the Instrument Of the Staffe The Staffe Lastly vnto this Instrument there belongeth a Staffe 4 foote long with a good stéele pike in the foote thereof this Staffe serueth to plant your Instrument vpon for which purpose in the top thereof is placed a round pin of wood or brasse and through the midst of the Instrument is bored a hole to fit the said pin so when the Instrument is placed vpon the said pin hée will moue round about but the best staffe is that which is made with thrée staues ioyned together like to a 3 footed paire of compasses CHAP. LXII Of the Circumferentor his appellation and such things as are to be considered generally therein and of the protractor The definition of the Circumferentor WHat the intention of the first composer of this Instrument was in calling it a Circumferentor I know not but this I affirme the name was not vnaptly giuen for if we well consider hereof it will be apparent that the working thereby giues or afoords the name it selfe for when we worke in platting of fields c. wée bée instructed to moue or beare the Instrument about vntill hée point vnto the proposed angle whereby you sée wée beare him about vpon the top of the Staffe whereon he is planted so that he is properly called a Circumferentor of the Lattin word Circum which signifieth about or round about and fero the verbe signifying to beare or cary so Circumfero is to beare about whereupon the Circumferentor taketh his name which you may take in mouing him about the Staffe or bearing him about the field in working whereby you must alwaies haue a special care vnto the paralelty thereof so that it is not lawfull for him to leane one way or another but the plaine thereof must alwaies lye paralell to the Horizon which the plumet in the shorter fight will helpe you to do one way Then must you prouide a Protractor The Protractor see the Chap. 26. which is a halfe circle diuided vpon the vpside in the line into 60 such equall parts as the Carde in the first Chapter was the diameter whereof must agree with the diameter of the Carde the lower side of this protractor is diuided into 60 such equall parts procéeding from 60 vnto 120 so that All the diuisions to 60 be vpon the vpside and that is called the East side Then all the diuisions vnto 120 aboue 60 be vpon the lower side and that is called the West side The diameter of this Protractor representeth a Meridian Vpon the vtter side of this diameter is roome left for to make a scale which is diuided according vnto 12 in the inch make not your protractor as the common order is See the 6 booke Chap. 53 of the Geod Staffe if the scale had 12 parts in the inch vpon the one side and 11 on the other it would do you pleasure CHAP. LXIII To take the Almicanter and Azimuth of the Sun or Starre by the old Circumferentor To take the altitude and Azimuth of the Sun or Starre PLant your Instrument so that hee may lye paralell vnto the Horizon then turne him about vntill through the sight hole and slit in the longer sight and by the pins hend in the shorter sight you see the Sunne or Starre bringing downe the vane vntill through the hole therein and by the foresaid pinnes head you see the said Sunne or Starre then the degrée cut by the siâ—e of the â—ane sheweth the Almicanter or altitude of the Sun and the degrée in the Card cut by the South end of the néedle sheweth the Azimuth or the distance of the Sun from the Meridian But if the Sunne or Star be higher then 25 degrees so that you cannot bring downe the vane to worke vpon the longer sight then put the Index vpon the center pin looking through the sight in the Index vntill through the same hole and by the center pin you see the Sun or Star for the degr then cut vpon the edge of the Instrument by the edge of the Index is the altitude And by this Proposition may you obserue all the Stars in the Globe together with their motions in the heauens Example The 6 of October in the Morning I made obseruation according vnto the first difference where hauing planted my Instrument paralell and spied the Sunne through the hole in the vane and by the pins head I found the vane to out 12 degrees vpon the sight and the South end of the needle to cut 19 â— 60 degrees which shewed me that the Sunne was 1 degrees high and that he wanreth 58 degrees of the Meridian for the South point cutting 29 degrees 20 minutes I multiply the same by 3 there commeth 58 which sheweth me there is so many degrees included betwixt the Sun and the Meridian and so of the rest CHAP. LXIIII. To finde in what point of the Horizon any thing seene lyeth by the old Cirferentor To know in what point of the coÌ„passe any thing lyeth HEre it is requisite first to vnderstand that 120 degrées represent the South and that the degrées are numbred into the East so that to find what point of the Horizon any thing lyeth from you do thus Let the Instrument be placed paralel vpon the staffe then cease not to moue the same With more ease see the 28 Chapter vntill through the hole in the vane and by the pins head you sée the thing desired note the degrée then cut by the South end of the néedle with which resort vnto this Table so haue you your demande 15 30 45 60 Sou East East Nor East North 75 90 105 120 Nor West West Sou West North Example I find the South point cut 45 degrees I conclude the thing seene is North-east CHAP. LXV To finde the houre of the day by sight of the Sunne To know the houre of the day WOrke the instrument lying paralell vntill the shadow of the pins head point or fall iust in the slit in the longer sight the intersection of the néedle I meane the South part with the paralell of the month or signe take whether you please is the houre which you shall know by the houre line passing thereby And you must vnderstand that those circles I call paralels be such as are described about the center of the Carde and those I call houre circles bée those that passe as it were from the center to the limbe crossing the paralels CHAP. LXVI To find the houre of Sunne rising and setting at any time proposed and the length of the day and night HEre you must note that this Card is made but for one latitude and therefore his worke in that behalfe cannot be generall but it may serue without any notable error ouer the most part of England You shall obserue where the paralel of the moneth cutteth the Horizon for the houre circle passing thereby or the néerest therevnto sheweth your demand remembring to séeke
the setting vpon the West side and the rising vpon the East side of the Card. So shall you find the 11 day of May the Sunne to rise néere 4 and set néere 8 then if you would knowe the length of the day and night you may repaire vnto the second Booke Chap. 10. of the Geodeticall Staffe CHAP. LXVII To find the amplitude of the rising of the Sunne and Starres To find the amplitude of the Sunne or stars IT is not vnknowne to any man tho meanely traueld in Astronomie that euery Horizon hath foure principall points viz. East West North and South then you must vnderstand that there is no starre nor the sunne that riseth iust East or setteth iust West vnlesse they be in the Equinoctiall which happeneth vnto the sunne but twice in the whole yeare but for starres if they rise once East or set West so doe they alwaies whereof there be but a few the starre in the pinion of the left wing of the Virgin the starre in Antinous left arme c. come néere thereunto but as the amplitude of a starre obserued one day is certaine and all one in any other day for that latitude so in the sunne doth it differ euery day and is called Amplitudo ortus This had Obserue the sunne or starre when they seeme as it were to touch the earth as béeing at point of rising or setting wherevnto turne the Instrument vntill through the slit in the longer sight and by the pinnes head you sée the sunne or starre then note the degr cut If you sought the setting multiply the degr cut by the West end in 3 which take from 90 so haue you your desire so the degr were vnder 30 but if the degr cut be aboue 30 multiply the degr cut by the East end in 3 then from the totall take 90 so haue you your desire and the setting shall be North from the Equinoctiall But if you séeke a rising you must consider whether the degrées cut by the East end be vnder 30 or aboue if they be vnder 30 multiply them by 3 so haue you your demand and it is North if they be aboue 30 sée what degrées the South end cuts which multiply by 3 substract from 90 to haue you your desire and the rising is South from the Equinoctiall Or thus with more ease hauing made your obseruation sée how many degrées are contained betwixt the West point of the Card and the South end of the Néedle for arising but for a setting sée how many degrées be included betwixt the East point of the Card and the South end of the Néedle which treble so haue you your desire But this Chapter is performed with farre more ease truth by my Topographicall Glasse CHAP. LXVIII Of the opposite degrees and how to find them Opposite degrees BY an opposite degrée is meant the opposite point of a Diameter or the point opposite vnto the degr cut by the South end of the Néedle that is the degr which the North end should fall vpon which is alwaies the halfe of a circle distant from the South end in this instrument 60 degrées so that if the degrées be lesse then 60 adde 60 thereunto but if more then 60 substract 60 from it and the total of the â—ne or the remainder of the other is your desire This néedeth no example CHAP. LXIX To find the quantitie of an Angle To find the quantitie of an angle THe quantitie of an angle is the portion of a circle included betwixt the 2 sides of any angle which is found vpon this instrument by the cutting of the Néedle at two obseruations in one place the lesser of which must be taken from the greater and the degrées which remain after substraction is the quantitie thereof But if the remainder after substraction excéed 60 then must the said remainder be taken from 120 so haue you the quantitie if your degrées be not direct then must you worke by the opposite degrees as in the 9 Chapter taking the lesser of those degrées from the greater And you must here note that all degrées cut at diuers obseruations in one or more places be called direct And such degrées as be opposite vnto direct degrées be called indirect and here note the tediousnesse of taking an angle by this instrument inrespect of my Staffe CHAP. LXX To take the distance of any marke by the old Circumferentor To take a distance AS I haue often times said in the 2 Booke of the Geodeticall staffe that there must be 3 things giuen as 2 lines and one angle or 2 angles and one line by which all dimensions are performed so in this kind of working you must alwaies haue two angles and one line giuen by helpe of which you may séeke any distance proposed thus Plant your instrument at the place appointed whence you desire the distance and there looking towards the said marke note the deg cut by the South end of the Néedle then appoint another place for your second station to which bring the sight as before noting the degr cut that done measure the distance betwixt the place you then stand at and the place appointed for your second station there againe plant your instrument looking through the fights vnto the marke whose distance is required then note the degr cut and so get the quantitie of both the angles as in the last Chapter When you haue gotten these two angles adde them both together which take from 60 so haue you the quantity of the angle at your marke then must you resort vnto the table of signes placed in the Instrument and there â—ind the signe of euery angle and note it downe and if the quantity of the angle excéed 30 substract the excesse or ouerplus from 30 and take the signe of the remainder These signes had and noted downe worke by the golden rule wherein the signe of the angle at the marke must be the first number the measure betwixt the two stations the second number and the signe of the other angles seuerally the third number according to the side which is sought and this worke is grounded vpon this Chapter In all right-lined Triangles the proportion of the one side vnto the other is such as the signe representing the angles be Or more briefe See the 7 Booke Axioma 2. of the Geo. St. The sides of opposite angles bee direct proportionall to their signes CHAP. LXXI To performe the last Chap. by protracting with the old or new Circumferentor To take a distance HAuing made your obseruations at each station note downe the degr cut by the South end of the needle and then protract thus Take a faire sheet of paper and fasten the same vpon a Plaine Table or such like with mouth glewe then shall you make a point vpon your paper to represent your first station there keepe the side of your instrument turning him vntill the needle cut the degree first noted then draw a
Diameter thereof standing paralel with the fiduciall edge of the Index g and f. 9 In the middest of this Demicircle vnder 12 in the Hysometricall Scale may you fixe a plumbe and ouer the Bore with the Needle a certaine point iust vnder 12 which will serue to keepe the Instrument paralel and vpright which the crosse Needle will as wel doe but both are not amisse the old song is Two strings are good to one bowe Some reasonable distance as an inch and better drawe a line b m paralel to h g whereunto drawe 11 paralels at such distance as they be in the figure wherein must be placed the degr figures and characters of the 12 Signes 〈◊〉 as in the demonstration they be euery paralel is diuided as g k is by placing the one foote of your compasse in f and so fetching each degree from the line g f to the other paralel and at the ending of euery third degree the line is strooke quite through so that there be two lines paralel to g m and k l strooke quite through and these lines doe limit the beginning and ending of euery signe You must also note the South and North signes at the head as here they be In the very point h there is the ordinary fight placed such as be in Quadrants so is the graduating of this sight finished This fore peece of the moueable Sight so finished there must be another peece of like quantity soldred thereunto or lâ—ft growing vnto the same peece and after bended in such sort that it may claspe ouer the Demicircle so doe these two peeces hold the said Demicircle straitely betwixt the same that it may mooue straitly and equally along the same in so much that the arch h b will alwaies bee carried vpon the Circumference b c in the Demi-circle C g and g h doe represent the distance of the two peeces one from the other which is the iust thickenesse of the Demicircle Neither would it be amisse to haue a small screw pinne vpon the backe or further side of this moueable Sight which would make the said Sight mooue the more steddie 10 The next thing pertinent vnto this Instrument is a Boxe to hold the Needle The Boxe The Circumference of this Boxe must agree with the circle p q in the great figure for within that ciccle must he stand the Diameter whereof must be 3 inches and in this Boxe must be placed a Needle and a glasse as the order is and the Card in the bottome which I described before 120 standing in the South 60 in the North 90 in the East and 30 in the West About this Boxe must moue the Circle that beares 4 Indexes with the Sights the which Boxe must be turned with certaine shoulderings to come halfe a quarter of an inch vpon the said circle to the end that it may keepe the same downe close to the body of the instrument and that he may mooue stedfastly about This Boxe is to be fastened through the backe side of the body of the Instrument with screw pins so may he be taken off at pleasure the two screw pins that screw on the socket vpon the backe side may also screw this Boxe by fastening a rib of Brasse vpon the bottome of the boxe with screw holes answering to the holes in the socket Vpon the Boxe aboue the glasse stands a certaine crooked wire bearing a rounâ— knob in the middest iust ouer the areltree that beares the Needle and iust vnder the plumbe when the Instrument stands vpright The Needle 11 The next thing is a Needle which must be prouided in manner following As for the Needle I would haue it made like two Needles ioyned together at right angles as you may see in the ensuing figure and you shall flâ—d it hereby more true and apt to worke then the single Needle is for it will keepe the instrument paralel and vpright without the helpe of the plumbe cut the degrée more precisely and stand more directly Now this needle must be touched with a Lord stone and it is very requisite that the said stone be good therefore make choyse of one thus The best stones be those that come from the coasts of China and Bengalia the colour whereof is like to yron or somewhat sanguine if they be right they will drawe vp their owne weight they be heauier then other there is another neere as good which commeth from Arabia they be broad like a tyle-stone and somewhat red coloured If the Magnes stone haue lost his vertue throwe it into the fire and let it lie there vntill it be neere red hot and then quench it in the oyle of Crocus Martis so shall his power bee multiplied Your stone thus ordered you shal make cleane the North end of your needle and rub the very end thereof with the stone this preconsidered that the north point of the stone touching the needle causeth that end touched to point into the South so contrariwise the end touched with the South part turneth into the North so that you must haue a care in this point After you haue touched the end of the needle if it were equiballanced before you shal find the same end to hang downwards as it were the heauier whereby the vnskilfull spoyle many needles and this is called the Declination of the needle vnder the Horizon therefore let the end that shall not be touched be the heauier before you vse the stone and after the application of the stone if it be too heauie you may amend the same The needle so touched the South end thereof will not poynt iust into the South Magneticall meridian for that the Magneticall meridian whereto the needle poynts and the common meridian wherein the iust South stands differ for the Magneticall meridian is a great circle as the other is and also passing by the Zenith diuiding the Horizon into two equall parts the intersection of which meridian with the Horizon is the point whereunto the needle turneth which is called the Variation of the needle The variation of the Needle and at London is one point of the compasse or 11. degr and 15 minuts west from our common meridian and this is the cause that in all portable sun Dials the line which the needle standeth ouer doth not point iust vnto the 12 of clocke marke nor lie vnder our common ineridian Lastly prepare a hollow socket of brasse with a screw pin the socket to be scrwed on as the order is so is your Instrument finished onely prouiding a Staffe for the same Portable Dyals the thrée footed staffe is best to place it at all heights and in all places And one speciall note you most here obserue in the delineating of this instrument that is tâ— haue a care that the body of the instrument be iust foure squarâ— and that the sides of the square lye parallel to the diameter of the circle that is diuided into 360. degrées viz. that
proportion the Radius being in the first place For as the Secant is to the Radius so is the Radius to the signe of the Complement Any other difference that may happen in any kinde of obtuse angled triangle is resolued in the manuduction in Trigonometria by making a dislocation of the oblike triangles and conuerting any one of them into two right angled triangles which for that it is briefly set downe there I will here open it with an example Example SALOPIA CHAP. XXXIII To square lands and to reduce irregular plaines into some regular Figure and that in the open Field TO square any any field is to reduce the whole body of the same into one square reiecting the corners angles and crooked hedges which must be after measured according to the figure they represent Now for the corners and fragments that doe remaine you must measure them according vnto the figure that they most resemble euen as you may best gather by the pricked lines in the demonstration without any more circumstance of words But say the irregular field lyeth most apt to be reduced into a triangle which is thus performed CHAP. XXXIIII To search out the Perpendicular in any Triangle or other Figure according as it lyeth in the open Field NOw hauing reduced any plaine irregular Poligon into a Triangle or such other Figure whose superficiall content is found by the helpe of a perpendicular and for that the length of the said perpendicular is something difficult to be attained vnto the open field because it is vncertaine vpon what part of the base your said perpendicular falleth I haue not therefore thought it much heere to deliuer you the order how to performe the same Let a b c bee a certaine plaine field which you are put to measure the question is to finde in what part of the base b c a perpendicular would happen falling from the angle a. First therefore I plant my Glasse in the line b c as néere as I can gesse vnder the angle a as at d then I moue the Indexes about vntill the Index with the shorter fights lye directly ouer the line b c then I looke through the sights in the Demicircle if then the visuall bâ—â—mes runne to a my instrument stands right and d is the place where the perpendicular a d should fall but if it had not so happened I must haue remoued the Instrument as I had seene occasion oâ— the like must you doe in any other figure in the like case whereby you may see how necessary the foure Indexes be for the false taking of perpendiculars is a chiefe occasion of those palpable errors that be daily committed and a principall cause wherefore the common practisers so often differ CHAP. XXXV To reduce many plats or all your obseruations into one and thereby to make a faire Map thereof according to the quantity assigned BRriefly to teach you to performe this chapter you must first appoint the Card of the bignesse that you intend to make your Map crossing the same with two lines at right angles that about the middest of your Map writing at the ends thereof East West North and South Now you are to seeke in your Tables gathered at your obseruations the greatest distance betwixt the most Easterne and Westerne place and also the greatest distance betwixt the most Northerne and Southernely place and so accordingly choose you a Scale that those places beeing laid down by the same may fall within your Card. ANGLIA Example Let the proposition be to describe England and therein to situate such townes as shall be required in that bignesse as is here set downe according to my Scale the first thing that I doe hauing appointed my Card I crosse the same with two right lines at right angles appointing at the end thereof the foure quarters of the world as in the Type then I find out some towne that I coniecture by conference with my tables lieth about the midst of the land which let for examples sake be Middle Wiche a towne situate in Cheshire the which towne I place vpon the very intersection of the foresaid lines and thereby write the name of the same searching in my tables for some other towne that lieth direct East West North or South I find none therefore I take some other towne as Bristow drawing a line according to the position of the same getting also from your tables the distance of that towne from Middle Wiche as 97 miles to which widenesse vpon your Scale open the feete of your compasse and then place that widenesse vpon the line of position for Bristow placing the one foote in the marke made for Middle Wiche making a note with the other in the said line of position where write Bristow These two townes so placed let vs now go situate Northampton first by my tables I finde the distance of Middle Wiche from Northampton and according to that distance the one foote resting in the marke for Middle Wiche with the other I strike the portion of any arch the like I doe with the distance of Northampton from Bristow as in the 12 Chapter is plaine Now the intersection of these two arches is the true place of Northampton where make a marke for the towne and write the name thereof by the said marke and so proceed limiting all the townes ports angles and nookes in the Island in their proper places as you may sufficiently gather by the former demonstration Hauing finished in some void place you may appoint the Mariners compasse as in the Card before and this compasse will serue you for many necessarie vses as it is not vnknowne to men seene that way CHAP. XXXVI To diuide any Empire Kingdome or Continent into Prouinces Regiments or Shires WHen you haue taken the plat of any countrey and therein situated all the townes ports and such like yet happily shall it be expedient or rather of you required to separate and distinguish the same into such Prouinces Shires or Regiments as the said Kingdome is diuided into So is England or the South part of great Britanie being a peninsula diuided into 52 parts but not equall parts which we call Shires then is euery Shire subdiuided into other certaine vnequall parts as Worcester Shire into 12 which be called Hundreds either for that there were but at first so many townes or villages therein or for that there is to be required 100 able men in euery of them Other diuisions is England yet subiect vnto as first the whole Kingdome is diuided into two Prouinces or Archbishoprickes to wit Canterbury and Yorke then these Prouinces are subdiuided into Bishoprickes and euery Bishopricke is resubdiuided into Parishes according to which diuisions I minde God willing to describe a Mappe of all England c. But now the way how to attaine vnto these subdiuisions is not knowne It is therefore to be performed after two kind of waies the first whereof is you must in your Perambulation as
come vnto the 26 day I end with the number of 12 whereby I conclude the sunne was in the 12 degree of Scorpio So of any other here the losse of a day doth nothing hinder CHAP. XLII To finde the houre of the Night by the Tpographicall Glasse and to know the time of high water and also the place of the Sunne or Moone SEe in any ordinarie Sunne diall what of the clocke the shadow of the Moone yeeldeth then turne the Index that is marked with f vnto the said houre in the Planispheare which so resting seeke the age of the Moone in the circle whereto the Index is fixed for the houre line in the innermost circle in the Planispheare passing by the said age of the Moone is the true houre of the night So likewise doth the houre line and the foresaid Index shewe vpon what point of the compasse the Sunne and Moone then be and the number of points included betwixt the said houre line and Index acquaints you with the distance of the Sunne and Moone which the circle in the Peripher expresseth in degrées and minutes which is more then was proposed To know the tides or high water by the Topographicall Glasse Seeke as hereafter what Rombe or Wind maketh a full sea at the proposed place and then learne the age of the Moone these two things had put the Index where 29 ½ standeth vpon the said Rombe or Wind found which resting seeke the age o the moone in the mooueable circle for the houre in the inward circle of the Planispheare answering thereunto acquaints you with the houre of the full sea in the proposed place and for your practise and ease behold the table of tides ensuing The moone south or north maketh a full sea at Lands end south and by east at the Gore end south south west betwéene holy Island and Tynemouth south west and north west betwéene Tynemouth and Flambrough head south west and by west betwéen Flamb and Bridlington in the Bay west south west betwéene Bridligton and Laurenas east west betweene Laur. and Cromer south east betwéene Cromer and Yarmouth rode to Laystow north rode south east and by south betweene Layst rode and Orfordenas south south east between Orf. Orewell woods south by east between Naase the Ware head of Colnes south south west at Grauesend south west at Lon. bridge south and by east at Portsmouth east and west at Waymouth west and by South along the coasts vp to Bristow and the coast of Ireland from Waterford to Kynsale if you desire more you may haue it of any skilfull Mariner or in the tables of the Regiment of the sea One thing note that it floweth sooner by one point of the compasse in the Spring tides then it doth in any of the quarters of the moone especially if the Riuer haue any indrafte and distance from the Sea A note of additions to the Planispheare in the Glasse To the Planispheare in this Topographicall Glasse you may also adde the Celestiall Zodiacke and another circle of the daies of the moneth inclusiuely the same or such like that are placed vpon the Horizon in Sandersons Globes by which you may gather the signe and neere the degr that the Sunne and Moone be in and if you doe but note the aspects in the Rundle of the moones age in their proper places you may thereby find what aspect the sunne and moone haue one to the other at any time Or thus you may find what signe the moone is in place the Index marked with f vpon a in the Planispheare where the degrees doe take beginning then count the age of the moone in her proper circle vnder which in the Planispheare make a marke to which marke turne the foresaid Index f noting the degree cut in the circumference for that is the distance of the sunne and moon which parted by 30 the quotient yeelds the number of signes and the remainder the degrées so that knowing the place of the sunne by any ordinarie Almanacke hereby haue you also the place of the moone by adding the distance of the sunne moone vnto the place of the sunne in the Almanacke as in March after the 10 day the signe is in Aries and by the rules before I find her distant from the sunne 60 degrees or 2 signes Therefore the moons must be in Taurus the deg are knowne by the deg that the sunne is in and by the deg cut by the Indexes as before Finally if in this vtter circle you character the aspects then also may you find the aspects betwixt the sunne and moone Many things Astronomicall might I open in the vse of this Glasse which for breuities sake I am forced to omit At this time I will conclude the vse of the Topographicall Glasse hoping I haue said sufficient to open the whole vse therof which containes matter sit for a great volume THE DESCRIPTION AND vse of the Plaine Table containing all such propositions as are most fit and familiar to be wrought thereon setting aside others as pertinent to curious demonstrations rather then apt to produce exactnesse and truth CHAP. XLIII To vse the Topographicall Glasse as the Plaine Table To alter the Topographicall Glasse to a plain Table YOu must take the circular sight boxe needle and all things of the foreside the Planisphere of the Glasse and so set the socket that is vpon the backside vpon the foreside the instrument so doth the backeside beeing a foure square plaine board stand vpwards next must you couer this smooth board with a sheet of white paper which fasten thereunto with mouth Glewe or you may haue folding Rulers as the plaine table it selfe to performe the same Lastly haue a Ruler with Sights as in the next Chapter to stand vpon this plaine Superficies and to the one side of the board in the thicknesse thereof with screw pins fixe the néedle and boxe in such order that the South line I meane not the line of variation make right angles with the side of the said board so haue you finished CHAP. XLIIII Of the Plaine Table with a description thereof and the parts thereunto belonging The Plaine Table THe Plaine Table or Geometricall Table is a right angled aequilater paralelogram made of a board of halfe an inch in thickenesse whose equall sides containe 9 or 12 inches the superficies whereof is made smooth and plaine some vse to make him represēt an Oblong al is one Some for ease in cariage vse to make this square board to consist of thrée péeces which they vse to ioyne together with certaine ledges such as bee at the end of Table boards as you may gather by the figure The edges of this table round about be abated with certaine square channels to the thicknesse of halfe the board according as you may gather by the shadowed lines about the table The ribs or for rulers of the Plaine Table 2 The peeces of this table being set
this Instrument which at this time I omit CHAP. XLVI Things belonging to the vse of the Plaine Table Things belonging to the plaine Table TO this instrument as to all other appertaines a chaine or wire line of foure pearches long according to 16. foote and ½ or of thrée pearches long which is 16. yards and ½ let the pearches be noted with brasse rings at the ends thereof and then diuided into halfes quarters The Line with lesser rings fixed at each quarter and halfe that you may distinguish the same A Scale Compasse You must also prouide a scale of brasse or wood whether you please with a paire of brasse compasses pointed with stéele very neate and sharpe for it is rude to draw your lines Geometricall with Painters kéelers or blacke lead as M. Lucar would Also you must haue such sights for this Table as bee described in the vse of the Circumferentor whose vse are set downe in the 16. Chapter of the same booke or else you may haue such a quadrant as is spoken of in the first part of my Art of Geodetia as in the 26. Chapter These things had you may fall to worke CHAP. XLVII To take any Horizontall distance by the Plaine Table To take any distance by the Plaine Table IT were vaine to make many demonstrations of this worke since a few may as well suffice for this Instrument is but only fit to take longitudes and latitudes as for altitudes I hold him very troublesome and vnapt to performe the same though M. Lucar haue taken paines to illustrate him in that point howbeit finding by experience the cumbersome and vncertaine working thereby I thinke it better omitted then remembred You shall then vnderstand that you may performe any distance vpon this Table in the same order as you doe with my Staffe onely heere you must drawe lines vpon the paper and measure the same by your scale whereas the legges of the Staffe represent the lines and the diuisions your scale Therefore at the place whence the distance is required to any marke proposed place your Table which place call your first station then your Table lying parallel with your Compasses make a point in the paper to represent that first station wherevnto bring the fiduciall edge of your rule kéeping the one end of the said ruler vpon the point mouing the other vntill through the groue or sights you espye the marke whose distance is required the rule so resting drawe a line by the fiduciall edge thereof the Table resting espye out a second station let it make as néere as you may a right angle with the marke whose distance is required This marke so appointed out for your second station kéep the fidutiall edge of the rule vpon the foresaid point and so draw a line to point to your second station then let one measure the distance betwixt your first and second station which were best to be 1 10 part of the distance required So haue you finished all at your first station with this Prouiso that you haue regard to the degrées cut by the South end of the Néedle in the Card in the bottome of the boxe before you any wise alter the table and that you lay downe your stationary line by your scale and compasses limiting the same according to the line measured at the end thereof marke another pricke which call the pricke of your second station Then take vp your Table leauing a marke at your first station vnder the pricke made vpon the table representing the same Now must you beare your instrument to your second station where hauing placed the same in such sort that the pricke of your second station may directly stand ouer the marke representing your second station lay then the edge of your ruler vpon the stationary line kéeping the pricke of your second station next to your body turning about the table the ruler resting as before til through the sight you espy the marke left at your first station which done make fast the table with your screw A proofe of the worke Now for proofe of the exactnesse of your worke and to know if you haue truly taken your backe sight haue respect to the south end of the néedle for if it cut the like dgrées at this second station aâ— at the first you haue done well Hauing so done place againe the fiduciall edge of the rule vpon this point of your second station the one end being there fixed moue the other end vntill through the sights you sée the marke whose distance is required then draw a line by the fiduciall edge of the rule which will intercept with the line drawne from your first station thereunto therefore note the point of intersection and by your scale measure the distance from any one point to the other I meane by the same scale you laid downe your stationary line so haue you your desire Example The distance a b is required first thererfore I plant my Table at b then working as before I finde c my second station and so draw a line to point from b to a and another from b to c. Next I measure the line b c and finde it 7â— yaâ—dâ— which I lay downe vpon my paper with my Scale and Compasses Lastly I note the degrees cut by the South end of the needle which let be 40. This done I go to c and there againe plant the Table as before So do I make the stationary line protracted point iust to b and then noting the degrees cut a gaine by the needle I finde theÌ„ 40. as before which argues I haue well planted my Table To concluÌ„de I place the fiduciall edge of my rule vpon c mouing â—he other end vntill it intersect with the line representing a b therefore by my Scale I measure the line representing b a so haue I the distance of b a 135. yards by the same Scale might you haue expressed c a. CHAP. XLVIII The part of the distance of any thing being giuen to finde the rest VNderstanding the last Chapter so wee may thereby auoid many words and may most easily be performed by the Geodeticall Staffe as may appeare in the Propositions of the 18.19 or 32. Chapters of the second booke of the Geodeticall Staffe But to procéed a b is a distance required the part of that distance giuen is a c 50. pearches Then do I plant my instrument at a as I did in the last chapter at my first station drawing a line to represent a b infinitely then laying downe my scale vpon the same line the part giuen representing a c 50. pearches the instrument vnremoued I séeke a second station as in the last chapter which is d but the stationary line shall not be measured Lastly I note the degrée cut by the South end of my néedle then leauing one at a I cary my Instrument to d where I plant him in an respects as at a now must I finde the point vpon the paper which represented c and thereupon lay the fiduciall edge of the rule mouing the other end vntill
line from that point along the edge of the instrument then kéeping the edge still at that point moue the instrument vntill the South end of the néedle cut the degrées noted at your second obseruation then draw another line by the edge of your instrument whereupon lay the line measured betwixt both your stations counted from the point first made towards the end of the said line and where that number ends there make a point which let represent your second station where place the edge of your instrument turning him about vntill the south end of the néedle cut the degrées you noted at the second station then by the fiduciall edge of the instrument draw a line note where it intersecteth with the first line for that is the place of the marke whose distance is required the distance of which from either of your stations may you measure by the Scale that you expressed the length of your stationary line by CHAP. LXXI To take an altitude onely by the old Circumferentor To take an altitude YOu must first get the horizontall distance vnto the thing whose length is required then plant your instrument perpendicular and moue the vane vntill through the hole therein you sée the top or the summitie of the altitude note then the equall parts cut by the side of the vane for such proportion as they beare vnto 100. the like doth the altitude vnto the distance multiply therefore the distance by the parts cut and diuide by 100. the quotient she weth the height which is correspondent to the leuell of your eye The ground of this worke is borrowed from the Iacobs Staffe as may appeare in the ninth Chapter of the fifth booke of the Geodeticall Staffe An inconuenience like to that in the Theodelitus But in taking of altitudes you shall haue it oftentimes so fall out that the altitude will be so high that you cannot bring the vane so low as to sée the top of the altitude by the hole and pins head When it so happens you must place the center of the Index vpon the wire in the shorter sight looking through the sight hole in the Index vntill by the wire and through the said sight you sée the summitie of the altitude then note the equall parts cut by the fiduciall edge of the Index vpon the right edge of the instrument for as those parts are in proportion to 60. the like proportion hath the distance vnto the height And so that proportion as those parts cut haue to the parts cut in the Index the very proportion hath the distance to the visuall line Therefore multiply the horizontall distance by 60. and diuide by the parts cut on the right edge of the instrument the quotient will shew the height Againe multiply the horizontall distance by the parts cut in the Index and diuide the same by the parts cut in the edge of the instrument the quotient sheweth the visual or hipothenusall line As you séeke altitudes so must you sinde profundities as I haue said often in the Geodeticall Staffe but the errour is great if the instrument be not exact paralell CHAP. LXXIII To take the plat of a peece of ground by the old or new Circumferentor DIuers wayes may bee set downe to fetch the plat of a péece of ground by this instrument To measure woodland or any other ground but I hold that most easie which is to be protracted by the Instrument it selfe because you shall not bee troubled to séeke the quantitie of angles which in this Instrument is ouer tedious Hauing therefore a péece of ground giuen you shall begin at some one corner and there plant your Instrument looking vnto the next corner and note what degrée the south end of your néedle cuts then with a chaine measure from the first corner to the second and note downe the degrées cut by the south end of the néedle and the length of the line measured Next go to the second angle and there conuey your sight to the third angle paralell to the hedge then measure the distance from the second corner vnto the third noting downe the degrées cut by the south end of the néedle the length of the line at your second obseruation Then go vnto the third angle and note the degrées cut and the length of them and so procéede from angle to angle noting the degrées cut and the length of euery line answering thereunto vntill you haue gone round about And if you being at any one angle and from thence can sée two or three angles more you shall not néed to remooue your instrument to any of them but onely from that angle obserue all the rest onely measuring the hedges With these notes you shall resort vnto a faire shéete of paper and there protract it downe thus In some place of the paper make a point and there place the fiduciall edge of your Instrument turning it about vntill the south end of the néedle cut like degrées as he did at your first obseruation then drawe a line by the fiduciall edge of the instrument whereupon from the said point to wards the other end lay downe the length of the first measured line which you must take with your compasse from your scale where that number ends in the said line there make a point where place the edge of your instrument mouing him about vntill the South end of your néedle cut like degrées hee did at your second obseruation then drawe a line by the fiduciall edge thereof whereupon lay the length of your second line and where that number ends make a point where as before place the edge of your instrument mouing him vntill the South end of the néedle cut like parts hee did at the third obseruation then drawe a line by the edge thereof whereupon lay the third line and where that number ends make a point as before placing there the edge of your Instrument turning him vntill the South end of the néedle cut like parts as at the fourth obseruation and so procéed laying downe the parts cut and the length of the lines vntill you haue gone round about by which meanes you shall lay downe the plat of the péece of ground in true forme then for the casting vp thereof resort vnto my booke of the art of measuring ground CHAP. LXXIIII To take a plat at one station from whence you you may see all the angles in the field by the old or new Circumferentor To take a plat at one station THis kinde of working is performed with as much ease as the former You shall therefore repaire into the field and finde some such place from whence you may behold all the corners in the said field where plant your instrument and then begin at some one angle whereunto direct your sight noting the degrées cut by the South end of the néedle then direct your sight vnto the second corner vpon the right hand and there againe note the
degrées cut by the South end of the néedle which note downe and so procéed rightwards from angle to angle noting the degrées cut by the South end You are taught this chapter with a demonstration lib. 6. cap. 3. of the Geodeticall staffe vntill you haue gone round about the field of which degrées cut you shall make a little Table to the end you may remember how many degrées were cut at the first second third c. corner Next shall you cause one to mete with a chaine the true distance of the first corner from your staffe which note downe against the the first degrée cut in your Table then mete the distance of the second corner from your instrument which note downe in your Table against the number of degrées cut at the second corner and thus procéed vntill you haue gone round about the field laying downe the distance of euery angle from your instrument against his proper degrée cut which done fall to protracting thus Hauing prepared a faire shéet of paper as you be taught before about the middest thereof make a point which call your station then apply the edge of your instrument thereunto mouing him about vntill the South end of the néedle cut the degrées you noted at the first corner which done draw a line by the edge of the instrument from the point made in the paper out at length then moue him rightwards vntill the South end of the néedle cut the degrées noted at the second corner and then by the edge of the instrument draw another line as before so go forward vntill you haue finished all the degrées cut by the south end of your néedle noted in your Table then with your compasse take from your scale the distance of the first angle from your instrument which lay in the line first drawne from the point made in the paper towards the other end of the line then take the distance of the second corner from your instrument which apply to the second line drawne in the paper and so procéed from line to line according as you be taught in the third chapter of the Art of measuring ground The length of euery line laid downe in such order as is said then must you draw lines from point to point in each line so shall you drawe the limits and proportion of the ground according as in the foresaid third chapter of the art of measuring ground by the Staffe And by this meanes may you measure ground at two stations measuring but one line in the whole plat in such order as I set downe in the fourth chapter of the sixth booke of the Geodetical Staffe And since what is said before may giue sufficient light to performe both this way and many other I will omit further spéech least I rather seeme tedious to the wise then facile to the vnlearned And you shall heere note that by taking perfect notes in the field where one closse boundeth vpon another you may take the plat of many flelds lying together and so saue a great labour CHAP. LXXIIII The degrees of a field being taken to finde whether the plat will close the lines being truly taken To know if your plat will close NOte downe the quantity of euery angle at each seuerall station as well as you doe the degrées cut then adde vp all the quantities together then multiply 60. by a number lesse by 2 then the number of the angles and if your worke be right the product thereof shall be equall to the totall of the quantities Example Let the number of angles be 8. froÌ„ which take 6. which is a lesse then multiply 60. by 6. and the product will be 360. which agrâ—â—ing with the totall of all your quantities of angles added together is one argument that the plat will close CHAP. LXXV To reduce Hipothenusall lines vnto Horizontall after another way then in the 6 booke 8 Chapter of the Geodeticall Staffe onely by the sights in the old Circumferentor To reduce Hypothenusall lines to Horizontal lines PRepare a marke to bee carried before you the just height of your line of leuel from the ground when the iustrument is planted vpon his rest this marke must be placed in the angle whereunto you looke hee must stand perpendicular and when you take the degrée looke your instrument stand perpendicular and then moue the vane vpon the sight vntill you sée the top of the marke before planted through the hole in the vane and by the pins head then in the Hypothenusall diuisions cut by the vane vpon the sight for they will shew you how much that line you shall measure will differ vpon the 100 from that line you should measure if the ground were leuel therefore when you haue measured that line proportion him according to the parts cut Example Suppose the parts of the Hipothenusall diuisions cut to be 4 and the line measured to be 30 pearches now you are to finde a number to beare like proportion to 30 as 100 beareth to 104 which you shall find to be 28 1 5 1 1 so that the line measured by the cheine to be 30 pearches must be laid downe 28 1 1 1 3 pearches in your protracting But for asmuch as these calculations be tedious in the field your best way is to note the Hipothenusall parts cut and then reduce them when you come home CHAP. LXXVII To performe the same by a Quadrant made of purpose A new Quadrant to proportion lines YOu shal prepare a Quadrant and then diuide the limbe thereof in 30 equall degrees setting number therupon as the coÌ„mon order is then shall you diuide the lower side of the Quadrant the is betwixt the first degrée the center into 30 equall parts raising perpendicular lines vpon each diuision which will be paralell vnto the other side this done prepare an Index of the length of the semidiameter of the Quadrant with a center hole therein this Index is to be fastened to the center of the Quadrant with a brasse pin or such like which also must be diuided into 30 such equall parts as the semidiameter was the Quadrant thus prepared you shall fore shorten the lines thus First for the taking of your notes in the field you must work as in the last Chapter onely here you must note the degrée of a circle cut by the vane in stéed of the Hypothenusall diuisions and then procéed thus Put the Index to the different angles in the limbe then number the line measured vpon the Index and note the perpendicular there cut by the edge of the Index for that shall shew you the length of the Horizontall line which must be protracted Example Let the different angles from the Horizon be taken 18 degr and the line measured 20 perches first count 18 degrees in the limbe then thereunto bring the edge of the Index next count the line measured viz. 20. pearches vpon the Index fromwards the center so shall you there
see the 19 perpendicular counted from the center intersect which sheweth that the line measured 20 perches must be protracted 19. And if the length of the line measured exceed 30 pearches and be lesse then 60 then take halfe the number vpon the Index and the perpendicular will answere to halfe the length of the Horizontall line but if the line exceed 60 take then ¼ ¾ c. the perpendicular will answer proportionally CHAP. LXXVIII To seeke any altitude by this Quadrant To seeke an altitude TAke the angle of altitude whereunto bring the Index the same being counted in the lymb then number the Horizontal distance in the semidiameter the portion of the perpendicular to the Index sheweth the heigth CHAP. LXXIX To take the declination of any wall by the old or new Circumferentor To get the declination of any wall BY the declination of any wall is meant the bending or leaning of the surface from the Meridian If a wall be not direct hee is then declining if the wall point iust East West North or South he is direct otherwise declining All walles decline either South or North the quantity whereof is thus had Set the North end of the Instrument vnto the wall now if the néedle cut 30 60 90 or 120 it is an East a North a West or a South wall 1 But if the néedle cut betwixt 120 and 30 the wall is South East declining to the East 2 If the Néedle cut betwixt 120 and 90 that wall is South West declining 3 If the Néedle cut betwixt 30 and 60 that wall is North declining to the East 4 It betwixt 60 and 90 the wall is North declining to the West 1 If the wall decline South East multiply the degr cut by 3. 2 If West take the degr cut from 120 and the remainder multiply by 3 which produceth your desire 3 If North East take the degrée cut from 60 and the remainder multiply by 3. 4 If North West take 60 from the degrée cut and multiply by 3 so haue you your desire Com. Heref. Manerium de Sale In Superuis manerij praed ibid. fact xiij xiiij diebus Septembris anno regni Dom. nost Iacobi Dei grā Ang. Scotiae Frā Hibern Reg. fidei defensor c. viz. Angl. Franc. Hibern sexto Scotiae xlij Per B. G. gent. virtute commissionis dicti Domin Reg. extra Scaccar suū sibi direct continetur inter alia vt sequitur viz. R. G. gent. tenet per copiam dat xxviij die Septembris anno Regni Regis nunc Angl. c. Quinto cert terr tenement Custumar infra maner praed nuper I.G. armig ante A. Hos gent. ante B.D. armig patris sui viz. Dom. mansional .viij. spac vnum horr vij vnam coquinā iij. spac vnum stabulum ij spac vnum bouile v. spac vnum columbar vnum gardinum tria pomar vnde 2 voc le North Orchard long Orchard cont per estimac iiij acr Terr ar iacen in quodam claus inter al. voc the West inclosure cont per estimat l. acr Parcel vnius Claus prat voc le Heald per estimation xx acr Parcel vnius claus pastur voc le White field cont per estimat xiij ac Habend sibi suis secund consuetud Maner per Redd per Annum xij s. ij d. An. val dimit x. l. In like manner must you deale with all the other tenements of the said Mannor noting the quantitie of euery particular then the rent paid and at the lower end a reasonable improouement And if there be any other commodities in the said Mannor accrewing to the Lord thereof they may be noted as followeth Manerium de Sale valet in Redd vxx l.xij s. viz. Nundinum tentum annuatim ibidem die Iouis proxim post festum beatae Mariae iij. l. Nundinum tentum annuatim die Veneris proxim post festum c. l. s. Markets 3. l. x. s. Mercat hebdomadatim ibidem tenent dimiss G. I. per annum 4. l. Shamellorum scal tam. carnium quam piscium ibid. per annum 30. s. Milles. vij l. Vnius molendini aquatici iiij l. Vnius molendini ventricij iij. l. Fish-pooles xlij s. Vna piscaria vocat le White poole xx s. Piscar communis aquae ibidem vocat le Blacke Moore xxij s. Pawnage xxx s. Pannagio porcorum tenent ibidem quam aliorum infra communem boscum c. x. s. Pannag porcorum tenent ibidem in parco vocat c. at 3. d. the peece per annum xx s. Swannes Cignorum in aqua Domini vocat le Broad Poole c. Quarreyes ix l Quarreum lapidum vocat le Free stone per annum iij. l. Quarreum lapidum vocat le Slate vj. l. Perquisites of Courts Amerciaments c. iij. l. If there be any reprises wherewith the Mannor is charged as money for the yeerely repairing of some bridge high way or any other annuall pension whatsoeuer let it be noted as the former and in the conclusion say Ei remanet clare per annum vltra repris 306. l. 14. s. 8. d. And you must further note that the first thing you haue to deale with is the sight of the Mannor house the buildings and demesne then the parke parsonage c. if any bee and then procéed to the Tenements as before To make a plat or map and place a Sea-Card therein VPon the middest of your plat describe a circle as vpon a which diuide into 32 parts and then about the map describe another circle which wil likewise be diuided into 30 parts by drawing lines from the center a by each of the 32 equal parts in the first circle now if vpon euery of those intersections as a center you describe a circle diuiding euery of their circumferences into 32 equall parts extending from them right lines through the body of the map you haue finished the Sea-Card and will beautifie your map and serue to expresse many prettie conclusions which at this time I mind not to repeat prouided that you drawe the lines there of in some colour as red or such like that they may be readily distinguished from the lines of the map or plat You may distinguish all the windes in your Card otherwise if you please by placing a circle containing the same in some voyd place in your plat as you may sée in the 7 Chapter of the Topographicall Glasse and drawe them forth onely to touch the circumference of the plat as in the 6 Booke and Chapter 49 of Geodetia CHAP. LXXX The order how to discouer the true plat of any parke forrest or such like standing vpon the top of some hill not approaching vnto the same THis Chapter is easily performed if you doe but call to mind how to séeke the true proportion of any field Island or such like euen as you be taught in the Chapter but indéed I hold this Chapter for that it is to be performed only by two stations
through the sights you seâ— c so wilt the edge of the ruler in the line vpon the paper representing â— d thâ—â— kâ—â—ping the â—uler â—pon that point d I moue the other 〈◊〉 vntill it pâ—â—oâ— to 〈◊〉 shall the fiduciall edge of the rule intersectâ— witâ— the â—â—â—e 〈◊〉 the papâ—â— represenâ—â—ng a b from the point of which intersection to the point a is b the termes of the line a b which being measured by your scale and compasses is found 133 pearches CHAP. XLIX To take the distance of any two townes or such like COnsider well the premises and this labour is already effected therefore plant your Instrument at a Latitudes as you were directed in the 29 chapter and let the latitude required be d c noâ—â—raw lines from a to point to d and c and also to b your second station now obseruing the former directions I â—emoue my instrument to b and so draw lines from b to point againe to d and c then doe I note the concurse or intersection of the said lines which I measure by the scale and compasses as before so will the stationary line a b bee 316 perches and the distance required d c 131 perches A note for many distances And here note if you had sought more distances as the distance of f e e d d c c. the labour is no more but to draw lines at euery station to point â—nto the distances required and then to note the intersection of matchy lines vpon the paper which after measure by your scale and compasses so shall you haue your stationary line g h 10 score the distance f e 12 score c. whereby you may plat any field and come not within the same as in the 8 chapter CHAP. L. To finde the Horizontall distance of any place from you standing by a new way vpon the Plaine-Table To finde any Horizontall distance after a new way IN the 44 chap. at twice I told you of 4 certaine rulers or ribs that were belonging vnto the Plaine-Table euery one being diuided into a 100 equall parts or more by these rulers ordered in their due place vpon the Plaine-Table shall I teach you to séeke the Horozintall distance of any place thus Lay the ruler with the sights vpon the very edge of one of the sides of the Plaine-table turning the Table about vntill through the sights you espy the marke whose distance is required but with this prouiso that the corner of the Table where the diuision take begining be neerest vnto you this done take the ruler with the sights the Table vnmoned and place the same vpon the right side the Table as before and then looking through the sights espy your second station in a knowne distance from your first station Next shall you beare your Instrument to your second station situating the Instrument by helpe of the Needle and backe sights here in all respects as it was at the first which being done lay the ruler ouer the corner or both sides of the Instrument remoouing the same vntill through the sights you espy the marke whose distance is required lastly note the equall parts vpon the ribs cut by each end of the ruler or sight hauing regarde to those parts that doe responde to the statinary line and also to the distance required for as the parts respondent to the stationary line are to the line it selfe being measured and knowne so are the parts respondent to the distance vnto the distance required therefore worke by the golden rule in this worke the line of distance and stationary line alwiaes cut at right angles this needeth no example for as it is most exact so it is most plaine easy The premises béeing considered and the doctrine before well vnderstood you may produce infinite wates to performe many rare conclusions but we cannot stand to set downe a demonstration to suite to euery proposition that may happen in the field chiefly for that let the demand stand howit will you may resolue the same by due regarding the prescript Now I will briefly touch the order of taking a plat of a field mannor c. by the plain Table according as we haue dealt with the Geodeticall staffe and other instruments before ayming to performe some such propositions here that were omitted in the other bookes for it would increase the volume ouer much to set downe euery kind in the vse of euery instrument since wee understanding what is said of the one may also be performed in the other and that much after one kind of method as I haue said before but indeed I haue here set downe such propositions that will best agrée with the Plaine Table and are aptest to be wrought thereon setting aside all impertinent demonstrations And you shall note for diuers good respects that I shall omit one thing that standeth firme and is ordinarily vsed in demonstrations of this nature that is lines to represent the Instrument the lines also drawne thereupon my reason is because I will not confound the worke with multitude of lines as also to saue the cutting of many figures whereby such that serued in the Glasse likewise serue in the Plaine Table CHAP. LI. To draw the plat of a peece of ground at one station where all the angles of the field may be seene from that place of standing At one station to get a plat FIrst goe round about the field and in euery angle set vp some marke then plant your table couered with paper in such a place as from thence you may sée all the angles of the field that done in a place conuenient of your table make a pricke or point to represent the place of standing from the point to each marke draw a visuall line by the edge of your Ruler then from your place of standing measure exactly with your wire line the iust distance in pearches to each seuerall mark and set those distances by the scale each vpon his own line which was drawne to those markes noting these seuerall points where these measures end Lastly from point to point by the edge of your Ruler drawe lines which shall include a figure proportionall to the field to be measured and the lines so drawne shall represent the hedges of the field as in this demonstration Your station is i the lines drawne from i to point to euery angle are i a i b i c i d i k i e i f i g and i h which are measured as is noted vpon each line as i a 27 pearches i b 9 ¾ pearches c. then from a to b I drawe a line and so go round so haue I made a figure proportionall which was required CHAP. LII To drawe the plat of any field by the rule taught in the last Chapter where you cannot from one place of the field see
of the field a is my first station b my second and so working by the doctrine of the 31 Chapter I obtaine a line like proportionall to the field which was required CHAP. LVI To draw the plat of a field by many stations and and yet to measure but one line in the whole FIrst set vp marks in euery angle then point out your first station where your instrument being placed draw from the pricke of your station lines to as many angles as you can conueniently see then appoint out your station in such a place from whence you may see all those marks to which you draw lines at your first station to which station draw a line and measuring the distance betwixt those two stations vpon that line set your distance by your scale and then remoue your Table to your second station where plant it in his due situation and then from the center of that situation draw lines againe to each angle whereunto you drew lines at the first and note the interception ech with his match line and then draw lines from point to point which shall represent somuch of the hedges of the field as you haue gotten by these two stations Now your instrument standing thus at your second station vntemoued from the center of your second station againe draw lines to as many new angles as you sée that is from whence you haue not drawne lines before then chuse out a third station from whence you may sée all those angles whereunto you drew lines last before and then draw that station line and then againe remoue your Table and hauing placed it in his due forme to find the center of this your third station doe thus lay the edge of the ruler to any point in the paper which doth represent some marke in the field and remoue your ruler to or fro till through the sight thereof you sée that marke in the field which the point on the paper doth represent by which the edge of the ruler doth lye and then draw a line towards you till it cut the station line and note the interception for that point representeth the pricke of your third station And from the pricke or center of your second station to that point sheweth the distance betwixt the second and third station viz. that point on the paper sheweth in what part of the field your instrument is placed Now from that center draw lines to all the angles which you drew to your second station where they intercept or crosse each his match lines make prickes or points there and so from point to point draw lines which shall represent so much of the hedges of the field as there you could see and draw lines vnto This done and the Table vnremoued from that point or center of your standing or third station draw lines to as many angles as you can sée which haue not lines drawne to them already Then chuse out a fourth station in such sort as you did chuse out your third and to this get your distance as there you did and then intercept those lines as before is taught and in this order make so many stations as neede shall require till you haue ended your whole worke and at last you shall produce a figure with lines proportionall and equal angles to the plat of the field Example My first station is a whence I obserue the angles d e f k l m my second station is b whence I draw lines to point to as many of the angles I obserued at my first statioÌ„ as you can see as b d d e b f. and so noting the intersection of matchy lines draw the lines d e and e f which is so much of the hedges that you haue obserued now the Instrument vnremoued at b I espy as many more angles from b as I well can as g h and i and so draw lines to represent b g b h and b i. Lastly I espy some other place whence I may see all these three former angles but the way to finde your third station c is thus vpon some point on the paper representing some angle in the field as e laying there the edge of your ruler mouing the other end vntill you obserue through the sights the angle e then note where the edge of your rule and the line b c intersecte as at c so shall you finde the true place where your instrument stands your instrument resting situate at c in all respects as at the other stations draw lines to point from c to g h and i and so note the intersection of these lines with their matchy lines drawn froÌ„ b so haue you another part of the perimeter by drawing lines from one intersection to another as g h and h i and for that you may see from c to all the rest of the angles k l and m obserued at a therefore I draw lines to point from c to k to l and m and so noting the intersections as before and drawing lines I haue included a figure proportionall and like to the proposed figure Note I draw no figure vpon a b or c to represent the Table because I will omit the multitude of lines and letters and this kind of intersection of lines being duely ordered of all other is the best because by apt chusing of your stations you may auoide acute angles CHAP. LVII To draw the plat of a peece of wood ground where for the thickenesse of the wood a man cannot place his Instrument but onely in the angles of the perimeter IN this manner of worke you shall vse 4 men to helpe you whose labour shall he thus two measure with the line the distance from angle to angle one man to go before you into euery angle and the fourth man to be left standing in the place where you planted your Instrument because you must for the more precise planting your Instrument at euery remoue looke backe to him Being thus furnished you shal begin your worke as followeth First plant your Instrument in any angle and appoint for your place of standing some pricke in your paper then draw a line into the next angle which line measure on the ground and set those measures by the scale on the line drawn then place your instrument in the angle say the ruler along the line drawne theÌ„ turne the Table about til you sée the angle or the man left in the angle froÌ„ whence you came last where screw fast the Table and for your more assurance you may behold your néedle The singâ—lar vse of the backe sight which in this kind of platting will stand you in great stéed For looke what degrée your néedle did cut your first standing the same degrée must it stand on at your other standing wherefore it were good at the first placing of his instrument to write downe the degrées cut by the néedle for the helpe of memory in the rest of the angles I say this done and
your Table made fast from the point of your standing draw a line into the next angle and measure the distance thither which measure set on the line drawne and then plant your Table againe in your third angle and in this order worke till you haue compassed the whole ground and if it fall out in the conclusion of your worke that the line and angle of your figure agrée with the line angle of the field then is your plat perfect if not you haue some errour And herein if I may aduise you begin your worke againe to finde your fault trust not to any helpe for the closing thereof wherein you shall but deceiue your selfe and happly of a small errour increase a greater for that you know not whether your saulte be in the lines or in the angles wherefore if your figures misse of closing aboue one pearche neuer trust vpon your worke And be sure when you plant your Instrument in one angle looke to the next that you so direct the sights that the visuall lines lye paralell to the hedge measured neither obseruing this paralelly is it materiall how far off the perimeter you place the Instrument alwaies prouided that you take your measure in the true direct place where the very hedge or bounds go for if you measure much within the hedge your lines fall too short if without too long therefore obserue the meane for in all things obseruare decorum is best This kind of measuring is principally and commonly vsed for woods for that in them a man cannot see the angles by any other me anes and may serue for all kind of other grounds and indéed commonly vsed of land meaters who hauing but this one Chapter and that rawly presume of the full knowledge of the vse of this instrument but how they performe it I leaue to those that shall try them which is but had as others before me haue reported CHAP. LVIII To draw the Plat of a field by placing the Instrument in euery angle thereof as in the last Proposition and yet measuring but one line in the whole Perimeter To draw the plâ—t of any field by going round about yet me asuring but one line FIrst place your instrument in that angle where you will begin which let be in such a place that the first line you go vpon may he of reasenable length then set vp a marke in the field in such a place as from thence you may see as many angles of the field as possible may bee which marke call your principall point and to that marke get the distance by your first and second station which let be in the first second angle in the field in order as before is set downe so shall you haue a point in your Table to represent that principall point in the field This done draw a line into the third angle and thereto remoue your instrument and hauing there placed it get the distance betwixt your two stations as you got your distance in the like case before which you shall performe thus Hauing first placed your Instrument by looking backe or by the néedle at his due situation lay your ruler either by the pricke on the paper that representeth the principall point in the field or by any point on the paper that you know representeth some marke in the field then turne your ruler about till you sée that marke in the field which the pricke by which your ruler lyeth doth represent and draw a line till it cut your stationary line and that point of interception sheweth the point on the paper where you stand in the field So in this order by placing your instrument in euery angle you may get the length of euery hedge seuerally with measuring but one in the whole and the conclusion will bee that in the end you shall make a figure with equall angles and lines proportionall to the plat of the field The premises bâ—â—ig well vnderstood and all things else well considered I will â—raue pardon and so cease further prosecution hereof presuming that there is sufficient said to open the whose scope of this chapter neither would I go about to fill the booke with many curious demonstrations and difficult questions to beguile the aspiring wit of the yong practitioner but onely set downe some such fewe things that were most requisite to bee knowne lest otherwise I should be held rather tedious then compendious and therefore I will hast to an end CHAP. LIX To take the plat of any Champion Field containing 2000. or 3000. Acres of ground by the plaine Table and yet neuer bee forced to change your paper YEt againe before I conclude I will giue you another way to séeke the plat of great Champion fields that containe 3000. or 2000. Acres by the Plaine Table which is not much differing from your worke by the Geodeticall Staffe You shall therefere place your Instrument in euery angle and so get euery angle and his sides To vse the plain Table and neuer change the paper not regarding the length of the conteining sides as you be wont then must you measure euery hedge and as you were wont to lay the same downe by your scale and compasse heere you shall but write the length of euery hedge vpon the lines drawne vpon your paper and responding thereunto so haue you finished and you shall neuer be forced to shift your paper nor haue the lines to runne off the same for that you may draw them as long or as short as you please Now when you come home vpon some shéete of paper protract all the angles one after another See the 3. chap. pro. 5. as you found them in the field allowing by your Scale and Compasse euery line his due length according as you finde the same note those figures vpon the said respondent lines and your conclusion will be to produce a figure like and proportionall to the field proposed This chapter is most excellent for the purpose before said and therefore worthy of note as they shall finde it that worke by the Plaine Table in countries that consist of great Champion fields CHAP. LX. What Chapter is most fit to vse in platting of ground as well such whose superficies is subiect to sight as others that be rough and full of wood as also to make choyce of the best instrument to performe the same as also to make a new kinde of particular YOu bee taught before to measure and plat any péece of ground whatsoeuer it resteth then for you to make choyce of such Propositions that are best as well in respect of the fashion of the field as in respect of the aptnesse of the Proposition Therefore for all grounds whose bounds and angles may all bée séene from one place vse the 51. Chapter and if you cannot trauers the same to measure it with your chaine by reason of pooles marshes or such like then is the 53. Chapter excellent as for the
CHAP. V. To find the true square of a squared peece of timber consisting of two vnequall sides and 4 right angles the one side being onely knowne YOu must take the length of the broader of the two sides the which fit ouer in 60 and 60 amongst the coard diuisions the legges of the Staffe so resting the distance taken from 36 to 36 yeelds the true square of a peece of timber that béeing of equall longitude is also of equall quantitie But if both the sides c d and d b be knowne then worke by the next Chapter for this takes no notice of the thicknesse CHAP. VI. To find the square of any broad or flat peece of timber that consists of 4 right angles and two equall sides SVch a péece of timber as this the end thereof doth represent the iust forme of an Oblong and is thus squared take the longer and shorter side and ioyne them together in one right line the which right line made of the length of both these lines so ioyned make the diameter of a circle lastly vpon the point where the two lines were ioyned raise a perpendicular forthe length of that perpendicular to the circumference is the true side of the square Example A b c d is the end of a peece of timber c d the longer side d b the shorter therefore I take the length of c d and d b and ioynt them together in v making one right line thereof as r s next I part r s into two equall parts at w then placing the one foote of my compasse in w extending the other to s or r t describe the semicircle r t s lastly vpon v where the two lines were ioyned together raise a perpendicular v t which is equal vnto p q I conclude the square made of the line t v is equall to c d b a and thus of any such other Or get the square thus multiply the breadth in the thickenesse so is the square roote of the product the true square which you may easily find in the Geodeticall Staffe fol. 142. CHAP. VII To find the true square of any peece of timber whose ends are formed like a Diamond THe end of such a peece of timber as this doth represent the iust forme of a Rombus therefore doth consist of equall sides and Oblique angles the square whereof find thus Drawe a right line betwixt any of the two opposite angles noting the length of that line vpon which line let fall a plumb line from one of the subtended angles so hauing those two lines find the square as in the last Chapter Example Or the length of the perpendicular b m is the square falling vpon b c at right angles CHAP. VIII To find the square of any peece of timber consisting of three sides THe true square of all kind of Triangles whatsoeuer are found out by the 44 Chap. Metamorphosis 7. of the 6. Booke of the Geodeticall Staffe and therefore it were vaine to repeat it here againe As if you ioyne the perpendicular b d and halfe the base a c in one right line according to the 6 Chap. you shal find the square of the triangle a b c to be h i. CHAP. IX To find the square of any peece of timber containing 5 6 7 or 8 sides c. YOu must imagine in this Chapter as also in all the other sauing for round timber that I goe not about to tell you how much square that peece of timber would beare if it were reduced into a 4 square but I doe deliuer you the side of a péece of timber béeing iust foure square and of equall height with the peece proposed shall also be of equall quantitie which is right necessarie for the attaining of the number of square feet or solide content of any péece of timber Thus are you taught to find the square of any peece of timber of what fashion soeuer and if it beare none of these regular formes or that there be wood wanting take from one place adding the same vnto another thereby making it perfect regular and in such cases you must alwaies so doe CHAP. X. The square of any peece of tymber being found to tell how much of the same in length will make a square foot of tymber and consequently how many foote is in the whole peece A Solid or Cubicall foote of tymber doth containe 1728 cubicall inches for so many foure square inches may be taken out of one cubicall foot I meane such Inches that are square euery way like vnto a dye now hauing the square of any péece of tymber giuen square the same diuiding 1728 by the product so doth the quotient shew you how much of the length of the tymber must be taken to make a square foote by the which diuide the whole length or altitude of the tymber so doth the quotient acquaint you how many foote of tymber is in the péece Example The square of the tree a b is found by the third Chapter to be 27 inches whose square is 719 by which diuide 1728 so haue you 2 2 7 9 2 0 8 inches which is 2 ⅜ inches or two inches a quarter halfe a quarter whereby I conclude that as often as I can finde 2 ⅜ inches in the length or height of the tree or tymber so many square foote of tymber is in the same the tree a b is 8 foote high which diuide by 2 ⅜ inches or lay somuch of your rule out measuring one from a towards b calling euery 2 ⅜ inches a foote so by either of the waies shall you finde 40 foote of tymber in the said tree being squared some small quantity being ouer more then the same In the like manner must you deale with all other peeces of timber of what fashion soeuer first finding their square as before next the solide capacity euen as you be taught in this chapter By this Chapter may you measure out as many foote of tymber stone or such like as you please thereby cut off any number of feet from any peece of tymber as you shall be occasioned CHAP. XI To measure all kind of Tymber c. after another sort without regarde of the square THis kind of measure taketh no regard to the square feete in the tymber but vnto the solid capacity thereof but for that it is not much pertinent to the Geodeticall Staffe requiring rather numerall then instrumentall operation I will be the more briefe When you haue any péece of tymber stone pillar or such like whose solid content is required by the rules taught in the sixt book part 2 of my Geodeticall Staffe seeke the superficiall contents of the end of the tymber the which augment in the altitude or length of the same so is the product your desire Example The like must you do with any other peece of tymber of what fashion soeuer but if the tymber trapeze much vse the middest or difference of the ends as in the 4 Chapter