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
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
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
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
but is best to agrée with the diameter of the Planisphere Appoint therefore a a center and thereupon describe a semicircle r r something more large then the circle p q in the Planisphere all within which circle is to be cut out vnlesse you please to leaue souâ—â— certaine artificiall branches to hang a plumbe neately at as in this figure which will also beautifie your Instrument but they must be so wrought by the workeman that they let not the Semicircle to fold downe Then some two inches or better distant from this circle r r describe another and according to that circle fyle all the rest of the plate that is superfluous away euen to the said circle See the precedent figures in the folded sheet This Demicircle so made he must be supported with Antickes artificially wrought and the said Semicircle so done must be placed vpon the Indexes g and f as hereafter but first I will teach you to describe the Astronomicall circles and Horologicall arkes as also to proiect Geometricall lines c. vpon the said demicircle As for the Astonomicall circles though the graduation thereof be after a new order yet will I not stand to proue the same with Geometrical demonstrations referring such to the fiftéenth booke of Ramus where they shal find the Circles are as the squares which are made of their diameters and that their diameters are as the Circumferences You shall therefore doe no more but diuide the circumference d c into 90. parts and so drawe paralel lines and figure the same accordingly as in the figure and note if you make the diameter of this circular sight to agree with the diameter of the Planisphere then haue you no supporters at all and this best 6 But now for the Horologicall arkes they be more difficult to performe you shall therefore at each end of the former demi-circle appoint the moitie of the Zodiacke euen as you be taught in the 9. place of this Chapter let the South moitie stand at b r and the North at o r then vpon the center a describe the circle the r r which we call the Equinoctiall and so vpon that center a describe the Tropique of Cancer and Capricorne which here are both but one circle Next vpon the said center describe other circles as the ☉ degree of â™ or â™ or any other as occasion requireth by placing the one foote in a and extending the other to the degrée in the Zodiaque assigned This so done repaire vnto the Table of the Suns altitude in the first Booke of the Geodeticall staffe Here serues the figure supported with Antickes againe there séeke the altitude of the Sun at 12 of the clocke he béeing in the o degrée of Aries or Libra then finding the like altitude in the Demicircie b c I place a ruler vpon the said degree of altitude and vpon the center a and so I make a small pricke in the circle of the Equinoctiall where the ruler cuts this so done I doe the like to the houres of 11 10 9 8 7 and 6 of the clocke for no further doe the houres extend in the Equinoctiall these prickes precisely done and apparantly noted I doe the like in the circle of the o degree of ♉ and ♋ so haue you thrée prickes then must you find the common center of each 3 match the pricks as you bée taught Chap. 3. Prop. 8. and thereby describe those horologicall arkes But now for that you shall want pricks to describe the houres of 7 and 8 afternoone and 4 and 5 before noone you most describe another circle vpon the center a representing the 30 degrée of Taurus making markes â—or 〈…〉 there and so procéed as before so haue you finisâ—â—â— al the houres belonging to the North moitie of the Zodiaque and they will bend towards the left hand Then for the houre liues answering to the South moitie of the zodiaque looke what you did to the Tropicke of Cancer and doe the same here vnto the Tropicke of Capricorne and as you vsed the o degree of Taurus so deale here with the o degree of Scorpio so haue you made two prickes to describe your arke by as for the 3 they bee the very same that formerly you made in the Equinoctiall and if points for the striking of the arkes of 7 and 8 before noone and 4 and 5 after noone be wanting drawe other blind paralels from some degrée of Libra or Scorpio or from both accordingly find the altitude in the table and afterwards proceed as before so haue you finished the arkes of the South moitie of the zodiaque and they will bend towards your right hand So hauing placed a small sight fixed in the 90 degrée the forepart of this Demicircle is finished 7 Vpon the backe side this Demicircle is proiected the parts of the Geometricall Quadrant and Hysometricall Scale thus Take the Diameter of the last Demicircle which make the Semidiameter of another circle as a b now making a a center and a b a Semidiameter strike the Quadrant of a circle b d c and within that Quadrant inscribe an ordinarie Geometricall square as f d e a then diuids d e and d f each into 60 equall parts next in the middest of the liue a b make a point at g on which as a center describe the Demicirle a i b equall vnto the former Demicircle now lay a Ruler vpon the center a and euery of those equall parts both in the line f d and d e making notes in the arch a i b where the said Ruler touched at euery part These parts so proiected vnto the circle a i b you shall vpon the backe side your Demicircle strike an arch of the bignesse of a i b as m n o where place all those parts as they be in the ensuing figure drawing paralel lines for figures accordingly Now if you would likewise place the Hysometricall Scale hereon also because there is roome sufficient and spare drawe a circle within the circle m n o as p q which furnish as the former with paralel lines and so from euery 15 part in the circle m n o the one and of the ruler fixed on s produce right lines ouer the paralel circles and number them by three as 3 6 9 ending in 12 iust at 60 in the first circle now diuide euery of those parts into thrée other parts by pulling right lines from euery 5 part in the said circle m n o and then write vmbra recta and vmbra versa as you may best perceiue in the ensuing figure this done your Demicircle is finished 8 This Semicircle so finished and supported as before with Antickes he must be placed vpon two of the Indexes in such sort that the one Anticke stand aâ— g the other at f bearing the foresaid Demicircle vp ouer the Boxe and the Needle prouided that he may fold downe at pleasure with certaine haspes or buttons likewise to fixe him vpright at pleasure the
conuey the Index with the sights vnto the marke or hedg vpon your right hand making the said Index point to the marke or lye paralell to the hedge note then the degrées cut by the fiduciall edge of the Index for that is the quantity of the angle This néedeth no Example CHAP. XXVI The making of a Protractor and Scale TAke a fine thinne and smooth péece of brasse of what bignes you please whereon describe a demicircle as a b c vpon the center f which diuide into 180 equall parts and so set figures thereunto as in the figure some vse to make the like circle vpon the other side the plate numbring therein the degrées from 180 to 360 but that is néedlesse now by the Diameter of this circle a c there is made a Scale according to 12 in the inch furnished with paralell lines and numbred with figures as the order is and as you may see in the figure at d e vpon the backe side the plate there is an other Scale made according to 11 parts in the inch or you may make the Scale d e according to 16 parts in the inch or more then take 12 of those parts which diuide into 11 parts make a Scale the vse whereof you may pâ—ainely see set downe in my Arte of Geodetia Chap. 53. but the best Scale is Lib. 5. of the Geodeticall Staffe Chap 2. where I treated of the Iacobs Staffe You must note further that for angles of position the one halfâ— of the circle containes the East part of the Horizon the other the West the diameter of which circle common to both the demicircles being the Meridian line or South and North points as in this figure CHAP. XXVII To protract an angle and lay downe the ends thereof HAuing learned to take the quantity of an angle by this Glasse it resteth that you also learne how to protract the same and to lay downe the sides thereof vpon paper by your â—cale and compasse First therefore to protract an angle vpon any point giuen you are to take the semidiameter of your protractor as f a This is performed with more ease and better in the 6 booke of Geodetia Cha. 2. and so placing the one fooâ—e of your compasse in g the point giuen with the other strike the portion of a circle h i k l now must you â—â—te the quantity of the angle you are to protract which let dâ— 40 degrées place therefore the one foote in a in the protractor and extend the other to 50 degrees in the demicircle a b c the which widenesse place in this circular base h i k so will the two points of your compasse fall the one at h the other at i finally draw a line from i to g and from h to g I conclude i g h is an angle of 50 degrées But say you would draw a line by some degree beyond 180 degr as by 230 degrees therefore you must take halfe 230 degr set that distance twice in the circular base viz. 115 set once there is h k which set twice there is h k l 230 degrees or deduct 230 from 360 so haue you 130 degrees and so protract an angle the contrary way of 130 degrees as h m l so shall l cut 230 degrees or be distant from h in the circular base h i k l 230 degrees and if you be regâ—â—red to lay downe the length of euery side by your Scale according as you found the same by measure first sée what length h g should be which let be 18 perches therâ—fore place the onâ— foote of your compasse in d in your Scale extâ—nding the other towards c as to 18 tâ—at widnesse of your compâ—sse place in g h fromwards g towards h as to n I conclude g n iâ— 18 pearches do so to g i g k and g l so shall you finde g o 12 pearches g k 24 and g p 6 pearches so of any other CHAP. XXVIII To obserue an angle of position and what it is as also to protract the same and to finde vpon what point of the compasse any thing seene in the Horizon lyeth AN Angle of position is such an angle that is taken in respect of the needle or in respect of the South point insomuch that the one side of euery angle of position is the Néedle and the 02 other the Alhidada the common section of the termes of which angle alwaies concurre vpon the very extrée of the Néedle differing from stationary angles because they conteine the number of degrées betwixt any two obiects proposed at euery particular station assigned and the angles of position the number of degrées distant from the Meridian To obserue therefore an angle of position you must place the Néedle ouer his true line in the bottome of the Boxe the Planisphere there resting conuey the Alhidada with the sights to the marke assigned noting the degrées cut in the Planisphere for that is the angle of position whereby you may see that the angle of position is not limited respectiuely according as hee is right acute or obtuse but onely doth extend it selfe to any degrée in the whole circle and therefore the termes of these angles might rather be called lines of position in respect of their situation and pointing into the seuerall parts of the Horizon Now to protract the said angles the difference is not any from the worke in the last Chapter onely where you beginne to protract call that point the South so forward in the other quarters of the world according as you shall be directed by the letters SEWN vpon the protractor signifying South East West North. And if you desire to know vpon what point of the compasse any thing séene in the Horizon lieth hauing planted the Glasse as before so that the Needle respect his due place turne the Index the assigned marke noting amongst the winds the wind cut by the Index for into that part of the Horizon the thing lyeth All these neede no example CHAP. XXIX To take the plat of any great Champion field or such like consisting of 1000 or 1500 acres or to take the plat of woodland and rough grounds by the Topographicall Glasse otherwise then in the eigth Chapter SVch a proposition as this cannot bee performed by one station in the midst of the field nor yet at two stations by the intersection of like lines because it is scarce possible to see all the angles at once from the said stations eithâ—r by reason of the long distance or by occasion of hils trees or such like therefore you must get the plat thereof by going round about the perimeter of the said field or wood and that you may doe either by angles stationary or angles of position but the operation by angles of position is more troublesome and lesse certaine therefore it shall bee here omitted To performe it therefore by angles stationary you must go vnto one of the corners vpon the vtter side
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
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