it hath hitherto been 
 found very difficult to make a large parcel of land, 
 when it came to belaid down in a map, clofe exactly 
 with regard both to the lines and angles meafured, 
 efpecially if it were mountainous and hilly ground, 
 nay even a {mall quantity of uneven land has often 
 puzzled thofe who otherwife thought themfelves ex- 
 pert furveyors, Now this difficulty in clofing the : 
 draught, arifes chiefly from the following caufes. . 
 : Firft, The not taking care to place the plane of 
 the inftrument truly horizontal or level, and which 
 indeed it is almoft impoffible to do by the eye alone, 
 efpecially on the fide of a hill ; and tho’ this may by 
 ' fome be thought of little fignification, yet thofe who 
 have any knowledge in geometry, mutt allow, that 
 very great and unavoidable errors will arife thereby $ 
 for it may be demonftrated, that if the plate of the 
 inftrument dip but 2 degrees at right angies to the 
 the line of obfervation, and the hill defcend 10 de- 
 grees, it will caufe an error of 42 minutes in the 
 
 * This SeGtion is part of Mr. Warner’s Appendix to the 
 fecond edition of this book. 
 angle, 
 
 
 

 
 
 
 (96) 
 
 anple, and the object will be thrown out of its true 4 
 place 12 links inthe diftance of ro chains; and how 
 
 great confufion muft this make in plotting the fuc- 
 ceeding angles which turn thereon as on a center ? 
 But if fo confiderable an error arife by miffing tlie 
 
 ‘level only 2 degrees, nearer than which I believe no 
 
 one will pretend to place an inftrument with by his 
 eye, what egregious blunders muft the _ practifers 
 with the plain table make, who, when they cannot 
 fee thro’ the fights of their inftrument on an afcent 
 or defcent, do commonly nfe, dip, or, as it may be 
 
 properly faid, twift the plane of their table more or — 
 
 lefs out of the level till they can fee their objects ? 
 Secondly, The not making due allowance for the 
 difference between the lines of afcent or defcent, and 
 the horizontal lines, which are the only lines that 
 ought to be laid down ; and though it is a common 
 practice on the fide of a fteep hill, to double the 
 chain, and fo in afcending to make the leader hold 
 the middle in his hand clofe to the ground, while 
 the follower raifes the end by the ftaff in his hand, 
 till he judges it to be ftrained on the level, and in 
 defcending, the leader elevates the middle by his 
 ftaff in like manner, while the follower keeps the 
 
 end clofe to the ground ; yet a true horizontal line ~ 
 
 can hardly be obtained this way, by reafon of the 
 fwaying of the chain, and the uncertainty of keep- 
 ing it in its due place. 
 
 Thirdly, The plotting the angles by removing the 
 Protractor from ftation to ftation ; in doing which, 
 if we confider the nicety required in laying the diame- 
 ter of the Protractor, and the variation of the hand 
 
 in pricking down the quantity of degrees and mi-— 
 
 nutes, and in drawing the ftation-lines, we muft al- 
 low it to be a very difficult matter to protraét fo 
 near as 10 minutes; whence, if there be a confide- 
 rable number of ftations in the circuit, the plot will 
 rarely be found to clofe as it ought, for an error in 
 
 any 
 
 
 

 
 
 
 F iC 97) 
 
 any one of the angles will be communicated to all 
 that follow, and each fucceeding ftation will be 
 thrown more and more out of its true place, as it is 
 farther from the angle where the error firft arofe ; 
 and though i it be a good way to protract. hadkewards 
 
 ; as well as forwards, yet even that will hardly bring 
 
 it to bear, unlefs the errors ee to counter- 
 pe. 
 
 _ The foregoing are. » the principal caufes that render 
 it difficult to make a corre¢t map ; and they are 
 
 2 ‘now intirely obviated by the New Improved Theodolite, — 
 
 var 5 
 
 as made by Mr. Heats, and the method of fur- 
 --veying and plotting hereafter defcribed. 
 
 fir, This inftrument has a fpirit-level affixed to 
 the telefcope, and another {pirit-level at right angles 
 thereto in the box ; by means of which ctofs levels, 
 and the help of four fcrews playing between two 
 plates in the brafs head of the ftaff, the plate or limb 
 of the inftrument is readily brought to a true hori- 
 zontal fituation. 
 
 Secondly, ‘Lhe telefcope with crofs hairs therein, 
 _ turns on an arch fixed to the index perpendicular to 
 the plate of the inftrument, the arch is of the fame 
 radius as the plate, and the telefcope may be elevated” 
 or depreffed thereon quite to a quadrant, or-go de- 
 erees, On this arch are graduated the degrees of a 
 circle, which are numbered from the vertex either 
 way, with10, 20, &¥c. and are cut by an index un- 
 der the telefcope, divided after Vernier’s (commonly 
 called Nonius’s) way, like thofe on the limb of the 
 inftrument, Within the degres are two lines num- 
 
 _ bered with 10, 20, €%c. down to 100, and cut by 
 
 4 
 
 the edges of the index; om the right whereof is 
 graved Elevation, and on the left Depreffion. ‘Thefe 
 dines ferve to fhew the altitude or depreffion of any 
 object in rooth parts of the diftance at which the in- 
 firument is planted to take the obfervation, and are 
 ufeful in finding the height of a tree in the Brune 
 ri ) 
 
 
 

 
 + 
 
 7 ‘(6 98") 
 Of timber ftanding ; as alfo to find the altitudes of a 
 the feveral parts of a building in drawing the per- 
 fpective appearance thereof, as will hereafter be — 
 fhewn. Below thefe are other graduations cut by — 
 the lower part of the index, which fhew the diffe- 
 rence between the hypothenufe and bafe of any — 
 right-angled triangle, (the hypothenufe being always 
 fuppofed to confift of 100 equal parts) and confe- — 
 quently they give by infpection the number of links 
 to be deducted out of each chain’s length in going up 
 or down any hill, for reducing the hypothenufal 
 
 lines tohorizontal. ‘There are aifo plain fights fixed 
 
 upon the telefcope to be ufed in fhort diftances, and 
 for continuing the fame ftrait line both ways from 
 the inftrument, as is neceflary to be done in — 
 cafes. 
 
 When the index under the telefcope is fet to 00° 
 at the vertex of the arch,.and the two bubbles 
 brought tothe middle of their tubes, then the hori- 
 zontal hair in the telefcope cuts an exact level, and 
 the plate of the inftrument becomes a true horizontal 
 plane; and if the interfection of the crofs hairs be fet 
 to any object by moving the telefcope above or be- 
 Jow the level, the divifions on the vertical arch will 
 
 fhew the elevation or depreffion of the object: Alfo, 
 when the telefcope is directed to any object, the in- 7 | 
 
 itrument may be readily fixed fo firmly in that di- 
 rection, by turning a fcrew under the center, that © 
 there can be no danger of being ftirred by removing 7 
 the index on the plate towards another object. The ~ 
 degrees on the plate are divided fo accurately, that — 
 though they are cut by three indices 120° diftant 
 from one another, having Vermier’s (or as vulgarly 
 called, Nonius’s) divifions on each, yet the eye can 
 
 perceive no inequality in the divigions all round thé 
 limb, but whatever part of a degree the index under 
 the eye glafs of the telefcope cuts, the fame will al- 
 
 ways be found to be cut by the other two; thereis 
 I alfo 
 
 
 

 
 
 
 4 4 
 
 
 
 oa. (55) 
 alfoa a finall Rides that cae to cut the particular dis 
 vifions s on the limb to be uféd for taking the breadths 
 
 in drawing the perfpective appearance of any build- 
 4 : earn whole index, with the box fixed thereon, 
 turns round ona conical center without ftirring the 
 ne edle, and may be fixed to any part of the limb, 
 _ by means of a {pring and fcrew adapted thereto. li 
 ‘a word, the entire inftrument is contrived fo com- 
 
 
 
 
 
 holes, portable and {trong in all its parts, that it 
 
 is allowed to be the beft of the kind ever yet made. 
 __ Thirdly, In order to avoid any error that may a- 
 rife in taking the angles in the field, or from pro- 
 tracting them angle ‘by angle, as has hitherto been 
 the univerfal cuftom, let the furveyor obferve, this 
 following method, which for its readinefs as well as 
 accuracy, will, no doubt, be preferred and practifed 
 by all who would excel in this art. 
 The inftrument being planted at the firft ftation, 
 ‘fix the index to 360 degrees on the limb, and fett- 
 ing the plate truly horizontal, turn it about till the 
 fouth end of the needle hangs over the Fleur-de-lys, 
 or 360 in the box, and fix it in that pofition by help 
 _ of the {crew underneath ; then difcharging the index, 
 turn that about, and direct the vertical hair in the 
 telefcope, to cut the fecond {tation ; there fix the 
 index to the plate again, and the fouth end of the 
 needle will fhew the bearing of the firft line, which 
 will alfo be cut by the index on the limb, and is to 
 be entered in the field-book, as before fhewn. Now 
 when the inftrument is removed and planted at the 
 fecond ftation, obferve that the index hath not been 
 fiirred, and turning the whole limb about, direct 
 the vertical hair in the telefcope back to cut the firft 
 ftation, fix the platein that pofition ; then difcharg- 
 ing the index, turn it about till the fame hair cuts 
 the third {tation ; there fix the index to the plate 
 again, and fet down the nuinber of degrees and mi- 
 nutes it cuts on the limb, which number will at the 
 
 H 2 fame 
 
 
 

 
 ( 100.) 4 
 fame time be cut by one end or other of the needle 
 in the box, if there be no miftakein the obfervation: _ 
 Proceed in like manner at the third and all the fol- _ 
 
 lowing, ftations, always remembring after you have 
 
 turned the plate about, and directed the telefcope 
 
 backwards, to obferve that the index remains fixed 
 
 at the decrees laft noted in the field-book, fo will % 
 
 the needle be always found to correfpond with the q 
 
 index fufficiently near, to difcover and prevent any 
 error in the work, 
 
 We have here added an example of part of the 
 field-book of an actual furvey, wherein the angles 
 were obferved by the method above defcribed; and 
 though there were 24 {tations in the circuit, yet for 
 proot, the inftrument being planted again at the firft 
 ftation, and the telefcope directed back to the 24th, 
 the plate being fixed in that pofition, the index was 
 difcharged, and the telefcope direéted to the fecond 
 {tation, and then the index cut the fame number of 
 deerees as was firft fet down in the field-book. 
 
 When there is occafion to return to fome former 
 ftation, in order to go off from thence for the clof- 
 ing fome particular part, as in the following ex- 
 ample, we return to ftation 23. Enter the number 
 of fuch ftation again in the field-book, with a {mall 
 figure at the fan of it, denoting hie often the in- 
 {trument has been planted at that ftation, thus 237 
 denotes the fecond time of planting the inftrument 
 
 at {tation 233 then confider from which itation you~ : 
 
 locked forwards to the prefent ftation 23, which was 
 ftation 22; feek in the field-book the bearing of the 
 line between the ftations 22 and 23, and fix the 
 index to that number on the limb; then turning the 
 plate about, direct the telefcope back to the former 
 {tation 22, fix the plate in that pofition, and dif- 
 charging the index, direét the telefcope forwards to 
 the next ftation, and thence proceed as before ; fo 
 will the needle be always found to bea fure cheque 
 
 on 
 
 
 

 
 Pa, v Hox”) © 
 
 a 4 on "he imb, tho’ the obfervations do not depend 
 ye thereon, 
 
 ey The letters affixed to the numbers of the ftations 
 
  in_the following field-book, are not to be 
 
  -ufed in praéiice, being here added only for the 
 more eafy referring to the plot, in defcribing 
 the new method of laying down. 
 
 
 
 Betinber ‘slows’ it, it means that both the numbers 
 f ; i. to be laid off on the off-fet line. 2, fignifies an 
 angle or corner. 
 
 
 
 a Bs FIELD- 
 
 
 

 
 
 
 F LELD-BOOK of Part 
 the Manor of RB » Ga 
 
 
 
 Remarks, Left. 
 
 
 
 
 
 
 
 
 Renciie - + oie , « = 
 Hedgebuts to Kiln Wood 20, 
 Againft Kiln Wood - -| 27 
 Hedgetoditta - - -| 3% 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2. + laff Bearing - |- - -\204:40 
 ; 30,175 
 15 280 
 301 400 
 : 21} 560 
 Hedgebuts to Furzfield 14 746 
 | ges, 
 : © 3 (©) 
 Againft Furzfield - - Ve Fern) 
 | Re rete oe. 
 I 100 
 31 200} 
 21 305 
 
 (44610 far clofi ing Furefeld and 4g 
 
 Hedgebuts to Furzfield Ne, oo aa”, A Lang re 
 
 againfi upper Poundfiel Bie) 5201 . . 
 
 | 0 4(D) 
 19550 
 | 46} 140 
 | —Hedgebytsto WoodsGa| 41 255 
 
 Depth of the Gard. 216 
 Pound begins, andFence-| 48 500 
 buts ends 46 527 
 

 
 \ J 8) toGareinto lower Pound 
 oe" ahi } : nd field, 
 | Woods Houfe 3 30 deep } ‘ é ; B . | 
 : | : ae ar 2h Hedgebuts to Lower 
 | PB Bp of Woods Garden| 2A) 272 | Poundjield againfe 
 E. ; 113 deep, and Hedge 300} 32 Pondjield. 
 Zz «buts to upper Pound- ! 
 ! a: field ua’ \aege 
 e 201 350 
 - Gate- - - - - 281/34 28318. 20 
 A44] 2 3!Hedeebuts toC awhou/e= 
 
 J 5 465 field. 
 : 127d eee). 25 
 : ® 6(F) 
 | 107350 
 Raid = Toe = SM 58 2 6'Gate. 
  Hedgebuts to Upper| 42 155 
 
 Poundfield againfi 200), 29 Hedgebuts to Ribas 
 
 Little Boggyfield 
 
 lige eG) > ee 238)- : -|Gate. 
 6" B00) j. 22 
 2 7(G) 
 ee ely ae 
 , 15 O12 
 170} 6 
 Lane returns + - - 21 186 
 
 Zr 4againfiGravel -pit- Wi 
 . field 
 
 Hedge to Barnfield - - 7 
 
 — 
 
 eat dae Ep eT) go 
 
 ro Osteen We 
 
 268320 
 50|x Gatelinto Pound Lane 
 
 feld againft the Hop- 
 222) 16) pit. 
 
 200) forlihe Return N° 32. 
 247)19 XiGate into Moor’s Bare: 
 
 field. 
 267 
 
 
 
 = 
 

 
 
 
 Ponds begin in Gravel- 
 pit field } 
 
 Ponds end - - ~ 
 Gap - - - = - 
 
 Fence changes to Gra- 
 wei-pit field, 
 
 Gate - - - 
 From bye ©) at 330 in 
 
 Line 11, 12. 
 } 5°}90 
 339123 
 319 to © |383|- -© 
 N° 11. [100] 6— 
 280} o 
 315139 
 Ba ia Bi 
 | 130} 4 
 oe 170! 
 . 286/58 
 ! Ns 375)69 
 : 440} O 
 -) IOl4.80 
 tla § 1951494 
 Field oS as 
 1568)x Hedze & 
 Brook into} Alders 
 
 
 
 34 xGravel-pit feld Hedge 
 45 into Ditto, againfR 
 Home field Hedge to 
 P21 ditto, eS 
 
 «bbl Hedgebuts to Dung field a 
 
 Gate. 
 
 oO 
 
 
 
 
 
 Cumbers’s 
 
 698| x Bill 330lbye @lfor the Alder Ground. 
 |FieldHedge Alder Ground. 
 
 {720\f0 © 13 
 
 x Hedge and Brook inte 
 

 
 Hedge. 
 
 
 
 
 ‘A5\t0 Gate-+-60 to Zr. 
 Hom fted. 
 
 
 
 
 
 
 
 
 
 
 Go Hillyfield Hedge - - 
 Againft Alder Ground 
 
 Be 
 
 
 
 
 To Alder Hedge 45 -- 
 
 
 
 field Hedge into Boggy- 
 
 Be I pans 6lx billy 
 To Al. hedge 81-4- Corn 44 “nel. 
 
 To Alders - - = - 
 Fo Kilnfield Hedge - - 
 To Alders een 
 To bunting Gate 55 -+- 
 
 Point of the Yland59+| 3° 
 
 
 
 
 
 
 

 
 Cea (eahoo ays: 
 
 
 
 + 
 
 Aan Lland - - -| 
 Fence toditta - - -| 
 
 Corner 2 = 2 
 
 Hedge to Bogeyfield - 
 | Wacdland ends - - 
 
 
 
 19] x |Bocgyfield Hedge to 
 Againft Acre Bit - - 240 Broomfield. 
 
 > 
 
 
 
 | 74, xX Acre Bit Hedge to dit. i 
 To Alders - + = |. 150 Oo 
 
 To Hedge : ns 
 
 To Hedgets-+- - - 
 25 -- aha 
 

 
 
 
 
 
 
 
 t : 
 \Acre Bit-hedge into lit-~ 
 tle Broomfield. 
 
 
 
 
 
 i 290310 
 e. 49 20 
 Again Kilnfield Gate |- - -|__ 17° 
 4 | 16 23 (Y)] 
 A 104:00 
 
 
 
 en enn 
 
 © 24(Z) 
 
 = 7 
 Twi 
 
 243) x jHedge into Warley Com. 
 
 To © 1 where the 
 1 7 from the laft Bear- 
 ing to ©) 2 was found 
 to be 43°:20 as at 
 
 firft fetting out. 
 
 lagainft Kilnfield Gate. 
 
 x \Gate into woody Ground 
 in Kilnfiela. 
 
 Q25%X\out of Wood into field 
 a | agft Kilnwd H. te dit. 
 
 
 

 
 
 
 
 
 
 
 
 
 
 324) 12 
 465, 26 
 510)" Ga 
 580, 72) 
 630] 55) 
 i 890) 
 ©25 (a) 
 is 84.240 aq 
 if 37| 18x into Posey Wood tie 
 ‘ So} 15) 4 ditto. 4 
 \ 1 | 246) aap E 
 P 3 ©26;b) | 
 — (284: 40 
 i Spe We 
 i 170; 50 
 i 209 x into Furzfeld Henge to dit. 
 ; | 224! 53 
 i ©27 (c) 
 it 105:30 
 \ | 100, 29) , 
 : 1QO; to Corner clofe Kiln Wood. q { 
 i Returnto- - +4 © j25* (alee - i ae Kilnfield. 
 | 
 
 
 
 . | 39; 33 again# Boggy Wood. 
 
 
 
 
 
 280] 37 é 
 396\- - -Hedgebuts to little Pies 4 
 424) gyfeld. Aa 
 ©28(d)| 
 : 2.52: 50 if 
 ft 34 X Bogoyfield Hedge inte 
 120) 45 ditto. 7 
 | 200} 42 
 “ae Be 
 : : 
 : 
 
f Me 
 Ope Waa: ele on 
 
 
 
 
 
 
 
 
 
 
 
 uae eA, 100”) 
 \O29 (e) 
 . hs 79:30 4 
 catia OR ee 1OooO 35 r 
 Strait Hedge to Pound-\- - - 161 x Upper Poundfeld Hedge 
 “eat 190 into ditto. 
 tig? ——!_—_— = |—— 
 ay J © 30 (f) : 
 ie 225:12 
 50, 28 : 
 158 x Furzfeld Hedge into dit. 
 187 : 
 ©O31(g) 
 184:00 
 35) 30 Corner. 
 | 65) 45 
 300 oe 5 
 eas 428 | 40 @\27 clofe Bogsy Wood. 
 Return to = - =) ss) 31” (g) 
 100 80 
 fie 314] © #0 for clofing Furxfield in 
 Ret. to© for the Re- ) -—— a5 Thy ———— Line 3, 4. 
 turn of Pound-lane O | 32 ( ) againft Gravel-pit field 
 at 200, in Line 7,8 68:20 Hedge to ditto. 
 147} 29 
 
 Hedgebuts to little Bog-) 11 212 
 
 
 
 Ki gyfield. 237\- - ~|Alders end. 
 | 306] 
 © 33 (1) 
 172:08 
 Stile in Boggyfield Hed.\ 110 118 
 7 8 390 Pond, 
 50} 454 
 28} 574 
 43) O15 
 
 670| to ©}28clofe little Bogeyfyld. 
 
 
 

 
 Return ita - - o 
 
 
 
 H Godel pie ‘fold H i 
 69 ‘into mete ee A. 
 
 
 
 Gy Kilnfeld ~~ - . 
 he hier: again | 
 
 Refura face ie es va 
 Kilnfield Gate. | 
 Nott : x out of Wood into. Kila- 4 
 Againfi Woody Ground jela. 
 j Kilnfield. 
 
 Corner - + © = 
 

 
 ‘Paffage to Iland - - - 30 50 X\into Woody Ground. 
 By uct | 165 x|Rill. 
 ee ; i 45 256 85 x into Land. 
 a 120} 390 
 455) 80 
 gol 520 
 57O.-- VO} Corner. | 
 50] | 594 To the Top of the Iland. 
 | FBciurk be on apie -| 0! (387 (0) 
 | 357:00 
 $71 
 
 4 
 
 bi 181:48 
 
 
 
 X|Kilnfield Fence inte 
 
 rough Ground. 
 
 451 XiGravel-pit field Hedve 
 473 into ditte. 
 ©39(p)) 
 235:55 
 248 15 Railshutt +- 61 to 
 
 ; rough Ground Fence. 
 
 ‘a 
 . (1Kilnhoufe 33 deep +x 
 be 16 35 to Fence. 
 
 674126 
 Hi f Workboufe 65 deep. 
 Chfe Gravel-pit field 7651 x linelz2, 33 clofe Kilnfeld. 
 
 
 
 Now 
 
 SRE a Rg oe PTE eer erage Pee ee ee ee ty eee er Se adiaisea ee 
 y= > : = Se See ei i Kak =i. ako o >in oon oon . Fg eg ag eg ee a ee a 
 ee eee cae ee ee ae ee eS oe ee ae ae ee oe yy Se = soe ae 
 

 
 - SO ae ee — o% 
 es a ne 
 
 er 
 
 
 
 Ses tn 
 
 
 
 
 
 al 
 5 
 
 (1921) 
 
 Now to protraét the foregoing obfervations, thro? 
 the middle of the paper defigned for the draught, 
 draw the right line NS for ameridian, Plate [I].and 
 therein chufe a convenient point C, to which lay the 
 center of acircular protraétor, the diameter coincid- 
 
 ing with the line NS, and the 360, or beginning of 
 the degrees being towards N the north, fix the pro- 
 tractor in that pofition by laying a weight thereon, 
 or pinning it down; then on the circumference of 
 che protractor prick down the feveral bearings noted 
 
 in the field-book, numbering from the north eaft- — 
 
 wards, or towards the right hand all round, and to 
 each point affix the number of the ftation to which 
 it belongs. 
 
 Chufe a convenient place on the paper foi the firft 
 flation, as at A, and laying the edge of a parallel 
 ruler to the center C, and the point ‘marked I, Open. 
 
 the ruler till the edge cuts the point A, and thereby | 3 
 
 draw an occult line ~ parallel toC 1, on which fet off 
 the firft length (165) from A to B, the ad ftation ; 
 then laying the parallel ruler to C and the point 2, 
 transfer it to B, and thereby draw an occult line, on 
 
 which fet off the fecond diftance (766) from Bto C, 
 
 the third ftation: Again, lay the parallel ruler to C 
 and the point 3, transfer it to C, through which 
 
 draw an occult line, and thereon fet the third di- 
 
 {tance (520) from C to D the fourth ftation. _Pro- 
 ceed in like manner all round, and if the work be 
 true, the laft line will pafs through the firft point ; 
 but if it doth not, and the error arifes by miftaking a 
 whole chain or fo, it may readily be difcovered in 
 which line it was committed by obferving whether 
 the laft point fall fhort of, or beyond, or above, or 
 below the firft point with which it ought to co- 
 
 incide, uae 
 The only feeming difficulty that can arife in draw- 
 ing the ftation lines by this method, will be to di- 
 ftinguifh between an infide and an outfide angle, 
 though 
 
 3 
 
 
 
 al 
 

 
 
 
 
 
 
 
 
 
 
 
 
 a ‘at i i ; nie } 
 
 an fel ca be any obftacle to the fur- 
 ft the dimenfions, and who by the idea 
 the nd, will, for the moft part, remem- 
 er he turned off to the right or left at fuch 
 a {tation ; yet, if he fhould at any time 
 
 lays work to protract, and a multitude of fhort 
 ions therein: Or, if any perfon who never faw 
 
 and, fhould attempt to draw it out by the feld~ 
 ky and find himfelf at a lofs about the quantity of 
 al ele; then let him fubtra& the bearing at the 
 ae ftation from the bearing at “the pre- 
 ent itation in queftion, increafed by 360, if fub- 
 ae raction cannot otherwife be made, and the> re- 
 mainder gives the prefent angle ; which if it be lefs 
 
 fe 
 ex 
 
 fs than i80°, fhews that the line flowine from the fta- 
 
 | ie at © 17 noted with R, ic might be doubted, 
 + sit the line from thence fhould be’ drawn in- 
 Fe = towards f, or outwards towards S ¢ to folve 
 be hich, from the bearing at the prefent © 175 280° 
 “ fe Bes fabtraét the bearing at the laft © 16, 23°: 20, 
 _and the remainder 247°: 30’being greater than 180: 
 a 
 ~~ 00, fhews that the line mut be drawn outwards to- 
 : * _ wards S 3 the fame doubt might alfoarife at © 18 (S), 
 but if from the bearing at © 18, 347°: 50’, we fub- 
 tract, the bearing at the laft © heel a Ss the re- 
 _ mainder 67°: 00 fhews it to be an infide angle: 
 ° Again, at © 19( T) the bearing is 27°: 25’, to which 
 _add 360° , and fubtraét the bearing at the laft © 18, 
 "349°: 50, and the remainder 39°: 35! fhews the 
 prefent angle tobe an infide angle, and ver y acute. 
 When the draught is fo large, that all the {tations 
 cannot conveniently be laid down about one centre, 
 the firft meridian line may be prolonged, or another 
 drawn parallel thereto, in which the furveyor may 
 Mmake choice of a new centre where he fhall think 
 moft proper, and round this he may place his re- 
 Maining {lations in like manner as before Hikes 
 I an 
 
 it may perhaps happen when he has {e- 
 
 _ tion mut be drawn inwards, BAC rore, outwards. 
 
 
 
 —e 
 
 - 
 xy 
 

 
 
 
 
 
 
 
 ( 114 ) 
 and thus, he may chufe as many centers as he 
 find necefiary, but the fewer he can difpenfe wit 
 the better. 
 
 Moreover, the bearings may be laid down by § : 
 femicircular protractor numbered, as it is commonly — 
 done, with a double row of figures to 360°, which — 
 fome may rather chufe to ufe, becaufe the limb_ 
 thereof may be turned wholly towards tHe light, that | : 
 fo the divifions may be more advantageoufly feen 5 ; 
 but confidering the edge of a protractor is always” 
 mace very thin, there can be no advantage gained ~ 
 thereby ; befides the circular ove is to be preferred 
 in‘that it hath twice the room, and confequently, — 
 when there is occafion for laying down a great num- ~ 
 ber of obfervations about the fame centre, they will — 
 be lefs liable to confufion. Again, the degrees on @ 
 the limb of the inftrument and in the box, may be 
 numbered only to 180, and then begin again with ~ 
 10, 20, &%c. to 180 more, by which means that © 
 end of the needle which is next the eye, will always 
 cut the fame divifion in the box as the index doth on © 
 the limb, and there will never be occafion to enter a k 
 bearing greater than 180° in the field-book ; fo a © 
 femicircular protractor numbered with a fingle row of 
 figures, will ferve to plot all the obiervations ; but 
 then there will be this great difadvantage (as wee as 
 the foregoing in point of room) that, fhould thea 
 furveyor forget whether any angle was more or lefs © 
 than 180°, he could not readily difcover which to : 
 - make ufe of ; and fhould.a perfon, who had never ~ 
 feen the Jand, go about to protract the work from 
 fuch a field- Bak alone, he muft be gravel’d at every 
 _ ftatton where the angle approaches near go° or 270°, : 
 as not having any means whereby to difcover on — 
 which fide it is to be formed, tho’ this doubt may © 
 in ei meafure be prevented by noting the angle ; 
 in’ the-held by the-mane-4:, Oray. according as it~ 
 is within or without; yet fhould the furveyor put 
 
 down 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 wrong: ak or forget to enter any (which 
 “happen when a multitude of obfervations 
 be taken, and the weather proves untoward) 
 
 cafe a great deal of time may be fpent before 
 -afcertained whether the angle be internal 
 -external, which is very readily known in the for- 
 er method ; therefore that mutt be the mott pre- 
 
 ‘oins part of this book, that a farther explanation 
 | ould be altogether needlef, 
 
 43 ngs, there never can arife any difficulty concerning 
 _ which way the line is to proceed from the laft fta- 
 tion ; for as every ftation line is to be drawn ina 
 
 of the protractor to the direction in its circumference 
 marked with the number of the ftation; therefore its 
 _ pofition is naturally afcertained by drawing the line 
 _ in that direction, 
 
 f The figure in Plate 1V. fhews how the contents 
 aot the foregoing example of part of an actual furvey 
 was caft up; and here are likewife fubjoined the di- 
 - menfions and calculations ; whereby it may be feen, 
 
 “that notwithftanding there are 10 feveral pieces mea- 
 
 tured feparately, yet when the whole plot was reduced 
 to the trapezium: MNOP equal thereto (by Prob.10. 
 page 8.) the content of this trapezium was found not 
 to differ from the fum_of the feveral contents by half 
 a pole, a confirmation of the truth furprizingly 
 “near, | 
 
 | , 
 
 I 2 Gravel- 
 
 ble, fince | it can never be fubject to any fuch in- 
 Tae : venience: And the practice thereof will be found | 
 very ealy to any perfon that underftands the fore- 
 
 
 
 
 
 direétion parallel to an imaginary line from the centre- 
 
 SS ee ee a 
 
 ayy 
 
 vat 
 j 
 
 ==> 
 
 erties 
 
 A 
 
 Set ty sy eee 
 

 
 Hi Gravel spit field with rhe 
 ~ fmall parcel of Alders 
 ~ gn the middle ‘of it. 
 
 reduced to the A 
 
 abe. 
 
 The bale ad: 
 | meafured - - tne 
 The Bets 1078, 
 cular from ¢ 
 14064 
 
 12306 
 
 17580 
 1819|5124. 
 ‘Area per? & ®_ F: 
 Sect. 4. 9 ae Se 36 
 Subit) itd. -:-o s12;' 14 
 
 Area of amy mass 
 thefieldg «= $3.72 
 
 
 
 The Alder wood on the 
 
 weft fide of Gravel- 
 pit field reduced to 
 the A ghz, 
 Ree do8 
 
 _ 805 
 
 from } - - 
 Bale es ° 
 
 "2990 
 
 47840 
 4|8|1390 
 
 Content - - 2:15 25 
 
 aes ia 
 
 
 
 
 
 
 
 
 
 
 
 The sfenill ean 
 Alders in the mid 
 Of ° Gravel-pit field 
 reduced to the ay 
 
 Od eR cae, 
 The bafe d: a 655 
 Perpendicular fy ‘ 4 : 
 from ¢ - ry Mies 
 
 ,. 28am 
 
 4585 
 
 “065. a 
 
 rn17245° 
 
 a A. ‘RE Pe 
 Content - + o:2:14 
 
 ‘a 
 A a 
 
 Kiln field reduced to! t t 
 Akilma . 
 The bafe Jaz - - 
 
 
 
 “Bag 
 
 from & - - har 
 
 
 
 3650 
 182500 — q 
 + 812186598 | 
 ee Py 4 : 
 7 9:0: 23% 
 
 Wooty 
 
 
 
 Content -— 
 
 ug 
 

 
 Upper Pound Field 
 oto fo. the A | 
 Fe MORE : | 
 _ The bate w x - = 930 
 Le ied aye c 404 
 3720 
 
 558 
 
 on 
 41311520 
 
 oe Aes Rs) P. 
 Content ee BO 26 
 
 Be rood Fealaced to 
 
 
 
 meine A DE s, 
 Wihe bale DE.- - 955 
 roms + - - - - 480 
 76400 
 3820 
 
 Be a 41518400 
 
 P. 
 Content - 
 
 
 
 A; o 
 Beat ins. O7 || 
 
 ‘Teele Bogey Seid: re= 
 duced to the Sa 
 
 ey Olan a 4 
 
 The Diagon. Fifi THz 
 
 | of la ce at 680 
 gu fromz- 300f - 
 
 
 
 Content - 
 
 
 
 Woods houfe and garden 
 reduced to the A 
 ABC, 
 
 The bafe BC - - 
 
 375 
 Perpend. from A 
 
 Oi QT 
 2625 
 3375 
 | Aree 
 1713875 
 
 A. Hts P. 
 
 Content - O:1: 19g 
 
 
 
 Furz-field reduced to the 
 A FGH., 
 
 The baleGH - 929 
 SPORE Ee Ne 249 30 
 5574 
 2787 
 2787 
 
 ARETE 
 AL a P- 
 Content = 1;2: 19 
 
 ] 3 Kaln 
 
 
 

 
 , , 
 
 Ons) 
 
 Kiln ‘wood eahibed: to 
 
 the ATKL, or as 
 
 The bafe KI." 14.47 7 
 
 Perpendic. from I 450 
 
 | 72,050 
 Zon 
 
 71912550 
 
 capuige Ahad Mies UE, 
 
 Content 4 a8) o's 9°: 334 
 
 
 
 The whole plot reduced 
 
 
 
 
 
 
 
 to the Trapezium 
 MN OP. 
 Perpendicular ae 
 from N - 1963 
 Ditto from PB. -.) 9470" 
 Sum - 2733 
 Diagonal MO ~- 2868 
 : 21864 
 16398 
 21864 
 5466 
 7813/8244 
 Ay Rees 
 Content - 39:90: 30 
 
 as on the nght. 
 
 a” 
 #0 
 
 ladies Field oy Ae ~ R 
 
 ‘baled Wood rie | Ne 
 
 
 
 
 
 T be Conte 
 
 with the dl- 
 
 ders eee 
 
 Oy Sinks 3 
 
 a ee 
 
 Kiln Field — pe 9: O 2 
 Woody Croan Cae es Y 
 Little Bogey al ak ne 9 q 
 Upper Pound Field 2: ° si ee 
 
 Weeds Houfeand acai 
 Garden - - oO Paha: | 
 Boggy Wood - = "a * 
 Faure Field = 0 > Te02. 
 Kilo Wed = -' 903 We cese 
 Toe Pde ae 
 
 im 
 oi 
 es 
 
 4 ee 
 

 
 
 
 
 ving of Shoals and ea by a of the 
 i New Theodolite. 
 
 Tt AHERE are three methods earn this may 
 fi sCbee: performed ; for the obfervations may be 
 
 de either on the water or on the land. ‘hofe 
 de on the water are of two kinds, one by the log- 
 
 | 7 courfe and diftance round the fand ; and then to be 
 plotted as a large wood, or any enclofure taken by 
 the circumferentor. d 
 This method I omit for two reafons ; firft, be- 
 - caule i it is to be deduced from the writers sof naviga- 
 tion; and, fecond ly, becaufe the difances thus mea- 
 P Priced are liable to the errors of currents, which ge- 
 _nerally attend fhoals or fands, that are near to the 
 fhore. © 
 The fecond method, where there are no diftances 
 to be meafured on the water, tho’ flill there is one 
 inconvenience, common alfo to the former, becaufe 
 | © the bearings or obfervations are to be taken on that 
 unftable element, (an-error fcarce mentioned by our 
 practical artifts ) 1 fhall briefly hint at; and {fo ra- 
 
 ‘ther chufe a third, which is liable to neither of thefe 
 
 imperfections. 
 
 Let (in Fig. 30) a boat be manned out witha fie- 
 nal flag, a log and line, lead and line, and to ob- 
 ferve the bearings of any land-mark, a cone fs with 
 _ fights : 
 
 ‘Take two or more places, as A, B,C, on the 
 -fhore, from whence the boat may be feen on the 
 feveral parts of this fhdal, . 
 I4 One 
 
 line and compafs (as in plain fail ling) meafuring the 
 
 ty 
 
 
 
 ry 
 

 
 
 
 
 
 
 (120 ) Ohya 
 
 One of the boat’s crew is to found till fe 
 himfelf on. the edge of the fand, by the dept 
 water, and then to come to an ‘anchor ; 3 which be: 4 
 to fignify to two perfons on the fhore, at B and C, — 
 by his fignal. And then from thofe known bas . 
 marks, B and C, the obfervers are to take the bear- | 
 irfgs of the boat, and to regifter their obfervations 5 
 which, when done, they are to fignify to the crew — 
 by waving a flag, or by fome other fignal. 4a 
 And in the mean time, to prevent miftakes, lee ya 
 the crew, take the bearings of each of thefe land- 
 sii = : Then weigh anchor, which fuppofe at D. 
 \ Then by founding, proceed to EB, and make like ~ 
 obfervations. And io at E, F, G, &é. till youl have 
 furrounded As fand. 7 
 And if in’ this procefs, you are about to lofe the 4 
 feht of oneof your land-marks, fuppofe C, let your © 
 afiftanc at C, who, at that time, will alfo be about | 
 to lofe the fight of the boat by fionals (before-hand 
 agreed on) remove to fome other “objet before-hand | 
 asreed on, fuppofe to H; and then to. proceed ag 
 before. 4 
 Laftly, ifthe fand runs fo far out to a that the 
 objeé& cannot be feen by the boat, nor the boat by — 
 the obferver on fhore , there may be rockets fired * 7 
 by t the boat’s crew. and alfo by the obfervers on fhore 
 in the night, whereby thofe bearings may be taken 
 almoft at as great a diftance as the ‘light can be feen. 7 
 For fuppofing th ey rife but a quarter ofa mile above 
 the apparent horizon, its ftay will be about 9 fe- 7 
 conds, and its diftance for this quarter of a mile will — 
 be vifible about 44 miles. - 
 ut rockets rife much higher, and then the di- = 
 ftances are much greater, “whereby they are vi- : | 
 fible. / 
 Or two boats may lay at anchor inftead of the : 
 Jand-marks, and then you may work as before. | 
 
 Now. 
 
Babi t = ; ' 
 
 iG yar ) | 
 
 Now, fince the land-marks B and C are fixed, 
 ofition may be Jaid down in the draught, as 
 on furveying, by plotting the diftance be- 
 B and C. ‘And then, by plotting the line 
 nd the line DC, according to their pofition, 
 eir common interfection, will give the point D. 
 din like manner EK, F, G, &c. may be plotted ; 
 
 fo the fhoal: And this froin the bearings taken 
 
 
 
 
 
 
 
 
 
 If this he a ftanding lake, environed by bogs, not 
 _ be walked on 3 che ewvacion: at D, FE, F, £5C, 
 taking their oppolites, may fuffice to plot the 
 fame from the land-marks A, B, C, &c. as well as 
 thofe taken on the land; or, indeed, by the courfe 
 and diftance, as in navigation, if the water be 
 -fmeoth and without a current. 
 ee; fea-fhoals, it is convenient to note at each ob- 
 fervation the depth of the water found by the lead, 
 and the drift and fetting of the current by the log 
 and compafs, while the boat is at an anchor, which 
 may be done with eafe and expedition enough. For 
 while the boat rides at an anchor, her ftern points 
 out the fetting of the current, and the log and glafs 
 will meafure its drift. 
 
 _ And thefe ought to be noted on the draught, 
 . which may be thus : : 
 
 The currents may be fhewn, by drawing a dart 
 
 pointing out its fetting, and its drift by the Roman 
 capital letters, and the depth of water by the {mail 
 figures, 
 
 All nocturnal obfervations ought to be feveral 
 times repeated. 
 
 SECT, 
 
 i 
 
 
 
 
 ——— 
 
 =s 
 7 
 
 > — eS = 
 
 wd tb bas 
 
 etre ne ey etek piel ett tele ters ety 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 RN SYilew Sa iy, 3 
 ES SNGe. <a} aa 
 Sie wag, Ol SARL @ 3 
 
 SOF Water-Levelling, or the conducting off Water: | 
 
 HE firft thing celery to this poeple is” ' 
 the adjufting of the level, which may be per- 
 formed feveral ways: This that follows is. eo my 
 and natural. 
 Chufe fome cround which is not abave 4 OF 5 Foon 
 out of the level, for the diftance of 8 or 10 chains 
 length, and fuppofe it be AB (Fig. 91.) and find the 
 middle between A and B, which fuppofe to be C; 
 plant the inftrument at C; direct the tube to a fta- 
 tion-ftaff, held up at A, and elevate or deprefs the — 
 tube, till the bubble is exactly in the middle of the 
 divifions ; then by fignals direct your affiftant at A,» 
 to raife or deprefs the vane, fliding on the ftation-- 
 -ftaff, till the horizontal hair in the glafs, cuts the 
 middle of that vane; then fee how many feet, inches, 
 and parts, are cut by the upper part of the vane, 
 which fuppofe to be 3 foot 4 inches and 6 tenths. 
 In ike manner direé&t to the other ftaff at B, and 
 fuppofe the upper edge of that vane to cut at the 
 height of 6 foot 5 inches and two tenths ; ; then will 
 thefe two vanes be on a level. 
 From 6 foot 5.2 inches fubtra&t 3 foot 4.6 eae 
 and referve the remainder 3 foot 0.6 inches, 
 Now, remove the inftrument as clofe to the higher 
 ftation-ftaff as you can; fo that the middle of the 
 telefcope may almoft touch | it, ‘Then bring the te- 
 Jefcope as near to a level as the judgment of the eye 
 will direct, . 
 Meafure 
 
of 123 vi : 
 
 oh ee the ‘ground, the height of the top 
 elefcope 5 and alfo of the bottom, in feet, 
 ni parts: Suppofe them to be 4 foot 10.5 
 ce 5 foot O. 3 ‘inches ; ; then half the fum 
 
 
 
 
 LAS 
 
 ug iNow, fo elevate or deprefs the hair or the bubble, 
 . “till the hair cut the middle of the vane at B, and at 
 “the fame time the bubble ftands in the middle of the 
 divifions ; and then will the inftrument be duly ad- 
 > jutted. 
 | pelt you have a mind to be curious, repeat the ope- 
 : ration ; but when you place the inftrument at C, 
 ‘turn the tube at right angles to the line AB, and 
 there fet it level ; then proceed with the repetition 
 of the work. Only obferve to crofs-level it in this 
 _ adjuftment, and in all future ufes whatfoever. 
 Or the level may be adjufted thus: As before, 
 firft plant the inftrument in the middle between A 
 and B ‘Fig. 32.) and obferve the heights on the fta- 
 tion-{taves, which fuppofe to be as above ; ; and con- 
 fequently their difference, as before, is 3 foot 0.6 
 inches, Now meafure from C towards the higheft 
 sround A, fome diftance that comes almoft to A’; 
 -fuppofe 4. ‘chains. to D, and DB will be 9 chains, 
 and DA one chain: Then plant the inftrument 
 at D, direct the telefcope to A, and, fetting the 
 bubble to the middle of the divifion, direct your af- 
 fiftant to move the vane, til! the hair cuts the middle 
 of it; and note down the feet, inches, and parts 
 eut by the upper edge of the vane; which fup- 
 pofe to 3 foot 8. 4 inches : : To this add the diffe- 
 rence 
 
 é : Sr 
 a ba : 2 Son es 3 ss ta Ba, VP Ei oe ion 
 : ae ere ° : Paseo Rem < SECS eae ee 
 ete Ye le hn OS ~ ~ a fa : ie ‘ , 
 3 3 - ~ av 
 Ty Ee ty ms we a aed tome te os on = _ 
 
 ~ eee SS — ee —— 
 
 —_ tsrae 
 
 > === {Tt a x. = = ———= 
 £ x. > 
 
 » = * 
 wot oat f ES Oe oe es ee ed 
 
 
 
 x 
 I 
 te 
 
 x 
 
 prt 
 
 ctr 
 
 ae 
 
 cee ee by * 
 

 
 (¥24 
 
 rence 3 foot 0.6 ‘inches, and the fum 6 foot g Soi 4 
 
 ches referve. 
 
 Now direc the telefcope to ite Raff at B, level ep 
 and direct your affiftant to move the vane, till ie 
 hair cuts the middle thereof; and then, if the — 
 upper edge of the vane cuts the foregoing fum6 foot 
 g inches, the hair and bubble are truly adjufted. But — 
 if not, fay, As BD wanting AD, is to the diffe- — 
 rence between the numbers cut by the upper edge of 4 
 
 the vane, and thenumber 6 foot g inches; fo isthe 
 
 diftance AD to a number, which added to that cut 
 by the vane, when lefs than 6 foot 9, and fubtracted 
 from the number cut by the vane, when it is greater 
 than 6 foot 9, will give a number, to which let the 
 affiftant fix the vane; then fo elevate or deprefs the 
 hair or the bubble, till the hair cuts the middle of the 
 vane at B, and the bubble ftands in the middle of 
 the divifions; for then the level will be adjufted. 
 The siya may be again repeated, and at every 
 
 aoe crofs-levelled, which will confirm the former a 
 
 adjutt ment. 
 
 After the inftrument is duly adjufted, you may 
 proceed to ufeit. Let the example be this annexed, 
 (fig. 23.) where A every where reprefents the level, 
 
 and B the ftation ftaves; and fuppofe the rout be 
 
 made from a to e; firft plant the inftrument between 
 the ftation ftaves a and b: at A direét the level to 
 aB, bring the bubble to the middle of the divifions, 
 and inftruct your affiftant fo to place the vane, that 
 the hair in the telefcope cuts the middle of the vane ; 
 then in a book divided into two columns, the one 
 intituled Back Sighis, the other Fore Sights, enter the 
 feet, inches, and parts cut by the upper edge of the 
 vane at aB, in the column intituled Back Sights. 
 Then look towards the other fiaff b B, bring the 
 bubble to the middle of the divifions, and ‘direét your 
 affiftant to place the vane'fo, that the hair cuts the 
 middle of the vane 5 then enter the feet, inches, and 
 
 4. parts» 
 
 a 
 
 BEN, 
 =a 
 he 
 | 
 a) 
 ee 
 ’ 
 omy 
 i” 
 ay 
 J- 
 i 
 i 
 a ¥ 
 BY 
 ah: 
 x 
 ‘on: 
 Vee) 
 A 
 ee 
 a 
 “e 
 eB 
 ¥ 
 . 
 ed 
 iF 
 ay 
 q? 
 a 
 
 thy Seis 2 : 
 
 
 
 
 
ae 
 
 
 
 
 
 
 
 
 
 
 
 + ae ; iat, See, y 
 parts cat by the upper edge of the vane, in the co- 
 | ymn of Fore Sights F | 
 
 “Now, plant the inftrument at A‘, ftill keeping the 
 
 ‘Bb exactly in the fame place, and carry the 
 a B forwards to the place cB; now look back 
 > ftaff bB, and enter the numbers cut’ by the 
 vane there, under the title Back Sights ; then look 
 forwards to cB, and enter the obfervation under the 
 title Fore Sights. Do the like when the inftrument 
 is planted at As, A+, &c. always taking care to keep 
 the ftaff in the fame place when you look’d at it for 
 a Fore Sight, till you have alfo taken with it a Back 
 «Sight. 
 Bes rites finifhed your level, add up the column of 
 Back Sights into one fum, and the column of Fore 
 Sights alfo into one {um ; and the difference between 
 thefe fms is the afcent or defcent required. And if 
 the fum of the Fore Sights is greater than the fum of 
 the Back Sights, then e is lower than a; but if the 
 fum of the Fore Sights is lefs than the fum of the 
 Back Sights, eis higher than a: For example-fake, 
 let the numbers be as in the following table. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Back Sights. Fore Sights. 
 
 Feet, nek, Tenths. Feet, — Inch, ‘4 Tenths. 
 SESS of Goan ae Beg Als sky 
 Pee Gist, 318 ee ae Mee 
 i 4220 © 152 Be as a OF 
 ie ts Bi 5/0 2 Fae rari 
 PAE GO! 4 .7 Pie 4520 
 “ee BBs iE): gry 
 | A AR EN ae 2 
 1 eye 
 
 \ 
 Now 
 
 rs det a Typ ty oo : — 
 ~ -~ 
 ae oe a ng tJ ay eT - . + 
 
 eran eee 
 
 Tee = te a ee oat a Sones 
 — x x 
 
 so Splplytely ess 4 
 
 — 
 
 preies 
 
 
 
 x 
 gy ty 
 
 r 
 9 & 
 
 =a 
 ' 
 
 4. = = 
 a 
 <= 
 
 xe Seen a » oy == 
 trier + ham GM Gad eee et ot wan te OO TE 
 

 
 
 
 v 
 
 pees 
 
 S 
 eet 
 
 SS EE ee SO 
 
 a a a Rt en 
 
 ogee 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Now follow ine servations well sores notice: oe 
 
 I. If the fum of the diftances in taking the Backs 
 Sights, is equal to the fum of the diftances in taking © a 
 the Fore Sights, all the minute errors of the inftru- 
 ment will mutually balance and cena each other. a 
 
 II. And if the diftances thus taken are thora the 
 curvature of the earth may be rejected. For, ifthe ~ 
 diftance from the inftrument be every where about 
 roo yards, all the curvatures in a mile’s gow 
 be lefs than half an inch, rie 
 
 Til. If the diftances from the infirument to the 
 hindermoft. ftaff, be every where equal to the dif- 
 tance from the inftrument to the correfponding ftaff 5 
 the curvature of the earth, and the minute errors of : 
 the inftrument will both be deftroyed. | 
 
 IV. If the diftances of the inftrument from the 
 ftaves, be very unequal and very long, the curva- 
 tures muft be accounted for, and the diftances, in 
 order thereto, muft be meafured, either by pacing, 
 by a chain, or a wheel. 
 
 V. For the more ready allowing for the curvature, 
 you may obferve, that the curvature for one mile, 
 taken at one obfervation, is extremely near to 8 in- 
 ches, And at all other diftances, itis as the fquare 
 of 1 mile is to 8 inches, fo is the fquare of any other 
 diftance to the allowance for the curvature ; that is, 
 
 Multiply the fquare of any diftance whofe meafure is 
 
 taken in miles, by 8, and the produc will give the allow- 
 ance for the earth’s curvature, in inches: This curva- 
 ture is always to be fubtraéted from the numbers 
 taken off the ftation ftaff. Or if the diftance be lefs 
 than a mile, and taken by the four pole chain: Sguare 
 
 the 
 

 
 
 
 
 
 
 e “ey a 8, and the quotient eit vs inches 
 parts of of inches to be allowed for the curvature. Sup- 
 2 the diftance be 30 chains ; then the {quare of 
 me: that i is, 900, when 2 places are cut off, gives 
 9,00 or 9, which divided by 8, sivey I inch and 
 thoufandth parts of an inch. 
 
 
 
 bee VI. If thefe diftances were taken ibe pacing, ac- 
 Bed ounting 25 to the chain, the curvature may be 
 und thus ; Square the paces, and double it, cut off 
 peg places jo the left-hand, and thofe to the right are the 
 inches of curvature: So, if the paces were goo, then 
 * from 810000 multiplied by 2, that is, 1620000, cut 
 off 6 figures, and you have 1.62, the curvature to 
 be allowed. To fave the trouble of continual calcu- 
 lations you may ufe the following table, wherein the 
 diftances are in chains, and the “allowance i in inches, 
 and xooth parts of an inch, 
 
 
 
 Diftan, 
 
 Sine aos 
 
 
 
 
 x 
 T 
 
 ma = = = . = = 
 meet men ont ~— ~ > ae a 
 
 =. 
 
 me 2. = pes — —— = —, 
 pontesses seesenrae naes ae 
 
 eat 
 
 — 
 
 ———— 
 oe ee 
 
 a — 
 
(128) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ditan, Allowance | Dillan. Allowance 
 Chain : SEnehes Pil Chain * a Inches. es 
 1 10,0012 -l 27 foe. é 
 i Ai 8 0,005 7 28 10,98 
 3 ot : 29 11,05 
 4 10,02 Q 390 {5,12 "ane 
 5 | 0303 at IE a TS 
 6 | 0,04 | daaliagy' 
 7 OOD. Me, 3 44535 
 810,08 - | 34 |tn44 0 
 9 Be bis | 85 Pee oy 
 tO 810.12 SO sue 
 Ir 10,15 37 1,71 
 12 |0,18 BS PE BON a. 
 13 10,21 39 11,91 | 
 14, 10,24 } 40 2,00 | 
 15 10,28 | 45 )2528, | | 
 16 |0,32 | 50 19,12 | 
 17 | 0,36 55 | 3578 
 18 |0,40 J pOQ 14450 
 19 ee | | 65 15.3% 
 20 | 0,50 70 | 6,12 
 2T |0,55 | 75 7993 
 ‘ 22 10,00 Ow hago 
 23 Be 85 | 9,03 
 24. 10,72 90 | 10,12 
 25 ozs 95 [11,28 
 26 oe | TOO | ¥2,50 
 
 
 
 VII. Therefore it appears, that a belt method _ 
 to take a level, is to meafure the feveral diftances © t 
 from the inftrument to the back and forward ftation 
 fiaffs ; and enter them in the. field-book, Serine 
 
 to” 
 
 | 
 
 
 

 
 
 
 
 thei ai fas as in the fol- 
 eg , and correct a8 heights from the. 
 
 be ae toa level | Reh a double dccores ; 
 would advife thofe who ufe the double tele- 
 ae ay {tation to. turn that end of the tele- 
 coward s the fpring, which, before was the cone 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Gear Forwards, 
 
 Height | Corrections Diftan. Height | Cor ‘rections 
 Inches | Links - Inches ‘Inches 
 3:24 | | 418 4,36 4534 
 6,08 | | 328 at 7917 
 584) 7.25| 7521 530 ie 959 
 3261 8,15] 38,14 485 |11,25|11,22 
 @. 658 10,25 | 10,20 379 | 8,65! 8,63 
 oehao 0,32) 6,29 | 720 {10,34}10,28 
 egene te 40,47. | + | 3146 57,85 
 3146 | 46,47 
 ‘ie 6 aay 4 : 13%. ey 
 
 56 thie the fall in 68 ae is about hts op ci 
 and 3 = of an inch, f 
 
 kK ‘ey SS OE 
 
 
 
 ary 
 
 Pa Re TEESE Ee Ea SS gl IS 
 

 
 
 
 
 
 'S E.Cots oe 
 Of CoLours, 
 
 T is not worth while to fpeak of the preparation 
 of colours, becaufe they may be had ready pre- 
 pared, at almoft every colour-fhop and fan-painter’s, 
 é§c. Nor to mention but as many as are neceflary 
 and moft fit for the furveyor. I judge thofe to be 
 the beft, which are moft tranfparent. 
 
 And for portability, I think liquids improper; . 
 therefore would rather chufe thofe colours, which, — 
 before tempered, are dry ; whether in powder, or in 
 - lumps: And fuch as require no other liquid to mix 
 with them (than what is to be had every where) wz. 
 fair water. 
 
 For Gum Water, with which many colours are 
 mixed, is made by barely fteeping Gum Arabick in 
 Tair water. 
 
 Carmine, a powder, mixed with Gum Water, is a 
 beautiful red may be fhaded with fome of the 
 fame, mix’d ftronger ; ; or with any reddifh brown, 
 or any fadder red. 
 
 Carmine is chiefly ufed for drawing of red lines to 
 reprefent the walls of gardens or other places ; and 
 alfo to colour the plans of buildings. 
 
 Ultramarine, a powder, mixed ate Gum Water, 
 is a moft valuable blue, ft to fhew ponds, lakes, 
 rivers, 
 
 
 

 
 
 
 
 
 & “i. at 131 Py, | 
 
 te rivers, ee it may be fhaded with Indigo Corns 
 | ‘ground with fair water on a white tyle, by the pref- 
 fure of a a knife’ $ point, and then mix’d with Gum 
 
 re ie 
 
 | Red alk, a lump, neces called French 
 Chal : 
 ter, and afterwards with Gum Water, {lightly laidon, 
 a is proper t to reprefent roads and pits; and is fhaded 
 by: ae more ftrongly mix’d, 
 
 
 
 
 
 
 
 geek a. 
 
 & Sap green, be eepid in water, is of itfelf a good 
 "green to colour trees. 
 
 be Verdegreece, in lumps, diffolved in vinegar, or in 
 water, makes a greenifh blue, or fea-colour, very 
 ee | 
 
 
 
 Gumbooge, ' in lumps, fteep’d in fair water, pro- 
 “duces a beautiful and tranfparent yellow. | 
 
 aa cllow berries, fteep’d in fair water, a yellow. 
 
 Verdegreece diffolved, mixed with Gumbooge, or 
 yellow berries, in different proportions, produces 
 ‘different greens, inclining either to the blue or yel- 
 low, paging to the quantities of either ufed. 
 
 Indian ink is ufed in drawing the firft lines of a 
 draught, and in fhading of hills and defcending 
 grounds: A proper quantity of it may be liquified 
 when wanted, by putting a few drops of water on a 
 cake, and rubbing i it with the finger until the colour 
 is as deep as defired, 
 
 
 
 But there muft be care taken in the ufing of In- 
 dian ink ; viz. to have three or four different tints 
 of colour prepared, of which the fainteft is to be 
 
 KS 3 laid 
 
 , ground by rubbing it on a tyle with fair wa- 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 af ( 132 . | 
 
 Bs: — Jaid on firft, and fo proceed to the detpett tint ee 
 - not to cover too great a fpace at once; for if the 
 . margins are not fpeedily wafhed off, the ink i vil 
 dry in ftreaks and fpots, and look very ill. a 
 
 —s 
 
 Colours are laid on with hale ie ; thofe fit ; 
 for moft ufes, are about the fize of a common writ- 
 ing ae and the length of the hair, without the 
 guill, not to exceed 6 or 7 tenths of an inch: ‘Ing 
 choofing them take fuch only as, when wetted either 
 in your mouth, or in water, will, by ftroaking them — 
 acrofs your finger, form a fine point, and are very® 
 {pringy: And as moft pencils have a hair or two at 
 their point longer than the reft, thefe may be taken 
 off, by cently drawing the point, when the hair is” 
 
 wet, once thro’ the border of the flame of a candle, 
 
 In the ufing of thefe pencils, it will be found con-" 
 venient to have them fixed on {mall fticks about 6— 
 inches long, one on each end; whereof one is to be 
 ufed with colour, and the other with fair water, to 
 lighten the margin of the colour, whereby it is in-— 
 
 
 
 4 
 fenfibly graduated till it vanifhes into the colour of 
 
 the paper. . : ‘ 
 
 All colours are fhaded by others oF the fame 
 fort, but of a ftronger tint: and the manner in’ 
 which they are ufed with the moft facility and fuccefs, 
 is better gained by practice than by precepts. 
 
 
 
SN ae aii ae Te cS ave Bae ye 
 Z SN AUS Se 
 
 
 
 
 
 
 Mg atsr XI. 
 
 ee or Fe dal ie Alfo bow to aod 
 for afcents or defcents by finding the borizontal 
 
 I |B principal difficulty in ufing this Sliding- 
 = Rule, is, in juftly diftinguithing the value of 
 eae ch divifion. And in order to this, it may be ob- 
 erved, that the divifions on this rule, may be di- 
 inou hed into three orders, &c. ie longeft, the 
 Be Beco the Werf And thele different marks di 
 2 fling uifh their value in a ten-fold proportion, in the — 
 fame manner as the places of a number is diftin- 
  guifhed. : 
 Ge So. that, if the longeft reprefent hundreds, the 
 * mean will reprefent tens, and the fhorteft units. 
 _ And if the longeft reprefent tens, the mean will 
 - reprfent units, and the fhorteft tenth parts. 
 Von Oy AL the longeft reprefent thoufands, the mean 
 a reprefent hundreds, and the fhorteft tens; and 
 in this cafe, the units muft be eftimated by the eye, 
 in judging at divifions, only fuppofed to be drawn, 
 becaule there is not room enough. 
 
 The longeft divifions are generally numbered by — 
 the figures 1, 2,3, 4, 5, €¥c. and when they are 
 ‘numbered ca 1, 25 3, 45 5: 6, 75 8,93 By 2s 3s 
 MGs 03975 -05:95°1'3 ‘the line: is called a double one. 
 And when the longer divifions are in number only 
 
 3 ten, 
 
 
 
 
 
 
 
 
 

 
 eee ner 
 
 ms 
 
 Swe 
 
 cannot be fo. Nor will they be eafily capable of © 
 
 rules of greater length; where the multitude of the — 
 
 alike; one of which moves againft the fixed line a- ~ 
 
 
 
 
 
 
 
 
 
 ( 134 ) 26 
 ten, and numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, V5 or 
 numbered 5, 6, 7, 8, 9, 10, 20, 30, 4G, 505 00nm 
 broken fo as to begin at any other number, fo as to 
 contain only ten long divifions ; the line is called a 
 fingle one. And thele are called Gunter’ s lines, — Sy 
 the name of their author. Z 
 
 reprefent equal diftances ; yet, from : ei ‘ 
 
 an equal number of divifions, in different parts of 
 the rules; either of mean, between the longeft, or . 
 of the thorteft between the mean. P 
 
 But in order to make this eafy, here follows an % 
 explanation of the divifions laid down on the Foot ~ 
 Sliding-Rule, which may eafily be applied to other © 
 
 intermediate divifions may be greater. k 
 On the flider are two of thefe double lines, ee * 
 
 bove, which is alfo exactly like to either of the ~ 
 other ; and the undermoft line on the flider moves © 
 againit a fingle line, beginning with the numbers 5» a 
 6, ic. and going on to 50. t 
 If the firft 1 be called 2 unit, the following num- 
 bered divifions, till you arrive at the middle 1, will i 
 be units, And the mean divifions will be tenth 
 | : 
 parts. iy 
 If the firft 1 be called ten, the figures 2, 3,4,&c. — 
 immediately following it, will denote 20, 30, 40, €Sc. 
 And the mean divifions, that is, the next longeft in 
 order, will denote units ; the fifth of which is, for — 
 diftinétion, made longer than the reft. And from 
 10 to 20, between each of thefe mean divifions, the 
 fhorteft denote each two tenth parts; becaufe the 
 diftances between the mean divifions, are divided 
 into five parts; but if the diftances between thefe 
 mean divifions were divided by fhorter lines into ten 
 parts, 
 

 
 ? 
 
 (1 35) 
 parts, which is | feldom done on rules fo fhort, each 
 would : eprefent one tenth part. 
 
 : a like manner from 20 to 30, that i is, between: 
 the divifions marked 2 and 3, the fame order fol- 
 Jows 3 fave that the diftances between the mean di- 
 vifions (becaufe of their nearnefs to one another) are 
 divided into two parts only ; and confequently each 
 of thefe fhorteft divifions will denote five tenth parts 5 
 and the eye muft eftimate the other tenths not cut, 
 
 but fuppofed to be cut between them : tho’ in larger 
 
 
 
 
 | -inftruments, even here, and elfewhere, the fhorteft 
 
 -divifions may be as many as thofe between the 10 
 
 E ‘ and 20. 
 
 _ This laft aticide of divifions, ufually continues 
 ‘to 40, 50, or perhaps farther, and are to be read as 
 Pita between 20 and 30. 
 
 But where the longeft divifions become clofer to- 
 gether, as generally they do, between 80 and go, 
 and between go and 100, which, on the {cale, is 
 denoted by the digits 8, 9, 1, there are but two or- 
 ders of fub-divifions ; the ereateft ftill keeping the 
 fame degree, and the other the next lower decree. 
 And in this one example, the figured divifions de- 
 mote tens, and the other units, 
 
 But when the firft 1 is called 1003 then the fi- 
 _ gured divifions will be accordingly 200, 300, 400, 
 €¥c. The mean divifions, or thofe the next fhort- 
 
 eft, will denote tens. The fhorteft between 100 | 
 and 200, where the diftance between the tens is di- 
 vided only into five parts; I fay, the fhorteft here 
 will denote two units each of them ; and the middle 
 between thefe, will denote the fingle units ; which, 
 
 if there had been divifions, as in large inftruments, 
 would have been denoted by thofe divifions. 
 
 But from 200 to 300, from 300 to 400, and from 
 400 to 500, the diftances of the divifions reprefent- 
 ‘ing tens, are divided only into two parts, and con- 
 fequently, each of thefe fhorteft divifions muft re- 
 
 K 4 prefent 
 
 
 

 
 ( 136.) 
 
 prefent five units; and all other units, cithel more — 
 or lefs than five, aut be eftimated by the eye, by q 
 fuppofing each of thefe diftances cut into five parts, 
 WNeverthelefs, in larger inftruments, thefe divifions 
 
 may: be cut and eftimated as before ec. 
 
 Towards the latter end of the line, the divifione i 
 en thefe fhort lines are fo near together, that they 
 {carce admit of three orders of divifions, and con- — 
 
 fequently (fuppoting the longer divifions to denote 
 
 hundreds, as in this example) ) the units mutt be efti- 
 
 mated by the eye. 
 
 And in like manner, if the longer or Genned di 4 
 
 vifions denote thoufands, the ines ‘of leffer length 
 
 will denote hundreds, the next inferior, tens, €8c. 
 But becaufe, by infpection, on this rule it will 
 
 appear, that more than three places cannot be di- 
 
 ftinctly eftimated; and, that thofe are iufficiently 4 
 exact for all the ufes it is defioned for; a farther die 
 
 : : 2 ; 
 vifion, and confideration thereon, are omitted. 
 
 If the firtt i, that is, the beginning of the firft — 
 
 line, denotes a unit; then the middle 1, or begin« 
 ning of the fecond line, denotes 10, and the laft 1 
 denotes 100, 
 
 So, if the firft 1 denotes 10 ; the fecond 1 denotes 
 roo, and the laft 1000. 
 
 In like manner, if the firft 1 denotes 1003; the 
 fecond denotes 1000, and the laft 10000. 
 
 And fince, when the value of the firft 1 of any 
 line is known, the value of the other figures and 
 divifions are known alfo ; therefore the Jatter line is 
 to be read by the former directions, And thus are 
 thefe three double lines to be read, as has been 
 fhewn, for the former. 
 
 But the fingle broken line, which is on the fixed 
 
 art of the Jeg of the rule, is not to be confidered 
 in this arbitrary manner. 
 
 For the longer divifions have affixed to them their 
 values, which ought to be confidered as unvariable, 
 
 unlefs 
 
 
 
 \G aoe, : Pi eat Se 
 ee via: ss ’ . fo tisiaey ne one . is caine, oo 7” a = ce es ; 
 
 Sy RA SRS ge te ae See 
 
07) 
 
 
 
 
 
 
 
 
 
 
 
 Pat 10, the diftances of the longer Ainere 
 which are numbered 5, 6, 7, 8, 9, 10, are divided 
 into 10 parts, by mean divifions ; ; and therefore, 
 
 fe mean divifions denote tenth parts. And thefe 
 
 each denoting therefore half of one tenth. 
 | ae a From to to the end of the rule, the diftances be- 
 tween the longer divifions, are each divided into 10 
 3 parts ; and therefore each denotes units. And the 
 4 - diftances between the units are each divided into 4 
 & parts 5 ; therefore each denotes one fourth part of an 
 Pmanit. °4 
 In the double lines, let the diftance between the 
 1 at the beginning, and the 1 in the middle, be 
 _ called the firft fcale ; and the diftance between that 
 * in the middle, and the 10 at the end, be called the 
 fecond fcale. The uppermoit of thefe double lines 
 is marked with the letter A, the next with B, the 
 | third with C; and the tnidermniont: which is alfo 
 called the girth-line, with D. | 
 On the lines A anal B, in the fecond fcale, there 
 
 are placed the {mall figures **, denoting an index — 
 
 fixed, tho’ the value of the divifions fhould vary. 
 Prd. on the girth-line, again{t 12, is generally 
 a hand or index for the like ule, 
 ~The two upper lines are generally ufed for cafting 
 up the furfaces of planks, - 
 The two under ones for finding the folidity of 
 timber. ~ 
 Having thus far defcribed and explained the read- 
 ing of this rule; I fhall proceed to fhew its ufe in 
 -meafuring planks and timber, But fhall firft fhew 
 the cuftoms ufed in taking their dimenfions, 
 
 And © 
 
 
 
 ules ig ea neceflities hereafter to be - 
 
 = ee eee 
 
 oe E15 
 
 ea 1 divifions are each fubdivided by one fhort line, - 
 
 = 
 
 eed 
 

 
 
 
 (138 ) 
 And fief for planks ; the buyer hath the liberty 
 
 of meafuring the dimenGone on that fide of the 
 
 plank he judges moft advantageous to himfelf. _ 
 Then the length is meafured either with two two- 
 
 feet rules, or two-feet rules, and five or ten-feet 
 
 rods. 
 
 The length is meafured in feet and half feet, andy 
 
 in fome places, to quarters of feet. 
 
 Then lay half this length from the upper part, 
 
 down towards the butt-end ; where, with a piece of 
 chalk, make a mark, 
 At that mark, or nearer the butt-end, if the buyer 
 
 think it to his advantage, is taken the breadth, in 
 
 inches and half inches. 
 
 If one fide be wainy, the breadth is taken to the 
 middle of the wain. 
 
 If both fides are wainy, one wain is imeatiieeele 
 the other rejected ; and either of them as the buyer 
 thinks fit. 
 
 Having thus got the length and breadth ; call the 
 firft long divifion on A, and alfo on B, each an u- 
 nit, ‘Then fet the index on B, againft the breadth 
 in inches on A, and againft the length in feet on B, 
 will ftand the content in feet on A. 
 
 EX AO McP loa 
 
 Let there be a plank, whofe length 1s 24 feet and 
 
 a half, and breadth 17 inches and a half; I demand 
 
 the content ? 
 
 Set the index (or 12, in the fecond fcale} on B; 
 againft 17 inches and a half on A, and then againft 
 24 feet and a half on B, ftands 35 and 3 nearly on 
 A; which is the meafure of the plank required. 
 
 But when the feet, in length, on B falls beyond 
 the end of the line A, then call the firft 1 on A, 
 a ten, and work as before fhewn. at 
 
 
 

 
 
 
 
 4,  . be 45. feet and a half long a and 39 
 road, what 1s the content § ? 
 
 - the index (or 12) on B, againtt 39 on A, ad 
 and a half on B, will fall. beyond the upper end 
 BE os 
 
 a ‘Therefore fet the index on B, againft 39 on A, 
 
 will and. a on A, the content required, 
 _ Thefe are all the varieties which happen in plank 
 ‘meafure. 
 
 But notice may be taken, that from this content | 
 mutt be fubtracted as much meafure as will ballance 
 all the vifible faults: and this is generally left to the 
 judgment of the two meafurers, and generally done 
 before the contents are entered in the accounts, or 
 indeed, before you pafs to another plank. 
 
 “There are fome differences in the cuftoms of dif- 
 ferent countries, tho’, for the moft part, the fore- 
 going are the molt generally ufed. 
 
 _ The Htias generally ufed in taking the dimen- 
 fions of timber, are not much different from thofe 
 ufed for plank. 
 
 For the whole length is firft taken in feet and 
 halves, then the middle is found and chalked, where, 
 
 _ Or nearer the butt-end, according as it is the buyer’s 
 advantage, the ftick is girthed with a {mall line, 
 which is exactly quartered by twice folding; this 
 quarter is meafured in inches, halves, and quarters. 
 find if the tree’s bark is not peeled, as always hap- 
 pens in ftanding timber; then from the foregoing 
 girth muit be made an allowance for the bark, which 
 
 is 
 
 
 

 
 ( 140.) oe 
 is ufually thus: for trees girthing one foot, allow 
 
 one inch, and fo proportionally for all others. But 
 for beech, elm; afh, and fuch as are thin barked, 
 
 the allowance muft be a {mall matter lefs, er. 
 It is alfo to be obferved, that, a ftick is not called 
 timber farther than it will hold half a foot girth. 
 
 Alfo, that if there be any confiderable arms which | 
 
 hold half a foot girth, they are alfo called timber, 
 and meafured as fuch. 
 
 CASES 
 
 Having thus taken the length in feet, &¢. and 
 quarter girths in inches, &¥c. fet 12 (the index) on 
 _ the girth line, to the length on C, and then againft 
 
 the girth on the girth line, is the folid content 
 on C. ees : 
 
 EX A Mee ee 2h 
 
 Let a tree be 24 foot and a half long, and its. 
 
 quarter girth 17 inches and one fourth ; to find the. 
 folid content : 
 
 Set 24 and a half on C, againft the index on D, 
 the girth line; and then againft 17 and one fourth 
 on the girth line, ftands 50 three fourths on C, the 
 folid content of the ftick. 
 
 € Ashe 
 When, by the foregoing directions, An rule is 
 fet, and the girth on the girth line is beyond the 
 
 upper end of C; call the firlt 1 on C 10; and then 
 work as before, 
 
 E X- 
 
 
 

 
 
 
 at ree be 20 Hate iy pa dos ost and 4 a 
 tO Bn the ae 
 
 TA 
 
 ee ng io 
 [aN When the girths on D fall fhort of the lower end 
 of ion ‘call the middle one on C, aunit; and then, 
 
 ae allt the figured divifions, below the middle 1, will 
 ee be tenth parts of feet ; then worl as above. 
 
 i 3 7] | yet i = X A M PLE mL 
 
 CASE Hil. 
 
 
 
 Vee fick be 3 foot tones and 6 fore oirth 5 
 to find the folid content; ~~ 
 
 WAcéountings the middle 1onC an unit, fet 3 on’ 
 __-C,, againft the index on D; and then, again{ft 6 on 
 ae D, ftand 7 ‘tenths and a half onC; Bie fcligiry’ re- 
 quired, | ' 
 
 kes Py EXA é PLE Iv. 
 
 - 
 
 Tes a ftick be feven Foot and a half long, and 
 Pa four inches ; ; to find the folidity : 
 
 | Set the index (12) on D ant 7 and a half in 
 » the fecond icale on BE; then againft 4 on D ftand 
 2 7 8 tenths 
 
 i) 
 
 
 

 
 ( 142 ) 
 j tenths and a third on C: fo that the folidivy 4 ay 
 * part in ro of one foot. 
 
 N. B. T ho’ ae i not what ts called timber, yet 
 fince alders and other fhrubs, ufed by turners and. 
 others, are often meafured, be they never fo {mall ; 
 
 I thought it proper to infert fome examples of this 
 kind. | 
 In the three foregoing cafes, the girths of the 
 fticks fell on the girth line C, without any arbitrary 
 alteration of the values affixed to the divifions ; 
 which fixed values are abundantly fufficient for com- 
 puting the folidity of moft fticks ufually to be met 
 with, if the fingle line C be advantageoufly broken. 
 For, if a perfon defigns his rule for the meafure of 
 timber only, that is, fuch as never girths lefs than 
 fix inches ; then the girth line beginning at fix, will — 
 run to fixty inches: above which, few fticks will — 
 out-run, But if he defiens to meafure alders, fhrubs 
 and fmall things, €&c. often meafured by turners, 
 wheelwrights, and other artificers, ufing this fmall 
 fluff, the beft way is to have the line C broke, and 
 to begin at 1 and a half, or 2, and end at 15 or 
 20, according to the fize of the ftuff they moft deal 
 in. 
 
 But that the line, as ufual or occafionally broken, 
 may ferve for the computing of common timber, 
 timber extraordinary large, out-running the girth 
 line, and alfo for fhrubs and fmall twigs; it may 
 not be amils to confider the following direétions and 
 examples. 
 
 And in the firft place, we will enquire into the 
 ufe of the rule in computing the folidity of fuch 
 large fticks, as out-run the affixed values. of the di- 
 vifions on the girth line. 
 
 For which obferve, that the length of a ftick al- 
 ways to be found on the upper end of the line C, 
 4s to be fet to the index; the divifions on the girth 
 line 
 
 
 
 
 
Eb be aah, Ny 
 
 | Tine numbered 6, 7, 8, &Fc. are to be accounted 60, 
 70, 80, &e. and that, in eftimating the folidity of 
 the ftick, the divifions on C are to rie eftimated by 
 100 times the value arbitrarily taken thereon by the 
 length : : that is, if the fecond fcale of C be called 
 units in the length; then, in the folidity, the fame 
 ‘upp per part fhall be called hundreds, and the lower 
 
 
 
 
 
 : Ween tens in the length; then, in the folidity, 
 Bs upper part fhall be called thoufands, and the 
 lower part hundreds, 
 
 | a EXAMPLE V. 
 
 
 
 ba Let there be a flick, whofe length is twenty-five 
 feet, and girth forty- fix inches ; and let forty-fix be 
 above the upper end of the girth line: to find the 
 
 folidity. 
 
 Then fet twenty-five in the fecond feale of C, a- 
 eainft the index on D; and then againft (4 and 6 
 tenths on D, which in this cafe reprefents) 4.6 inches 
 the girth, ftands 367 foot on the firft fcale of C; 
 eftimated according to the preceding directions, 
 
 EXAMPLE VI. 
 
 Let there be a ftick, whofe length is four feet, 
 and girth forty-fix inches ; and let forty-fix be above 
 ie upper end of the girth line: to find the foli- 
 
 ity. 
 
 Set 4 in the fecond fcale of C, againft the index 
 on D; and then againft the girth 46, on the lower 
 part of D (which, ; in this cafe, will be reprefented 
 by the affixed value, 4 and 6 tenths) ftands 59 feré 
 on the lower part of C, eftimated according to the 
 preceding directions, 
 
 For 
 
 3 
 
 
 

 
 (144 ) 
 
 For very {mall fticks, whofe girth falls below chs. ‘ ; 
 beginning of the girth line D; obferve, that the — 
 
 length of the ftick always to be found on the firft 
 
 feale of the line C, is to be fet to the index; the : ' 
 
 divifioris on the girth line numbered 10, 20, 30, 9c. 
 
 are to be accounted only 1, 2, 3,€8c. And that efti- 4 
 mating the folidity of the ftick, the divifions onC 
 
 are to be eftimated by the rooth part of the value 
 
 arbitrarily taken thereon by the length; that is, if 
 
 the firft fcale of C be called units in the length, then 
 in the folidity, the fame lower part fhall be called 
 hundredth parts only; and the upper end tenth 
 parts. But if the lower end of C be called tens in 
 
 the length, then, in the folidity, fhall the fame lower — 
 part be called tenth parts, and the upper end units, — 
 
 EX AM?P.E fev 
 Let a ftick be fifteen feet long, and let its girth 
 be three inches; and let three be below the lower 
 part of the girth line: to find the folidity. | 
 
 Set 15 feet, taken in the firtt fcale of C,.to: the 
 
 index on D 5 and then againft 3 (which, in this cafe, 
 
 will be reprefented by 30) in the upper part of D, 
 ftands the folidity 9 tenths of a foot, and a quarter 
 of another tenth, 
 
 EXAMPLE VII. 
 Let a ftick be three foot long, and Jet its girth be 
 
 two inches ; and let-two be below the lower part of 
 the girth line: to find the folidity, 
 
 Set 3 foot, taken in the firft fcale or lower end 
 of C, to the index on D; and then againft 2 (which, 
 
 in this cafe, will be reprefented by 20) in the upper 
 
 part — 
 
 an re 
 
 
 
 : 
 

 
 
 
 
 
 
 4 places where the cuftom alti the taking. 
 
 tuto! minute “athe of ‘a fasts or when» the 
 
 i (145 > 
 part of D; lands the’ folidity, eight hundredth parts 
 of a { foot, and'fomething more. 
 
 
 
 . wanes ;-the cuftom is to take the length, and find 
 | | amide: in the fame manner, and with the fame 
 allowances as were obferved in round timber; and 
 ‘then, ‘in this middle, either with a pair of callipers, 
 ‘or the edges of two rules applied to. the flat faces, 
 to take the breadth and depth of the ftick.. Then, 
 to add the breadth and depth together, and to ufe 
 half their fum, as you: before did the quarter girth 
 ‘of around’ ftick, | , 
 
 ths at: mY 
 
 Himes vin EX A MPLE, 
 
 ee Bick be twenty- ee foot long, fourteen 
 inches broad, and twelve deep : to find ‘the Bo 
 em ha to this i method. 
 
 Becaufe 14 and 12 vive 26, whofe half is 13, fet 
 
 25 on C againft the index on D; and then againft | 
 
 ‘13 on D, ‘ftands almoft 29 foot and a half folid. 
 
 And tho’ this cuftom makes the ftick fomething 
 more than in fact it is, by adding the breadth and 
 depth together, and taking their half for a girth; 
 yet, in a whole tree, only. hewn to a fquare, the 
 difference is fo very fmall, that the cuftom may be 
 admitted, 
 
 For in this example it may appear by the pen, 
 that the folidity thus is 29 42, foot; and the true 
 folidity, if the ftick be allof the fame bignefs, and 
 
 a : without 
 
 “Oe as" Bia for Gedien slither 5 mrtaret cathe iiaher 
 4s hewn to that form: which is ufually “called fquare,’ 
 ‘tho? att 1¢ fame time there is moft commonly four 
 
 
 

 
 ( 146 ) 
 
 without wanes, will be 29 24,, differing from ses 3 
 
 former only .32,, or % of a foot folid. 
 
 Neverthelefs, in fticks whofe breadth differs e ; 
 much from the depth ; the error is intolerable, and 7 
 
 ought not to be admitted. 
 
 For, lec there be a flick 26 foot Leia 20 — 
 broad, and 6 inches deep; then, by the cuftomary 
 way of adding, the width and doptt together, the fo- 
 
 lidity will, as before, be 29 442, foot; but the true — 
 
 eh will be only 20 442: and fo the error is 
 
 8 23. foot, almoft a third part of the ftick. 
 
 For the ready management of fuch timbers, there 
 may be placed on the other leg of the rule, another 
 flider ; having the fliding part and the upper fixed 
 _ line, exactly the fame as in the former leg; but on 
 the other fixed part, a double line of the fame ra- 
 dius with the former, but broken and inverted. And 
 as the lines on the former leg were diftincuifhed by 
 the letters A, B, C, D, fo the lines on the latter are 
 noted by che betes E, F,G,H. And as the divi- 
 fions on the lines A, B, C, were intirely arbitrary, 
 fo the lines FE, F, G, are alfo intirely arbitrary. And 
 on the line H, which is inverted, and beginning at 
 1 and a half, and running on to 140, the values 
 
 annexed to the divifions, may be varied, or remain 
 
 unvaried. But on the line E being direét, begin- 
 ning at 1, and running on to soo, the values an- 
 nexed to the divifions, may be conftant. 
 
 The line H, I call the depth line; the line G the 
 _ breadth line; the line E, I call the length line, and 
 ¥ the content line. 
 
 The ufe is fo fhort and fo eafy, that, in a few 
 words, and two or three examples, it will be plain. 
 
 For, fet the breadth on G, againft the depth on ° 
 
 H, and then the length on E will ftand againft the 
 folid content on F, 
 
 Let 
 
 
 
. ee | 
 
 | TB 
 
 | (147) = | 
 | Lethe fick ‘be that of the laft example ; where ob 
 19tl was” a5 foot, breadth 20 inches, and 
 
 
 
 aS gael 
 we 
 3B 
 
 iit Feliebhedch 20 on G, againft 6 on H; and 
 ee againft 25 on E, will ftand on F almoft 21, 
 e folidity required. | 
 Bere ‘to avoid confufion, remember, that what- 
 foever is is the value of the divifions on G, the fame 
 fhall be the value of the divifions on F. That is, 
 if the f rmer divifion on G be units, and the latter 
 tens, then the former divifion on F fhall. be units, 
 and the latter tens. And if the former divifions on 
 G be tens, and fo the latter hundreds ; then the for- 
 mer on F fhall be tens, and the latter hundreds. 
 Tf the length on E falls beyond F, call the for- 
 mer divifions on F, tens, and the latter hundreds. 
 TF thé length on D falls fhort of F, call the for- 
 mer divifions on E tenth parts, and che latter units, UE 
 
 EXAMPLE. 
 
 pg ey eg pee gine gene ey 
 
 
 
 _ Let a ftick hewn to unequal fquare fides, have its 
 length 46 foot, its breadth 30 inches, and its depth 
 20 inches; then, when 30 on G is fet agpainft 20 
 on H, £6 on E will fall beyond the line F'; there- 
 fore call the former divifion on F, tens ; and then 
 fet as before, and againft 46 on EF, will ftand 191 4 fait 
 on F, which is the folid content, Ki 
 The fhell, or flitch of timber, is readily caft up 
 
 by this rule ; for, take the breadth on the flat fide 
 in the middle, and one half the depth in the mid- 
 die, and work with the length and thefe, as tho’ it 
 were a fquare ftick, and you have the folidity fuf- 
 ficiently near. 
 
 ___It is indeed true, that this is lefs than the true 
 folidity ; but in regard of its value it is thoughe 
 pouet. : 
 
 L. 2 ite nee 
 
 
 
 =a -E-G_R- ELA ER LEO RAL LET EASE Sad LL BE LL RO RURUETA DESL ODES aha bekhatel EOL LE EULER OL Rat etrbatalk kt ch kit 1 27 ttetebate abet clk tt hee -L<e er@ ete ae ten 
 

 
 (148 ) : ‘q 
 
 Let there be a flitch, whofe. length ‘is ‘acistibiesal 
 
 breadth 16 inches, and. depth taken in the middle } 
 4 inthes. Set 16 upon G to 2 upon H, and a+ 3 
 gainft 30.0n E, ftands on F6 font ang two thirds, ; 
 
 the folidity required. — 
 
 The fawyers meafure is done by. one fering of 
 
 this rule: 
 
 For fet the aura oh etfs or. cuts on .G. to the . 
 bieadtl of the boards on H, and againft thet length i 
 of the flick on E, ftands on F the hundreds of feet . 
 
 econ 
 Eek ‘ M PL = nie 
 
 yy 
 ‘ oa ; ke . 
 
 Let a ftick, whofe length is 30 foot, breadth 22 
 inches, and depth 20 inches, be fo cut, that each — 
 board, with the wafte of the faw, may. we 2,inches.; a 
 that is, if it be cut parallel to the breadth, we fhall — 
 _. have ten boards, and fo g cuts or kerfs, and the f 
 
 breadth of each’ board will be 22 inches. 
 
 Set g on G againft 22 on H, and then againft 30 : 
 on E, ftands 4.12 on F, that is, 4 hundred and 12 — 
 
 | hundred! 1 parts of 120, or another hundred. 
 
 Any plank or board, whofe value is expreffed in : 
 pence per foot, may be caft up by this rule at one © 
 
 flip, withqut knowing the meafure of it, 
 EXAMPLE 
 
 A plank of walnut-tree is fold at as, ee or 33 
 pence per foot, its length is 30 isi its breadth 26 
 inches and a half. 
 
 Set the price in pence, 93 on G, againft 26 and 
 ahalf on-H, and then againft 39 on EK, flands 182 
 on F,,and a little more ; “that Sy: 482 fhil llings, or 
 g pounds and a fhillings. 
 
 Ha I¢ 
 
 
 
| 
 | 
 { 
 
 
 
 ( 149 ) 
 
 it may be obferved, that ee ii tied rule is fuf- 
 
 ly exact, and very ready for cubing ftone ; 
 pr vided, that the two fhorter dimenfions are olen 
 int ices, and the longer in feet, and decimal parts of 
 feetdobhe o- 
 . Alf, that. it may. be applied to the cubing in 
 feet, any folid in form of a parallelipipedon, whofe 
 content doth not confift of more than 3 places. | 
 | And if a line be properly broken, and put on in- 
 ftead of Hy, it might be applied to digging, &e. 
 -. Or if, the line H did flide as well as G, it might 
 be applied to the meafuring of all forts of paralleli- 
 
 
 
 
 
 pipedons, by one fetting of the rule, whether the 
 | oh potas be required 1 in feet, or ares or rods, €c, 
 
 lk i to fay fomething concerning the efti- 
 
 mation of the meafure of timber itanding, 
 
 
 
 Bade firtt, we may obferve, that, if we can get 
 the dimenfions, the manner of computing, after an 
 allowance for bark, is that already laid down. 
 
 But fince we cannot always get all the dimen- 
 fions, we muft take. thofe we can get at, and efti- 
 mate the reft. 
 
 And, farft, we may obferve, that the ae es 
 in a tapering ftick, which runs beyond timber, may 
 
 _be had thus: Girth the ftick breaft-high; to an 8th 
 
 part of this girth, add three inches; and the fum 
 Jefiened by allowance for bark, will give the girth 
 in the middle. And for the Jength, meafure from 
 the ground fo high as the tree runs timber, and then 
 “work as before. 
 
 E Mi Ay NER La Js, 
 Let the girth breaft high, be 6 foot, and length 
 
 _ 40 foot ; then, becaufe the 8th part of 6 foot is 9 
 
 inches, to this add 3 inches, and the fum is 123 
 L 3 from 
 
 
 
 ee 
 

 
 
 
 
 
 ( 150 ) 
 from this deduct an inch for bark, and there will be _ 
 left 11 inches ; which, with the length 40 foot, gives _ 
 33 foot and a half for the folid content. | 
 
 When the taper flick does not out-run timber at 
 the top, the whole girth, at top, fhall be added to 
 the whole girth breaft high; and an 8th part of this 
 fum fhall be the girth in the middle ; ; which, after 
 an allowance for bark, fhall be the girth to be ufed. 
 
 The ufual way of ‘eftimating the height of the 
 tree, is, by applying to it a ten or twenty foot rod, 
 and ftandine at a convenient diftance, and compar-. 
 ing the rod ‘with the tree, | 
 
 “But the moft certain method is by the Tbeodolite, 7 
 as now improved, thus: Meafure from the tree with 
 a ten-foot rod 100 foot, level the Theodolte, and 
 direct the telefcope to the top of the tree; and then 
 fhall the telefcope cut on the vertical arch (if the 
 ground, from the tree to the inftrument, be nearly — 
 upon a level) a certain number of feet; to which, 
 if you add the height of the telefcope, you will 
 have the height of the tree. 
 
 But if the ground, from the tree to the ‘ultra 
 ment, be not quite level, then direct the telefcope 
 to the top of the tree, and note the feet cut by the 
 telefcope ; and then direét the telefcope to the bot- 
 tom of the tree, and note the feet there cut. 
 
 And if one of thefe numbers of feet be above 
 the level, and the other below, then their fum is the 
 height of the tree; but if both are above, or both 
 below, then the leffer taken from the greater, will 
 give the height of the tree, without any other cal- 
 eulation, 
 
 _ When the ground, from the tree to the inftru- - 
 ment, is very ” fleep, take, with your off-fet ftaff, 
 or five-foot red, the height of the inftrument above 
 the ground, and at the fame height on the tree a- 
 bove the ground the tree flands on, make a mark. 
 Direct He teleicope to this mark, and it willcut on 
 
 the 
 
 
 
 
 

 
 
 
 (151 )) 
 
 the vertical arch among the divifions of reduction, 
 
 
 
 ng the difference between the hypothenufe - 
 bafe, a number of feet which added to 100, 
 will give the proper diftance to plant the inftrument 
 from the tree; or, what is the fame thing, it fhall 
 give a length on the afcent, anfwering to 100 
 foot meafured horizontally, very near. 
 
 ‘The inftrument being planted at this diftance, 
 work as before, and you will have the height of the 
 tree — 
 
 Having mentioned this vertical arch, and its ufe 
 in taking heights, I will now proceed to fhew its 
 ‘farther ules in Sems land. 
 
 If, in coming up an afcent, or going down a de- 
 feet, as foon as the inftrument is fet for obferving 
 the angle; you Jook on the vertical arch among 
 the divifions of reduction, you will find how many 
 links, in every chain’s length, this hypothenufal 
 line is to be fhortened, in order to get the horizon- 
 tal line, which ought to be laid down in your plan, 
 
 and mutt be entered in your book. 
 And thefe divifions of reduction are concentric. 
 
 with the divifions of altitude and depreffion, and 
 alfo with the divifions of degrees. 
 
 Laftly, if the diftance from the tree to the inftru- 
 ment be confined ; then multiply the horizontal di- 
 ftance in feet, by the feet given by the inftrument, 
 and from the product, towards the right-hand, cut 
 off two figures, and thofe to the left, will be the 
 height of the tree in feet. 
 
 La SECT. 
 
 ata. 
 
 oy 
 ree, 
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 4 
 ti { 
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 ik 
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 hag 
 Na 4) « 
 a 
 q ee 
 ty i 
 ta 
 Wi 3) 
 7 ;- - 
 i 
 Is 
 Hida) & 
 ha 
 Ie. 
 high 9 4 
 | 
 ae 
 } 
 sit 
 Mes 
 f 
 ¥ - 7 
 R i. 
 if 
 dh + 
 in HH 
 tad Fel 
 Mt ee 
 *Bsis! 
 REL 
 4 
 4 ' 
 ' Bt.’ 
 
 ee 
 
 
 

 
 | nti 
 
 S¥K) IME, SPL,  ghy 
 HOE Yas beg =k se 6) 
 BY GYD & ax 
 
 SE C°T. XII. 
 
 The ufe of the. Theodolite, iz drawing the per [pe five, a : 
 
 appearance of any tas without measuring one, 
 fingle line. 
 
 HIS will admit of fome variety 5 for either the 
 picture is fuppofed to be parallel to one. of the 
 fronts of the module or building ; or elfe oblique to 
 both; and then is either in a pofition affigned, or 
 in a pofition taken at pleafure. 
 Firft, fuppofe the picture parallel. to one MD the, 
 fronts; then plant the inftrument anda ftaff at any 
 equal diftances from the front, fuppofe 5, 10, or. 
 
 15 feet ; and direct the telefcope to. the ,ftaff, and > 
 
 the needle will point out. the bearing of that front : 
 to this add or fubtraét 90 degrees, you. will have. 
 the directing number ; that is, the bearing of the. 
 line perpendicular to the front. 
 
 Now plant your inftrument at the place, whence 
 the original building is to be viewed. Bring the in- 
 dex to “the beginning of the divifions, and turn the 
 whole inftrument about, till che needle points at the 
 directing number; and then fcrew it faft. Bring 
 the telefcope to the beginning divifions in the verti- 
 cal arch, and level the “whole inftrument : fo will the 
 inftrument be duly feated and re@tified for obferva- 
 tion. 
 
 In order to get eafily a due knowledge of per- 
 fpective in general, and particularly of the ufe of 
 this infrument in drawing, turn to the figures in 
 Plate V, and raife up the draught PK (Fig. 1.) per- 
 
 pendicular 
 
 
 
 
ARS 8) 
 pendicular to the plane of the leaf upon the line . 
 W K, and life up the plane AY W (Fig. 2.) till it 
 is per rpendicular to both the plan of the leaf, and 
 alfo to the draught PK; then raife the draught 
 ABW (Fig. 3.) till it coincides ‘with AY W, and 
 confequently will be perpendicular to the plane ofthe ~ 
 leaf, and alfo to the draught PK; fo will the two. 
 draughts. AW, PK, be the two Grants of the mo- 
 dule, reprefented to the eye.” Lift up the draught: 
 aV (Fig. 4.) till it is: perpendicular to: the plane. of | 
 the leaf, and it will be the picture defigned to be 
 drawn ; and will coincide with PK, thé font of the 
 module. “I is the point on the sround whence the 
 ‘building is to be feen. Lift up ET, till the 
 point Eis perpendicularly over the point T: And 
 Eis the eye of the f{pectaror, or the centre of the 
 telefcope. Now if you conceive ftrait lines drawn 
 from the eye at FE, to the feveral points A, B,C, D, 
 €sc, in the module, they will meet the picture in 
 the points a, b, c,d, %¢.. which are therefore the 
 true appearances of thofe original pa A,B,C, D, 
 and a line drawn from a to b, will be the true ap- 
 pearance of AB; and fo of all-other lines: for the 
 rays of light come to the eye from the picture in the 
 very felf-lame direction that they would have come 
 from the original module, Thus much by way of 
 introduction, 
 
 
 
 Now, in order to draw the picture: Affign on 
 your drawing board any point C, at pleafure, for 
 the centre of the picture’; and ee CV. the hori- 
 zontal line, and perpendicular to it, the vertical line 
 CX; from thefe two lines, all the parts of the build- 
 ing are to be laid down by their apparent diftances 
 from them, | 
 
 N.B. By ie centre of the sistas I mean that 
 point, whence, a line drawn to the eye is perpendicular 
 Yo 
 
 
 

 
 
 
 , ( 154 ) 
 to the plane of the picture. The horizontal line is that 
 which paffes thro’ the centre, and is parallel to the bo- 
 
 vizon 3 and therefore is the common interfection of ibe 
 
 pifture, with the plane of the ocular horizon. 
 
 The principal line in thefe draughts is, that coin, 
 or that angle which is common to both the picture 
 and the module 5 and confequently every where pro- 
 portional to the building it felf: and is the firft Jine 
 to be laid down and divided ; which may be done 
 thus: Let the example be as in the preceding 
 {cheme. 
 
 Direét the telefcope tothe point P in ‘the build- 
 ing, and you will find the index on the horizontal 
 
 plate of the inftrument cut 32 foot and a half, and 
 on the vertical arch 2 5 foot; lay the latter above 
 the horizontal line CV, perpendicular to it, from | 
 
 C to X; and the former from C to x. Then, by 
 help of the fquare, draw x P, X P perpendicular to 
 
 CV, CS, wheace the abeage appearance of the’ 
 
 point P is found. 
 
 In like manner may be found the perfpective ap- 
 pearance of any point whatfoever, whether it be co- 
 incident to both the module and picture or not. _ 
 
 Deprefs the telefcope to W, in the building, and 
 (in this example) it will cut on the vertical arch g 
 foot ; which, becaufe you look downwards, lay 
 from x downwards to W in the picture, and fo you 
 have the true appearance of W. And confequent- 
 He if you draw P W in the picture, you have the 
 
 rue appearance of the line P W in the building, 
 
 If you elevate the telefcope to A’, in the build- 
 ing, it will cut on the vertical arch 15 foot; which 
 laid from x to A‘ in the picture upwards, ‘becaufe 
 
 the point is above the horizontal line CV, will give 
 the reprefentative of that point in the picture. And 
 thus may every one of the points B’, O', D’, &e. be 
 laid down in the picture. 
 
 Direct 
 
 
 
 
 
RFP: ( 155) ¢ 
 
 ‘Direé the telefcope to K’ in the building, and 
 you will find on the horizontal arch, that the index 
 cuts 69 foot and a half; which laid from C to L’, 
 gives in the picture, the reprefentation of the 
 point L’. : 
 
 Thro’? L’, draw FE’ L’K’ perpendicular to CV, 
 and A’E’, BF, C’G’, ce. parallel to it, thro’ the | 
 points A’B’C’, &c. and fo the coins EK, and the 
 ‘tops and bottoms of the doors and windows may be 
 limited in refpect of their heights. | 
 
 Direct the telefcope to Q, and it will cut on the 
 . horizontal arch 38 foot anda half; which lay from 
 C to Q’, and it will determine the appearance of Q’, 
 Jn like manner may N’; and the jaumbs of the win- 
 dows Q.N, M O’, be laid down. As alfo the other 
 windows, doors, €3c. 
 
 For the returned front aW, draw PC, WC, 
 AC, BC, CC, DC, &e. and they will limit the 
 heights of the parapets, facia’s, windows, €&c. 
 
 Direc the telefcope to b, d, f, h, &c. and it will 
 cut on the horizontal plate 16 foot, 17 foot and a 
 half, 19 foot and one third, &c.----, which laid 
 from the vertical line XS, will give the breadths, 
 reprefenting the piers and windows. 
 
 The fame may be done for the chimneys and their 
 returns ; or for any other lines, breaks, &@c. And 
 io the feveral parts of the perfpective appearance of 
 a building may be drawn without meafuring. 
 
 That this compendium of perfpective may be 
 compleat,- it may not be amifs to lay down the ne- 
 ceflary Theorems in the moft general manner poffible ; 
 and herein I fhall ufe thofe terms which Dr. Brook 
 Taylor hath thought fit to mention, they being more 
 comprehenfive than fuch as are ufed by the other 
 writers on this fubject. 
 
 
 
 
 
 
 
 ty 
 
 x 
 _— 
 
 —- cS sae 
 Tetpiyt Tyr 
 > ? a ae - 
 
 
 
 = 
 
 
 
 Theor. 1. All the lines of any object (as in a mo- 
 dule or building) which are parallel to one another, 
 and 
 

 
 (956) 
 
 and to the pidture ; will be hepactenton by parallel ’ 
 
 on the picture. 
 
 Theor. VW. All bate parallel in Mahe oll ies or 
 building, which are perpendicular to the picture, 
 will, if continued, run to the centre of the picture. 
 
 Tho? thefe parallels be or be not ali in the fame. 
 
 plane. 
 
 Theor. I. All lines in the module or building, 
 
 perpendicular to the plane of the horizon, will be 
 in the picture, perpendicular to the horizontal line. 
 And thefe three Theorems are fufficiently allie: in 
 the preceding example. , 
 
 Theor. IV. All lines in the modale or oom 
 parallel to one another, and to the plane of the ho- 
 
 rizon, but oblique to the picture (as in the follow- 
 
 ing cxample, fee Plate VI.) will meet in fome one 
 
 point in the horizontal line CV. Thus the paral- 
 le] lines in the front Wa, meet in the point V-3 
 and thofe of the front PQ, meet in the point Y. 
 
 Thefe points V and Y are (by Dr. Zaylor) called the 
 vanifhing points of thefe parallels, and vy him are 
 ‘thus found : 
 
 From T, the point reprefenting the place from - 
 
 whence the building is to be viewed, draw a line pa- 
 rallel to thofe parallel lines in any front or face. of 
 the object ; and where it meets the ground-line SR, 
 draw a line RY perpendicular toS -R, and its inter- 
 fection Y with the horizontal line V Y, will.be the 
 vanifhing point required. 
 
 ® 
 
 Theor. V. All the lines of an. objeét which are 
 
 parallel to one another, but oblique to the picture, 
 and not parallel to the plane of the horizon, will 
 be reprefented by lines meeting in a vanifhing point, 
 found by the interfection of the picture, and a line 
 
 4. drawn 
 
 
 
 
 
o 4 157.) | j 
 
 drawn from the eye parallel to thofe parallel. lines. 
 But this vanifhing point will not be in the horizon- 
 | tal line, but either above it or. below it. 
 
 Theor. VI The fhadows of all parallel lines oe 
 oa by the interfetion of the fun’s rays, will, on the 
 ground, be. parallel; and confequently in ‘the pic- 
 ture, either be parallel, as in Theorem I. or elfe meet 
 ata point in the ana) line, as in T. heorem Il, 
 
 ue ¥ pa% 
 aaikter,. as in the former example, the centre of the 
 _ picture being determined, the parailels which were 
 perpendicular to it, and alfo parallel to the plane of 
 the horizon, were, by the help thereof, eafily drawn ; 
 fo in this example following, fince the vanifhing 
 - points are of no lefs ufe to draw all parallels, I fhall, 
 _for this purpofe, thew one general rule, without any 
 exceptions; not in the geometrical manner {hewn by 
 Dr. Taylor, but by the help of the new Theodolite, 
 as now improvea by Tuo. Hearn, mathematical 
 inftrument maker, at the Hercules and Globe, near 
 Eixeter-Exchange in the Strand. | 
 Let the example be that contained in Plate VI. 
 where, as before, .raife the draughts PQ, AYW, ~- 
 ABW, (AW Y coinciding with A W B,) Fig. 1, 
 ay 3. and you have the module reprefented to the 
 eye; raife the drawing a Q perpendicular to the 
 plane of the- leaf Fig. 4; and it is the :plane of 
 the picture defigned to be drawn ; but it is oblique 
 to each front of the module:.and the coin or ner 
 PW is the only part of the ee or building 
 which coincides with the picture. Raife up TE 
 (Fig. 5.) as in the former example : ae E repre- 
 fents the eye beholding the building or picture. 
 Plant the inftrument and a ftaff in the line S W, 
 which is the ground-line of the picture, or elle at : 
 equal diftances from it, that is, parallel to it. And 
 | | find, 
 
 
 

 
 
 
 (158 ) 
 find, as in the foregoing example, the dieing, 
 number. 
 
 Plant the inftrument at your defigned avitit Ts 
 and rectify it as in the preceding example. Affume 
 the centre C, on the drawing board, draw cv, 
 CX, as before. 
 
 Then lay down PW, and its feveral divifions- — 
 A’, B, &c, and the two points a, b, as in the for- 4 
 mer example. Draw Pa, and Wb, and produce 
 them till they meet: fo fhall their interfection V be 
 the vanifhing point fought. . 
 
 Ufe this point V as you did the centre of the _ 
 picture in the preceding example ; and then goon 
 to draw the front aW as before. 
 
 In like manner find the vanifhing i as wid 
 proceed to draw the front P 
 
 As to the pofition of the picture, fome peHious 
 will have it parallel to a front, others parallel to the 
 diagonal of the plane ; others chufe rather that po- 
 fition to which a line drawn from the eye to the 
 common coin PW may be perpendicular to the plane 
 of the picture. 
 
 And in this latter, there is no occafion for the di- 
 recting number, or the bearing of any front: for 
 take T the ftation at pleafure ; bring the index to the 
 beginning of the degrees on the horizontal plate, 
 and turn the whole inftrument about till you fee 
 thro’ the telefcope the coin P'W, there fcrew it faft, 
 and level it; and proceed in all refpects as in the 
 laft example. 
 
 
 
( 159 3 
 
 
 
 a: SECT. XIV. 
 
 ‘Ter pai tsin and ufe of the Perambulator, or mea- 
 furinge wheel. 
 
 PP AAIS inftrument, as it is now made, confifts of 
 Ger, a light wooden wheel fhod with a thin iron 
 ring, the outfide circumference whereof is 99 inches, 
 or half a ftatute poles a frame of wood of about 
 three feet long, including the handle and the two 
 _ cheeks, between which the wheel moves ; alfo a box 
 of about 10 inches diameter, containing a motion 
 | work ; on the face whereof are three circles, and their 
 _ indexes or hands; a revolution in the fmalleft circle 
 -anfwers to the length of one gunter’s chain, a revo- 
 lution in the greateft circle anfwers to one mile, and 
 a revolution in the other circle anf{wers to 50 miles. 
 The circle of one chain is divided into 100 equal 
 parts, fhewing the links; that of one mile is divided 
 into 320 equal parts, fhewing the poles; and the 
 other circle is divided into 50 equal parts, fhewing 
 the miles: So that the meafure of any diftance, run 
 over by the wheel, will be expreffed in miles, poles, 
 and links. 
 
 The motion of thefe indices is produced by the ro- 
 tation of the wheel,-whofe axis, as it revolves, com- 
 municates motion to the work in the box through 
 a groove or channel cut in one of the cheeks, 
 
 The length of the initrament, from the extremity 
 of the wheel to the handle, is about four feet and a 
 half ; and its weicht is about twenty-three pounds, 
 the wood work being of mahogany, and the mo- 
 
 4 tion 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 4 160 ) 4 
 tion work of brafs: Buti it may be made much fhorter 4 
 and lighter. te 
 
 in 
 vk eater 
 
 To ufe the perambulator in the meafuring of diftances. 
 
 Being well afcertained of the accuracy of each 
 pait of the inftrument, open the lid of the box, 
 fet all the hands to the mark o, or beginning of 
 their refpective circles, and fhut the box; then tak- 
 ing the handle in both hands, drive the wheel before 
 you, directing it towards fome fixed point; when 
 the propofed diftance is run over, obferve the pofi- 
 tion of each hand, and thefe being rightly eftimated, 
 will give the meafure’ of that diftance,, reckoning: al- 
 ways from the point on which the wheel refts, at the 
 beginning and end, or the point perpposiicularty: un- 
 der the axle, | ail5 
 
 To find che diftance run over; obférve, firft, the 
 ‘mile index ; fecondly, the pole index ; ‘and, thirdly, 
 the link index: If the mile index has not moved’ one 
 divifion, the diftance is lefs than a mile ; then the 
 pole index will fhew the whole poles,» and the link 
 index fhews the links above the even poles: But, if 
 the mile index has moved one or more divifions, the 
 diftance run will be fo many miles, and the -over- 
 plus poles and links will be fhewed ewer theis « eed 
 ‘tive indices. 
 
 Example %. Suppok the mile index ftands sha: 
 tween the beginning of is divifions and the firft 
 mark ; the pole index at 221 ; andthe link index 
 ato; "then the diftance run over will be 224 poles, 
 or §5-chaing and 25 links, or 5 furlongs and 2x 
 poles. 
 
 Example XI. Suppofe the mile index ftands be- 
 tween the gd and 4th divifion; the'pole index be- 
 tween the 184th and 185th divifiens ; and the dink 
 
 index 
 
 
 

 
 
 ; ( 161 ) 
 
 inde at its 67th divin’) then the diftance run 
 ove r will be 3 miles, 184 poles, and 17 links ; the 
 ther 50 links being equal to 2 a are accounted 
 
 for in‘ a the pole circle. 
 
 
 
 ! When you have feveral fircceffive lines to mea- 
 _fure, or one great diftance, in the rout of which the 
 ermediate diftances of feveral places are to be 
 noted ; the three indexes may be fet at the begin- 
 ning of their refpect circles, at the commencing each 
 new line or diftance 5 or, “which i8 the better way, 
 do not fet the indices anew, but let them continue 
 to revolve, and note at each diftance the numbers — 
  fhewn by the indices; and thus the whole diftance 
 pafied over in any given time will be at once thewn 3 
 then the intermediate diftances, which were mined. 
 will be found, by fubtracting the aha entered 
 in the field. book from-one another. 
 
 
 
 
 
 To this inftrument may be annexed two iron rods, 
 which may lie clofe under the cheeks, and when 
 wanted may be let down and ferve as legs, like thofe 
 : “of a wheel-barrow : Allo to the cheeks may be fixed 
 two ftandards, which reaching above the wheel may 
 : fupport a crofs piece, whereon a Theodelite, or 
 other furveying inftrument may be fixed, whofe 
 centre ftanding over the axle-tree, will always cor- 
 refpond to the place where the line begins, and, con- 
 _ dequently, the trouble of fetting the head of the 
 three legged ftaff over the (ation-ftaff hole, will be 
 avoided; befide which, a furveyor ufing fuch an in- 
 _ ftrument, will be benefited’ in the following’ par- 
 | ‘ticulars, | | 
 
 ee 
 
 
 
 The tirefome re pckbion of ftooping with the chain 
 or pole, will be avoided. 
 
 
 
 M In 
 
 
 
( 162 ' : 
 In the trouble of handling the arrows, chee ace 
 count, and the difficulty of flicking them into — 
 hard gravelly or rocky ground, or into the ground s 
 ‘when frozen. , 
 The expence of one, or both chain-men will be 
 faved. § 
 ‘There can arife no fuch errors as frequently hap- 
 pen to the chain, fuch as its {waying, yawing, the 
 difference of pricking down the arrows, or the di- 
 verfity in the lengths of chains. 
 
 The length of a days journey may be meafured 
 without keeping any account, till the end. 
 
 
 
 In taking the angles of elevation or defcent, the 
 Theodelite always ftands at the fame height from 
 the ground, } 
 
 A. furveyor with one or two affiftants, and this — 
 inftrument, can meafure any quantity of land in a~ 
 bout half the time he could do it in by any other 
 means. 
 
 To the ufe of this inftrument it may be okiected, 
 that in going over many plough ridges, or ant-hills, 
 there will be a confiderable difference in the lengths- 
 given by the chain and wheel; there will, indeed, 
 Be fone difference, and athe more than will hap- 
 pen in meafuring the fame diftance forwards and 
 backwards by the chain; for, by a trial on a com- 
 mon full of large ant-hills, in the moft uneven part 
 thereof, the wheel gave a pole more than the chain, 
 in the length of a quarter of a mile, and going 
 over more than roo hills; and in meafuring this 
 length back again, the wheel gave the fame di- 
 ftance ; but the chain gaye near half a pole more 
 
 i , than 
 
 
 

 
 ate 
 
 | oe 
 a 
 than before: Befides, an experienced artift would 
 avoid taking the worft place. 
 
 
 
 Ei 
 
 
 
 paffing of rivers, ponds, woods, brakes, &¢.. they 
 are of fmall import; for a perfon of any fhare of 
 fagacity, will readily know how to proceed on fuch 
 
 _ €mergencies. 
 
 sates, €fc, and without varying the indices ; thefe 
 
 _ contrivance to do this being provided, the indices 
 are fixed ; and the weight. of the whole, though 
 “increafed by the Theodelite, will not much exceed 
 
 and may be fo contrived, both frame arid wheel, as 
 to take to pieces for the convenience of carriage, 
 and packed up in the fpace of little more than a 
 cubic foot, ; 
 
 M 2 OS Reo 
 
 ith regard to the objections concetning the 
 
 By With regard to the paffing of hedges, ditches, 
 
 are eafily anfwered; for by hafping the wheel, a © 
 
 
 
 
 ene ene ae ese ee 
 
 FES 
 = 
 
 thirty pounds: But they may be made much lighter; 
 
 Fe i ag a on we on ne aie Be oe ee 
 
 x 
 _ 
 
 So 9 ot Ee nn we ae oe we oe ee 
 
 SS 
 
 
 
 
 — 
 
 x, 
 — 
 
 fect 
 
 - 
 
 ieee: 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 the pe 
 
 T has been fuppofed, that a needle, playing free 
 ‘ly, which has had a ftrong touch from the load- 
 {tone, points exactly north and fouth. But by num- 
 berlefs experiments it has been proved, That the 
 needle does not point exaétly north and fouth, any 
 where but in fuch places on the earth as lie on one 
 particular line, which is therefore called, The Line of 
 no Variation; and this line is found to change its fi-’ 
 tuation by a flow motion, from eaft to weft. ley 
 now pafies from the weftward of the Cape of Goody 
 Hope to the Weft-Indies. And the variation of they 
 needle in all other places is known conftantly to alter) 
 by a flow change. In England that end of the needle™ 
 which has been fuppofed to point full north, de- 
 viates from it now about 14 * degrees to the ‘welt- | 
 ward ; and is ftill, and alfo will for many years con-— 
 tinue to increafe, even till it arrive at its Maximum 3” | 
 and then will decreafe till it vanifhes, and then” 
 change to the eaftward, as it formerly, was; and by : 
 ano fcillatory change will fo continue to alter, | 
 This variation of the needle'would no ways hin-)) 
 der the exactnefs of the furvey, if it was conftant ; 
 nor is the alteration of the variation capable of cate | 
 
 * “Inthe year 1749, the deviation to the weftward was about 
 i7 degrees. . i 
 * o 
 
 ee) 
 

 
 
 
 
 
 
 (1 és) ns 
 pace of ti time not exceeding four or five years. 
 it if the quantity of the variation be not known, 
 
 | and confequently not allowed for, the north point of 
 the compals, which the furveyor draws on his map, 
 
 convenient i in all places to find it; and this may be 
 | eee ways: But by none more readily, more 
 | cafily, or more exactly, than by the univerfa! dial, 
 as now made by Mr. Hearn, the inftrument- 
 _ maker mentioned before, the figure whereof is in the 
 | plate fronting the title. 
 
 | _ This dial confifts of four principal parts, viz. the 
 Foot or Pedeftal, the Meridian, the Equinoffial, and 
 | the Bridge. 
 
 The Pedefial contains a box and a ne edle, and 
 
 _ three {crews in the foot, it may be placed truly hori- 
 _ zontal; and while the ‘pedettal remains in this firu- 
 ‘ation, the box and the circles of the inftrument may 
 | be turned: round to acquire a proper pofition of the 
 | 
 
 ‘meridian. ‘The circumference of the box is divided’ | 
 Into 360 degrees, and within this is another circle. 
 
 divided into four quadrants, and each numbered 
 with go degrees. On the plane of that part of the 
 pedeftal which is moveable are fegments of circles, 
 
 | a any fenfible error in a furvey that is performed _ 
 
 | will err as much as that variation is. It is therefore. 
 
 two crofs levels; whereby, with the help of the | 
 
 7 
 
 containing a table of the equation of time; fhewing | 
 
 the months, and days of the month, together with 
 the minutes which watches, or equal time-keepers, 
 are too faft or too flow for the motion of the fun: 
 And on the outer margin of this moveable part, is 
 a circle divided and numbered, either into 360 de- 
 grees, or into four quadrants, containing go degrees 
 
 , 
 
 each ; beginning with o degrees, at two points dia- | 
 
 metrically oppofite: This circle flides againft the 
 fixed ring of the cote on which is a Vernier’s 
 icale, (commonly called Nonius’s) for obtaining parts 
 of degrees. 
 
 M 3 The 
 
 
 

 
 
 
 
 
 
 C60: 5° eg 
 The two {crolls which ftand upright on the cham 
 of the pedeftal, and fupport the rings of the inftru- 
 ment, have fixed to them aftrong ring, whofe plane 
 is at right angles to the divifion o degrees on the 
 plane of the pedeftal 5 within this ring flides the me= 
 vidian, on one fide whereof are engraved the names 
 of places, with their latitudes; and the other fide 
 is divided into four quadrants of go degrees each: 
 To the upper part of the ring, within which flides 
 the. meridian, is fixed an inde, on which is a Ver-— 
 nier’s {cale, ferving to fhew the parts of degrees on” 
 the meridian; and to this piece is fixed a ring, by 
 which the whole inftrument may be lifted. | 
 Concentric within the meridian is the equinotlial 
 ring; having on one fide the names of forne places’ 
 with their laneudes : ; on the other fide the hours’of a 
 day, each divided into every fecond minute; and the. 
 infide of the ring divided in the fame manner. ‘This — 
 ying turns on two points diametrically oppofite, — 
 fixed at the divifions XII and XII, and the fame 
 points are fixed on the infide of the meridian ring, — 
 againit the diametrical divifions o and o, The equi- ~ 
 nocual ring turning on thefe points, may be fhut up 
 within the meridian ring, or fet at right angles to it, 
 beyond which pofition it is not foflered s to pafs, ae 
 there being two pieces fixed to the meridian which ~ 
 {tops the equinoétial ring when in the faid pofition. 
 The Bridge is a ftrait flat piece, fo fixed to the — 
 meridian ring as to turn on two points in the direc: 
 tion of the middle of the bridge, and oppofite to — 
 the divifions go and go on the meridian, On one ~ 
 fide of the bridge are the names of the months, with 
 divifions to every fecond day; on the other fide are 
 the figns of the Ecliptic, with their diftances gra- 
 duated to every fecond: degree ; alfo the degrees and 
 half degrees of deglination® north and ee ; and in 
 the middle of the bridge is a flit, in which is placed 
 a flider, with a hole in its middle, 
 When 
 
( 167 ) 
 When an obfervation is made with this inftru- 
 ment, ‘the latitude of the place counted on the me- 
 ridian according, as it is north or fouth, diftinguifhed 
  N. and S. mutt be brought to the index at top; 
 the flider on the bridge muft be brought to either 
 the day of the month, the Sun’s declination, or the 
 _ Sun’s place, and then it will accordingly fhew the 
 _ other two: The equinoctial circle muft be thruft 
 out of the meridian, till it is at right angles to it. 
 _ Then bring the beginning of the degrees on the ho- 
  rizontal part of the pedeftal to the index there : 
 | a the whole about upon the three feet, till the 
 un fhines equally on both faces of the plane of the 
 - meridian, the north part of the inftrument being 
 
 ‘towards the north part of the world, and fet the 
 horizontal plane level. Then fhall the dial be duly 
 . rectified for obfervation. 
 
 ‘It may be readily known when the plane of the 
 meridian is directed to the Sun’s centre, by holding 
 a piece of clean paper behind the meridian, and ob- 
 ferving that the fhade of the fore part of the ring 
 falls juft on the breadth of the infide of the back 
 part ; and that the fhade on the paper is of the fame 
 breadth with the thicknefs of the ring. 
 
 Now keeping the three feet in the fame place, 
 turn the dial about, till the fpot of light pafling 
 thro’ the hole in the flider, falls on the circle which 
 is divided into hours, €@c. in the middle of the in- 
 fide of that ring which reprefents the equinoctial ; 
 which will be among the morning hours, if before 
 noon; and among the evening hours, if after noon’: 
 then will the dial fhew thefe fol lowing very ufeful 
 and pleafant problems, 
 
 
 
 I. The fpot of light points out cally the hour 
 of the day. 
 
 M¢- II. The 
 
 
 
 
 
 
 > 
 ae 
 
 SR ESP ET EIS TOI SEI em ee 7 : 
 = Soon agen eae gh ee Ree = = ire SOE AS Ea Se é: SA in SSA 
 _ Se et a - ee = sae SRST 2 — 
 ur La - —— . =. - : ™ 
 a SS Se Se ELLE er Bares: : r 1 T.7 t on. us 
 
 rrr 
 t itt 
 
 
 
 
 
 
 x 
 ¥ 
 rr 
 
 - 
 = ae 
 rt 
 
 
 
 Es eyeynr-ror 
 ery ty tye re 
 opty leterrey 
 
 ere 
 
 + 
 tT 
 
 Tv 
 
 
 
 x 
 7 
 
 
 
 rete 
 re 
 
 pees perk 
 ARPETESSa est! 
 
 rae 
 = 
 
 — 
 
 
 
 
 
 
 -— 
 te 
 
 —: 
 zs 
 
 
 
 
 
 
 ae peste sea 
 practi Fett 
 eee te 
 
 x 
 = 
 

 
 ( 168 ) 
 
 ¥. The circle reprefenting the meridian, lies | 
 exactly in the plane of the celeftial meridian ; and 
 fo a thread ftretched over either face of it, draws a 
 true meridian line. a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ‘ 
 ‘4 
 
 III. The middle of the Bridee pout “Se to q 
 the true poles. : 
 
 IV. The needle in the box tiers the variation — 
 by the diftance of its end from the beginning of — 
 the degrees there mark’d ; and is weftward, if the — 
 north end of the needle be to the left-hand of the 
 beginning of thofe degrees, but eaftward when to 
 the right. | ee 
 . The index on the horizon, points out the 
 Sun’s Azimuth, which is to be reckoned from eatt 
 or weft, if the circle on the horizontal pay is di- 
 vided into four nineties. 
 
 Vi. Turn the meridian about the plane of the 
 horizon, till the Sun fhines equally on both its faces - 
 as at firft, the three feet ftill ftanding in the fame 
 place, Mid move the meridian towards % or from the 
 Sun, till the fpot of light coming thro’ the hole in 
 
 that fight which has the crofs hairs in it, falls exact- * 
 ly on ‘the little hole in the other fight which will ~~ 
 then be undermoft; and the index in the Zenith, 
 points to the Sun’s altitude, among, the divifions of 
 the meridian, 
 
 By this inftrument, may the pofition of any wall 
 be thus found: Let a flrait broad, ruler, whofe fides 
 ate parallel, be applied to a wall, on which a verti-. 
 cal dial is defigned to be drawn, and the two feet of 
 the dial. mark’d A, A, be applied to the other 
 edge of the ruler; then let the dial be reétified to 
 the latitude of the ‘place, with the day of the month 5 
 
 be 
 

 
 if» 489 y 
 Re levelled, st andthe upper part e the inftrument 
 
 
 
 
 that. wall, ufually called by diallers, The declination 
 of the p slane. Or, if the Sun does not fhine, apply 
 the legs A, A, tothe ruler, keep them in that po- 
 fition, and turn.the upper part about, till the north 
 
 
 
 
 end of the needle points at the variation; and then 
 
 vill the index on the pedeftal fhew the fituation, 
 
 This curious inftrument is of great ufe for the re- 
 ~golation of clocks and watches, “by the help of the 
 apparent time obferved by it (as fhewn above} and 
 the equation of time engraved on the horizontal part 
 
 E | of the spedeftal. 
 
 It is alfoa very ready inftrument for Seika an 
 horizontal dial duly: For after the apparent time is 
 found by it, and the horizontal dial fo feated, that 
 it may be turned about, and ftill be parallel to the 
 horizon ; then move it round, the Sun fhining there- 
 on, till it fhews the fame tie that the apart dial 
 fhews, and then it is,truly placed, and may be there 
 fixed to the pedeftal. 
 
 And becaufe the latitude of the plaee where the 
 inftrument is ufed, muft be known; there is en- 
 eraved on the backfide of the meridian, or the un- 
 
 derfide of the pedeftal, the latitudes of the cities, | 
 
 and moft remarkable towns in England, and other 
 parts of Europe. 
 
 But if any gentleman pleafes to communicate to 
 the workman, the latitudes of his country feats, 
 
 __ they may be particularly laid down on it. 
 
 
 
 
 
 Or if any gentleman about to travel, is pleafed to 
 communicate the tour he defigns to take, he may 
 have a catalogue of the towns in his way, and their 
 Jatitudes, from Mr. Heath, with the inftrument, in 
 order to eafe him of the trouble of fearching maps, 
 globes, or geographical books. 
 
 The 
 
 ned about till the fpot of light fall as before; then’ 
 index on the horizon will give the fituation of — 
 
 . : 
 
 h 
 . 
 ey { 
 if 
 > oa 
 j a 
 es! 
 at) 
 nf ‘ 
 r iia! 
 ie Laren 
 Lt 
 way 
 t bey 
 ' 4 
 res] 
 Lig lsd 
 i wt 
 
 i 
 nt 
 
 a TYy es Se ee? 
 
 ~~ 
 = 
 
 a 
 
 _ - 
 
 Sn = = Sat 
 Teter ft. ttt Tr? 
 
 
 
( 170 ) 
 _ The variation of the needle may be found by the 
 Theodolite, thus: Take the bearing of the Sun exaét- 
 ly at 12 at noon, and the north-end of the needle 
 pies the variation. 
 
 Or, take the bearing of the Sun, either at the 
 time of rifing or fetting; and then, fay : As the 
 fine of the complement of the latitude, is to the fine 
 of the declination; {fo is the fine of go degrees, to 
 the fine of the Sun’s diftance from the. eaft at rifing, 
 and from the weft at fetting ; and is always fouther- 
 ly, when the declination is fouth, and northerly 
 when north, And as much as this diftance differs. 
 from that obferved by the inftrument, fo much is 
 the variation: And if the bearing taken by the in- 
 itrument be to the left-hand of that calculated, it is 
 
 _ wefterly, otherwife eafterly. 
 
 
 
 
 
 Or it may be found, by an horizontal dial, duly 
 feated, without the Sun ; ; if you ftretch a thread on 
 ‘that dial’s meridian line, and the inftrument placed 
 near it, you turn the index about, till the telefcope 
 is parallel to that thread ; for then the bearing fhewn 
 by the north-end of the needle, is the variation. 
 
 Befide the preceding ufes of this univerfal dial ; 
 it may, with a very fmall addition, be applied in all 
 refpects as a Theodolite, or Circumferentor ; or this 
 dial may be aptly and eafily mounted on a Theodo- 
 lite, and be taken off at pleafure. 
 
 There is one inconvenience ufually attends the ufe 
 of thefe inftruments, which in this may be remedied : 
 From about an hour before, to an hour after noon, 
 the paflage of the {pot of light over the equinoétial, 
 forms with it fo acute an angle, that it is not very 
 eafy to obferve the point where it croffes it; and, 
 confequently, the preceding problems cannot be fo 
 exactly performed, And juft at noon, the thick. 
 
 nefs 
 
 
 
 
 

 
 ee 
 4 - 
 aes 
 
 i 
 4 
 if 
 
 (O78)? 
 
 i Aeatt of the brafs fhades the flider and bridge 5 and 
 
 fo no obfervation at all can be made. 
 
 In this cafe, bring the beginning of the degrees 
 to the index on the horizontal part, and Jet the hour 
 
 be taken by the inftrument fome time before, which 
 
 is remote from noon, whether before or after, on the 
 
 _ board of the window of your ftudy, where you de- 
 
 fg to ufe it; the index all the while pointing to the 
 
 eerenning of the degrees, Lay a ftrait ruler to 
 _ touch the feet marked A, A; and by its edge, draw 
 
 on the window-board a ‘enic line, or make two 
 
 points where that ftrait line fhould be drawn: And 
 then, at any time that is very near noon, -by laying 
 
 the ruler to the line or points, bringing the begin- 
 
 ning of the degrees on the horizontal part of the 
 
 pedeftal to the index, and applying the feet A, A, | 
 
 to the edge of the ruler, as before; if you rectify 
 the inftrument to the latitude and day, you may fee 
 the true time either before or after noon; and juft 
 at noon, the middle of the under part of the meri- 
 dian will be thaded by the upper; and confequently 
 the time of noon, is known, and determined, whe- 
 ther it be before or after noon. 
 
 If you are in a ftrange place, and the time be very 
 near noon, level the inftrument, and turn it about 
 till the north-end of the needle points at the varia- 
 
 tion, and then it is duly placed, and you may work 
 
 asin the laft. : 
 
 Much more might be faid of this inftrument’s 
 ufe, but my defigned brevity will not permit me to 
 enlarge any farther thereon. 
 
 The latitude of a place may be found by the 
 common Theodolite, thus: Turn the plate of the 
 in{trument fo that it be in a vertical pofition, in the 
 piane of the meridian, which may be readily known 
 by applying to the plate a {tring and plummet; with 
 this pofition, Set the fixed fights horizontal, either 
 
 by 
 
 
 
 "5 ty? fewer ce crearar 
 
 nan 
 
 ag Ee 
 
 
 
 
 
 
 =: 
 
 
 
 
 ee dah 
 
 
 
 ce « 
 - 
 
 7 de. 
 
 
 
 
 
 ass 
 
 
 
 a 
 Se 
 mt 
 
 
 
 re 
 
 tr 
 
 
 
 
 x . Ss 
 rors: ry 
 
 = 
 
 ——_ : " 
 - = - 1 
 se oe 
 WES ct 
 
 
 
 r 
 
 
 
 
 ay 
 
 i. 
 ly Byty t 
 SS ee 
 
 x 
 se ~ 
 Lest eieses. 
 
 
 
 
 
 
 
 Ranta age 
 iy mn on 
 etttesaa 
 
 
 
 
 
 os. 
 r 
 
 
 
 Feige 
 
 
 
 z 
 
 toons: 
 ty 
 ztr 
 
 
 
 
 a7 
 sr 
 
 
 
 Sa 
 _ 
 =. 
 
 
 
 x 
 teeth 
 oe 
 
 
 
 Si) tie ey 
 
 a Mersey = 
 
 z ~ 
 r 
 Eplyhy tet 
 “ x 
 

 
 Ne Sb 2 a ee. 
 by a level, or by the thread of a plummet.cutting® 
 the degree at right angles to the fixed fights; then 
 ‘a little before noon move the index fo thatthe Sun’s 
 
 _rays paffing thro’ the hole in one fight, the fpot' 
 may fall direétly on the middle line of the other 
 fight; and the degrees cut by the index will fhew 
 
 _ the Sun’s altitude at that time: As the Sun mounts 
 
 higher, the fpot will defcend on the fight, therefore 
 keep the index moving fo as to ftay the fpot on thé. 0g 
 line, until the fpot be obferved to begin to rifea- 
 bove the line, then obferve the degrees cut by the 
 
 index, and they will be the meridian‘ altitude, and 
 their complement to 90, will be the Sun’s zenith 
 diftance; which on this fide the tropic of Cancer 
 muft always be named fouth. | | 
 
 _ Now having the Sun’s meridian zenith diftance, 
 
 and his declination taken from tables, the latitude 
 of the place may be found by this 
 
 Rue. If the zenith diftance and deelina- 
 
 tion have contrary names, their fum gives the lati- 
 tude fought, of the fame name with the declination. 
 
 _ . But, if the zenith diftance and declination have 
 the fame name, the difference will be the latitude 
 fought, of the fame, or a contrary, mame with the 
 declination, as it is greater, or lefs, than the zenith 
 diftance. 
 
 A 
 
 
 

 
 
 ie re a E 
 
 
 
 ig x 
 t. rar Whew ys 
 ) $3 =9 se Oy 239) ei» 
 er Fey Gey © Sm Ae yD ca 
 ae ies Seen le RV 
 } io Aa Dy eo - - y 
 eae 4 ese” ' P ues 
 Ee The defcription and ufe of ibe Pantographia, or 
 bt ee Imitator. 
 2 HIS inftrument confifts of four rulers, two 
 
 large and two {mall: The two great ones are 
 joined at one of their extremities by a joint, ‘or cen- 
 tre, about which they are eafily moveable. At the 
 bottom of this joint is a little roller or cafter, whereon 
 the inftrument is to bear: One ead of each of the 
 two {mall rulers are pinned near the middle of each 
 great one, and the other ends fattened by a joint, fo 
 that in what manner foever the inftrument is moved, 
 | the four rulers always form a parallelogram, having 
 : two contiguous fides about as long again as the other 
 
 two fides, 
 
 The two longer, and one of the fhorter rulers 
 have each a box fitted to them, that may be moved 
 and fixed to any part of the faid rulers, by means 
 of a {crew fixed to the box. Thefe boxes have each 
 a cylindric hole, wherein may be alternately put 
 three things; namely, a tracing-point, a port- 
 crayon, that rifes and lowers of itfelf, according 
 to the unevennefs of the plane worked upon; 
 and, a fulcrum that {crews into the table, the top 
 whereof. is a cylinder fitting one of the boxes: 
 This fulcrum is the fixed point round which the in- 
 ftrument moves, when ufed to copy with. . There 
 are alfo other cafters on which the rulers reff, ferving 
 likewife to facilitate their motion. On thefe rulers are 
 divifions with figures, fhewing where to place the 
 
 . 4 cham- 
 
 
 
 
 
 a == = So Ip Keke Feta k 
 eee . 7 . ie a te we 
 Loe rerEr Pah Tes rn oe ap ene ee See Se Se EEE = 
 
 Ty 
 
 r 
 arse ———— 
 
 es 
 
 rt 
 
 ee 
 
 <a aes ne rt +3 tT : eth On 
 
 z 
 Perish: 
 
 cae eeaarte 
 

 
 oo Se 
 Eainfered. or bevel edge of the boxes, according to | 
 the intended reduction, 
 
 This inftrument is convenient for fuch who are 
 converfant in the art of drawing, as well as for thofe 
 who have made but little progrefs therein; for with 
 it, may be neatly taken, with great eafe and ac- 
 curacy, the copies of all manner of defigns, whe- 
 ther figures, ornaments, plans, geographic carts, 
 and fuch like, reducing them from a larger fize to 
 a fmaller, or from a fmaller to a larger. The re- 
 ferences in what follows is in plate VII, where the 
 three boxes are marked by the letters A, B, D. 
 
 To u/2 the Pantography. 
 
 Firfi, Having determined the proportion that is 
 to be between the original and copy, fet the bevel 
 edge of the boxes B and D to the divifion expref- 
 fing that proportion, there fcrew them faft ; and fix 
 the edge of the box A to the line C. 
 
 Second, Screw the fulcrum into fome convenient 
 part of the board on which the operation is to be 
 performed. 
 
 Third, Put the fulcrum into the hole of the box 
 B; the crayon into that of D, and the tracer into 
 that of A, when the copy is to be lefs than the ort- 
 ginal ; but when larger, put the crayon into A, and 
 the tracer into D, 
 
 Fourth, Open the inftrument fomewhat, fix the 
 original under the tracer, and clean paper under the 
 crayon ; then, while a fteady hand moves the tracer 
 over the lines of the original, the crayon or pencil 
 will draw the copy required. 
 
 The 
 
 
 

 
 
 
 
 
 eee a 1 
 ae ae ; | I 
 
 (175 ) 
 
 The divifions or ratios thought proper to be 
 placed on the rulers Band D of this inftrument, 
 are, Bees s> 65 4363s oo TON TH 123 and 4, 
 £5 4, $ 7 + > qo0 T9 753 thefe numbers de- 
 note the propofed ratios between the copy and ori- 
 ginal; thus, if the copy is to be half the length 
 
 and breadth of the original, the boxes B, D, and 
 
 
 
 
 A, are to be fet at the divifions 4 and C; then the 
 
 | ~ fulcrum is to be put into B, the crayon in D, and 
 the tracer into A: Ifthe length and breadth of the 
 a ‘copy is to be 2 of thofe of the original, the boxes 
 
 B and D are to be put to the divifions 3, the box 
 
 A, remaining at the mark C, where it is to be fet in 
 
 every operation ; the fulcrum to be put into D, and 
 the crayon into B. And in like manner any other 
 diminution, within. the limits of the divifions, may be 
 readily performed. Cay 
 
 When the copy is to be increafed in any ratio ex- 
 preffibie by one of thefe numbers, the boxes B and 
 D areto be fet to that number as before; the ful- 
 crum put in B, the tracer in D, and the crayon in 
 A; then the picture being put under the tracer D, 
 and the clean paper under the crayon A, the copy 
 may be taken as before. 
 
 When the copy is to be of the fame fize as the 
 original, fix the bevel edge of the boxes B and D, 
 
 _ to the marks 4, and the box A tothe mark C; put 
 
 the fulcrum into the box D, the crayon into B, and 
 the tracer into A; then will the crayon B move 
 over equal lines and fpaces with the tracer A, and, 
 confequently, delineate a copy equal in fize to the 
 original, ; 
 
 And thus may any picture be accurately copied 
 without damaging it in the leaft ; for the tracer may 
 be paffed over the lines without preffing on them, 
 or even touching them: But that this bufinefs of 
 copying may be rendered as perfect as can be de- 
 fired, it will be neceffary to be more circumftantial 
 
 in 
 
 
 
 
 
 es 
 
 x 
 
 oe 
 per tyt 
 
 
 
 
 
 
 
 r 
 
 
 
 
 9 oe ne Se oe in 
 eee 
 erty 
 PSS Se ee Se ae ee ee 
 
 
 
 
 vit. 
 
 - ~ ee 
 Pec 
 as 2 a 
 
 0S Ee os 5 
 ries! 
 oom Sn 8 
 
 rhs 
 
 tye 
 
 ee ee om a 
 1 a : 
 or 
 
 a a ne 
 
We | 
 hy i 
 
 i 
 a 
 
 a pa a aa 
 
 soe es 
 eee 
 
 
 
 Se 
 
 ( 176 ) 
 
 in deferibing the ufe of chis inftrument, particularly. 4 
 fome appendages and cautions not yet mentioned,’ ~ 
 
 In plate Vl. jig. 1. reprefents the plan of the in- if 
 ftroment, with all the divifions ; figure 2 is a per- 4 
 fpective view of it on a table, in ‘fie proper pofition 1 
 for ule. The boxes A, B and D are placed for rer J 
 
 ducing the original to one third of its fize, or as 1 
 to 3, fhewn in r the figure. The fulcrum f, ferewed - 
 into the table, is placed in the box B; this fulcrum, 
 
 as hitherto defcribed, is fixed, but a moveable one 
 
 may be fubftituted in its room, — as fhall be fhewed — 
 hereafter. | 
 
 Over fig. 2, the different pieces fret to the rulers 
 are feverally reprefented. The figures A and Ran | 
 prefent the two boxes. Eis the tracing point that 
 fits in the focket N, fixed to the boxes A and B. 
 Thefe fockets has a little {crew O, ferving to fix ae 
 tracing point when fec in the boxes, at phe ue 
 height. 
 
 Fioure F is the tube for the port crayon, G ‘ a 
 
 the port crayon to be put into the tube Fy at has a 
 {mall filken ftring fixed. to it, ferving to raife the 
 
 crayon or pencil, "fo that it may not touch the paper 7 
 while it is moving from one place to another. This — | 
 
 {tring is thus fed 3 when the crayon is in the box: D, 
 pals ‘the loofe end thr ough the nase ‘in che uprighe 
 pieces fixed at Z, S, X, fig. 2; then taking the 
 end’ into the hand hol ae the iit A, the crayon 
 may be raifed with the oreateft eae, | Henao it 1s 
 wanted, even while the ‘inttrument i is moving. - But 
 if the crayon is put into the box A, then the loofe 
 end muft pafs through the holes in the pieces X,.S,: 
 Z, and fo to the hand, which in this cafe will have 
 hold of the box D. 
 
 The ftring is reprefented in fig. 2. its length is al- 
 ways the fame, however the boxes are placed, be- 
 
 caufe it follows the direction of the rulers, 
 
 a he 
 
 
 

 
 C174.) 
 The cup H above the port crayon G, fcrews on 
 
 its upper part, and ferves to increafe ahs weight of 
 
 the crayon or pencil, making it prefs harder on the 
 
 pa when neceffary ; this is done by putting in | 
 
 eaden fhot, or any fuch like weight 
 The lit: ie wheel, or caftor, L, chat has a double 
 
 flit or groove, x and y, 1s fixed to the ruler B by. 
 
 the under groove x, when the crayon is put into the 
 box B. But if put into D, the caftor or wheel L, 
 
 then flips on the ruler D by the upper groove y. 
 Misa wheel or caftor to be put on the ruler A, 
 
 _ The fulcrum, fcrewing to the table, as mentioned 
 ‘in the foregoing defcription, and reprefented in fig. 2. 
 being proper only to copy fubjects of a middling 
 
 fize; a moveable fulcrum rape teaeee by fig. P, is 
 to be ufed when the picture is large. This fulcrum 
 is a piece of lead of fufficient weight fo prevent its 
 being difplaced by the motion of the inftrument. In 
 the middle thereof is {crewed a pin K, like the fixed 
 
 fulcrum [. The figure R is a little collar, ferving 
 
 equally to either the fixed or moveable fulcram, on 
 whofe pin it is put when either of them is placed 
 at the box D: But is not ufed when placed at the 
 box B, becaufe this is lefs diftant from the table. 
 Little collars, of different heights, are alfo ufed in 
 the fame manner to K and 1; the ufe thereof de- 
 
 pending on the prudence of the operator, taking” 
 
 care that the motion of the inftrument be performed 
 
 with the utmott freedom. 
 
 With this moveable fulcrum a picture or drawing 
 o Jany dimenfion may be copyed: For the pidure 
 being made faft on any table or plane, the fulcrum 
 mutt be fo fituated that a part thereof may be copyed 
 as far as the inftrument can extend at that time. 
 Then on the picture and paper mark three corref- 
 ponding i on each, to ferve as references for 
 finding the pofition of the fulcrum in the copy, Fe- 
 latively to what has been already drawn; move 
 N | the 
 
 Seater tree 
 
 ee epee 
 aPurert x* oe ¢ 
 
 zt 
 
 Hig 
 page) 
 
 ye Te 
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 — 
 
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 Sa aa as A 
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 a 
 
 t 
 
 
 

 
 Chetan 
 
 the fulcrum towards the picture, and when the three 
 
 points on each are found to correfpond, fix the copy: * 
 
 in that fituation with a little foft wax; then con-. 
 
 tinue drawing as far as the inftrument can extend, oi 
 
 as before, repeating this operation till the whole is, 
 ed, 
 
 we he ufefulnefs of ae moveable fulcrum is eafily 
 perceived ; for if towards the end of the operation 
 both the copy and fulcrurn fhould reft on the pic- 
 ture, it would be no inconvenience as they no ways. 
 damage it. By this means alfo the extraordinary — 
 length of the rulers is prevented, which are gene- 
 rally but of abour two foot anda half; a greater: 
 length would render them inaccurate, becaufe they 
 would then be more fubject to bend and {pring 
 
 It may happen, on account of the fize of the 
 paper, or otherwife, that the copy will not be ina 
 proportion to the original, expreffible by any of the 
 divifions on the inftrument; in fuch cafe a method. 
 muft be found to do without, by placing the crayon, 
 tracer and fulcrum in a pofition anfwering to the re-. 
 Jative dimenfions of the original and copy. 
 
 In order to which it is neceffary to obferve, that. 
 the fundamental principle, on which depends the ac. 
 curacy in operating by this inftrument is, that the. 
 fulcrum, crayon, and tracer, are always to ftand in 
 a right line, in every pofition of the rulers; when-. 
 ever they are fo, the copy will truly reprefent the 
 original. By the following method it will be known 
 if thofe three points ftand in a right line. 
 
 Let the fulcrum, crayon, and + tracer, be included , 
 between a doubled thread, as in the figures marked 
 1h, 25. 2, lange under the inftrument marked 
 fig. 1: Hold thefe threads faft at the mark Ef 
 
 and if the points are not in a right line, the thread 
 will be bent at the box D, marked 2; this box muft 
 then. be moved till the threads become parallel, by 
 4 touching 
 
 
 

 
 = ~“* 
 
 (179 ) 
 touching both fides of the three cylinders, which 
 will then be in aright line, 
 
 This principle being obferved in the dofition of 
 the abovementioned points, let there be given a picture 
 or drawing of any dimenfion to reduce to a fize that 
 is no aliquot part, or parts of the original ; then ope- 
 rate.in the following manner. 
 
 Examine, firft, i the given fize is greater or lefs 
 than half the original. | 
 
 ~ When lefs, always place ‘the fulcrum in the har 
 
 B, the crayon in the box D, and the tracer.in A; 
 thefe points being brought to a right line as before- 
 mentioned, run over with the tracing point, A, the 
 whole length or breadth of the original in a ‘ftrait 
 line ; then examine whether the Ime: miade by the 
 crayon agrees with the fize given, 
 
 Jf not, and that the fpace run through by the 
 crayon is lefs than the given fize, bring the box B 
 nearer to the line B on its ruler, and the box D 
 nearer the line D on its ruler. 
 
 If; on the contrary, the line traced. by the crayon 
 be greater than the given fize, bring the two boxes 
 B and D towards the junction Z of the rulers B 
 and D; and; by trials, the proper extent will be 
 found. coll 
 * By this method, a drawing of any dimenfion may 
 be copyéd on any given fide, without regard being 
 had to the divifions on the ruler. 
 
 _ If the given fize be greater than half the original, 
 then the fulcrum mult be placed in the box D, and 
 the crayon in the box B. 
 
 When the picture is fo large that the inftrument 
 cannot extend to its limits, then a third, fourth, &fc. 
 part fay be taken; proportioning the parts of the 
 copy to thofe on the original; and working accord- 
 ing to the foregoing directions,’ an accurate reduced 
 copy thereof may be obtained, 
 
 N 2 Te 
 
 Fs ee as mn Gap a ae Se aS A ce cn a ES ae gh ee ee 2 eee ee oe ne ee ap ee 
 
 
 
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 Le 
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 Fr) 
 
 : 
 fH 
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SS alee ee 
 
 
 
 “(180 fe 
 
 T 0 find the ae ifions on the legs S B, s D. 
 
 Let the lines AB, a On EG, GH, Fie: FA 
 
 Plgte VII. ) reprefent four rulers, fol conneéted toge- | 
 ther, that in any pofition of AB, AC, there may — 
 always be formed a parallelogram, whofe fides are a 
 
 As EG. ees HAL 
 
 Now if: ACi 1s af any fixed fenigieli and éhe ra- 1 
 
 tios of AE and ED to AC be aflumed, and thro’ 
 D be drawn the right line C D, rye A bil in 1B 
 
 Required the length of A B. 
 
 And AC: E Dita: m, Then ED=—x AC, 
 Now CF:FD::ED: EB, by mila tri- 
 
 | tag 
 
 Or AC—ED: FD: :-ED : AB—AE. 
 
 “EF Dx Hepes |e 
 
 Put AC=r, Then AE=—r; and ED=—r. 
 
 And r——ri—ri: —r:AB——r. Therefore 
 nN a n a 7 
 
 mM C MC me 
 ABxr—ABx —r—~a~—rrte—rro=—re. 
 fant ne a BE na | 
 
 ‘Therefore AB Xr—-ABX ~ ror r. > 
 
 n ¢ 
 Confequently A B= pra Sam 
 
 Hence 
 
 \ aa 
 
 Let ROOAE 202 eae 
 
 
 

 
 ( xi ) 
 “3 gee AB ei Kem a when AE=>AC. 
 
 
 
 3 Alfo = air, when AC'= 1. 
 
 PF. 4a . pp “eo 
 | 
 { 
 . 
 
 ‘ts | lithe ratioof AE and ABto AC were afigmed, 
 to find ED. | Bo? 
 
 | | Thea AB: AC::EB:ED. A a 
 ~—6hr Or AB: AC::AB—AE: ED. 
 
 Let AB: AC:is:2. ‘Then AB = £ KC. 
 
 
 
 dytyt yet 
 ~- 
 
 = 
 
 BL Ree 
 Sent 
 
 And— AC :AC:: = = AC——AC:ED. 
 
 
 
 : —tl 
 | Therefore w= (“5 seats), at ge od xr, 
 Hence ED=1— . xir, when AB=2 AC. 
 
 Alo E D— pax, when AC= 1. 
 
 And hence the numbers in the following table 
 were found. Where ED in the firft column, and 
 A B in the third, are each compared to AC, their 
 ratios being expreffed by the numbers in thafe co- 
 * Jumns ; arid the numbers in the fecond and third co- 
 lumns, are related to AC asthe unit; AE being 
 {uppofed =o toz AC. 
 
 
 
 
 
 SSS : pe eae a a 
 es So es ck ce aie oO a ae eo OT Se eh ee ie an OS OS 
 
 t=" 
 
 A ta 
 
 
 
( 182 ) 
 
 
 
 A TABLE for thedivifions of the Pantographer.| 
 
 
 
 
 
 
 
 When E D | Then AB When AB Then ED 
 is pNee 1S PED) PS oh 1s’: 1s <a 
 = 15 = 0525 
 n O75 = | %3333 
 + 0,625 $ Or4 
 Zs O, 1 0,4166 
 
 7 0,58 33 oe -0,4285 
 © 0,5714 so oh. 004375 
 5 0,5625 Ts 0544.44 
 To. 055555 TT 0545, 
 Tr 0355 TF 04545 
 
 a 
 
 
 
 rf 
 
 »| 
 
 05444 | 
 
 
 
 When the ratio of the copy to the original is — 
 Found in the firft column; the tracer is to be in A, 
 | the crayon in D, and the fulcrum in B, if the copy 
 
 ‘ is diminifhed ; but, if increafed, the tracer and pera 
 yee change places. 
 
 And if the ratio of the copy to the original is — 
 found in the third column, then the tracer is to be 
 in A, the crayon in B, and the fulcrum in D, if 
 the copy is diminifhed ; but if the copy is to be in- 
 creafed, the tracer 1s to >be put into B, and the crayor 
 into A. 
 
 
 
 
 
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