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
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
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
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
and one side giuen But if you would make experience of the height of hils onely by a leuell your best way is to finde out a third hill alike or néere a like distance from both the other hils so may you more truly iudge of both their heights and also of the difference thereof from the top of that hill euen as you bee directed by your line of leuell paralell to the Horizon CHAP. XXIIII To know if water will run vnto any appointed place IF you desire to know if water will be brought from any spring head vnto any appointed place you are first to consider how and in what you meane to bring it that is either by trenches and gutters or in pipes of lead or such like for those waters that will come in pipes of lead will not also come in gutters because the pipes may bring the water into a valley and so conuey the same againe vp ouer the top of any hill being not higher then the originall spring yea if it bee higher euen though you should fetch it at the bottome of an hill vpon the one side and bring it ouer the top of the said hill as low vpon the other side for if you once can set it running it will neuer ceasse vntill the pipes be burst or all the water spent the reason is because non potest esse vacuum in rerum natura And for a familiar example Take a number of quilles cut off at both ends and ioine them close together with waxe in a circular fashion and put the one end thereof into a vessel that hath water in the bottome let the other hang ouer the vessell brims the lower the better it sufficeth if so the one end of the quilles bee as lowe as the other Now if with your breath you draw the water into your mouth through these quilles and so take your mouth thence the water will run through the said quilles vntill all be spent in the vessel and this experience confirmes their opinion well that say Aqua ascendit quantum descendit But to know if water will come in pipes after the ordinary fashion to any appointed place you must first know that the ground whereupon the pipes lye must be lower at euery miles end by 4 ½ inches then it is at the spring head which considered plant your Glasse at the spring head so that the Diameter of the Demicircle lye paralell to the Horizon and equall in height to the head of the spring the two sights in the ends of of the Diameter looke through the same to the place whither the water should runne taking notice of what your eye apprehends through the sights for to that place will the water runne abating 4 ½ inches for euery mile the Tower is distant from you But say there be certaine hils betwixt the head of the spring and the place wherto the water should runne in such a case you must plant your Glasse at the head of the spring as before and looking through the sight note some marke in the next hill towards the place then go vnto that marke and if yet you cannot sée to the place obserue some other marke in an other hill and so foorth vntill from the last marke you may perceiue the appointed place in which make a note for abating as before the water will runne thereunto Example A is a place where water is found and the question is to know if it will be brought to the Tower at b which is distant from a 4 miles I plant my Instrument therefore at c so that the diameter p q lye paralell and also equall in heights to a the spring head then looking through q p towards b I cannot see the same by reason of a certaine hill that is betwixt me and b therefore I obserue a marke in that hill through the sight as at c where againe I plant my Glasse in some part of the hill so that the diameter of the semicircle lye paralell and in an equall heigth with the cundit head a the Instrument thus planted look againe through the sights towards the Tower and for that there is no other hill betwixt your sight and the same therefore through the sight espy some marke in the Tower as b which marke is iust leuell with the spring head a to which place the water may bee brought by pypes Note that some hold pipes of earth baked to be better then lead and some hold pipes of alderwood firre pine tree of such wood that hath rosen in it to be better then the former And if the ground lye reasonable leuell so that you conuey the water by trenches order the said trenches so by helpe of a plumbe that the water may haue currant 4 ½ inches at euery miles end then fill the gutter with pibble stones a foote or more deepe and vpon them throw earth so will the water run more cleere to the place appointed Note lastely that it is best if you bring your water by pipes What pipes bee best to beare water to let it come by many croked turnings and sometimes to fall directly downewards and then againe to rise by little and little by this meanes some thinke one may force the waters issue to be aboue the head of the spring so that in pipes you shall not need the foresaide abatement But now whereas in conueiance of waters by this way whether it be waters to houses or new riuers sometimes happely you shall meete with a deepe valley out of which you cannot get the water by ditches and to finde leuel ground you cannot without going a great compasse and hauing found it happely cannot haue liberty for to cut a trench through the same such a matter and such a difference I saw in bringing the new riuer from wards Ware to London for remedy whereof if the floud be great you must erect arches in manner of a bridg 1609 which may extend it selfe ouer the valley euen from the one banke to the other and if the water be but for a house postes may serue to beare the same the like must you do if you meete with a riuer brooke or such like M. L. doth teach you how to solder your pipes of earth or wood that is with vnquenched lime and hogs-grease or with rosen and white of egges or with lime white of egges and fylings of Iron CHAP. XXV To take the quantity of any stationary angle by the Topographicall Glasse YOu must put the Index with the sight vpon the Diameter in the Planisphere where the degr doe take beginning noting that a stationary angle is such an angle that hath no respect to the néedle but to the station The Instrument then duly planted vpon his Staffe you shall mooue the Planisphere the Index fixed as before vntill you espy through the sight the one marke vpon your left hand and for hedges vntill the Index lye paralell with the hedge the Instrument so resting
of the next Manour was in doubte least the veine of coale did run towards his adioyning Manour and that they were cōmon vnder his ground wherby the coales were his To resolue this doubt descend into the pit and then by the 72 chapter get the true way that the myners haue made euen as it were a hedge still noting the degrée cut by the Néedle at euery angle where the myne runneth one way or another out of the course of a right line and also measuring the side of euery angle then ascending out of the pit by your Instrument and cheine beginning perpendicular aboue the place where you began to make obseruations in the bottome of the pit lay downe the like angles and sides so obserued which hauing so done you shall soone sée if the myne or any part thereof haue run out of the one Manour into the other for if it do you shall be forced to measure out of the one into the other And as you note these angles of deuiation being in the darke bowels of the earth you were best to haue a candle fixed vpon the end of a staffe of equall hieght with your eye and the same to be fixed in the foote of the myne at euery angle that thereby you may the better direct your sight therunto CHAP. XCI To plant barrels of powder direct vnder Castles Forts or such like and to know how farre you be vnder the same IN performing this Chapter by some Proposition formerly published you must get the Horizontall and Hypothenusall distance of the Forte from you and thereby the height thereof aboue the Horizontal line which done you are also by helpe of your Néedle placed in the glasse to find out the angle of position which is the number of degrées from any principall quarter of the world that the iourney lyeth which done you must by the same Instrument euer direct the myne direct vpon that line or part of the world and kéeping your Instrument paralel the sight vpon the diameter of the demicircle thereby alwaies cary the floore of your mine leuell with a candle fixed vpon the end of a staffe of equall height with your eye as before will helpe you to do Now when you haue gone so farre vnder the ground as you found the length of the Horizontall line to conteine you may assure your selfe that you be direct vnder the Forte and that you are so many pases vnder or below the said Forte as you found the Forte to be about the Horizontall line CHAP. XCII A Mine running vpon some certaine point yet ascending or descending to know at any time how much you are aboue or vnder the Horizotall line COncerning your iourney vnder the earth you must obserue the doctrine of the last Chapter and when the mine happeneth to fall or rise according to the doctrine of Altitudes and profundities duely note at euery seuerall station the quantity of the ascent and descent that is how much you rise aboue or fal vnder the true Horizontall line and so kéepe two seuerall tables the one of the ascents and the other of the descents Now when you desire to know how you are situate adde all the ascents together and note the product do so to the descents then must you take the lesser out of the greater so doth the remainder acquaint you how you then differ from the Horizontall line for if the ascents excéed you may be assured that you be aboue the Horizontall line if the descents excéed you be vnder the said Horizontal line according to the difference of the said ascents descents neither néed you feare any collateral declining of the way of your myne for that nothing at al altereth the ascent or descent for that is onely altered by the directing line or line that you measure insomuch that if you well obserue the premisses you may precisely know at any time or place how much you are vnder or aboue the true Horizontal line and thereby come into him againe vpon any occasion CHAP. XCIII A Myne or trench collaterally declyning how to know when you come againe into the right line of position and also how farre you be from being iust vnder any Forte proposed TO cary a myne direct forward vpon any point of the Horizon you bée sufficiently taught in the 90 Chapter and if the Mine must ascend or descend aboue or below the line of leuel you be taught in the last Chapter at all times to know how much you be aboue or vnder the said line of leuell But say you were inforced by rockes waters or other such obstacles that you méete with vnder the earth contrary to the 90 Chapter to cary your Mine side wise from the direct line of position in such a case you are first vpon a faire large shéete of paper to extend a right liue ouer the same which call the line of position béeing the direct way that the Myne should go next note the angle of deuiation from that line that is to say how many degrées the Mine doth decline from the true line of position that leadeth on directly and accordingly plat it downe vpon the paper as you be often instructed in the vse of ech seuerall Instrument procéeding so far as your Myne continues in a right line and if you be occasioned againe to direct either further of or néerer vnto the line of position alwaies protract if downe vpon your paper exactly as well in measure as angle vntill such time that you can come to make your protracted collaterall lines or lines of deuiation to intersect with the right line of position first extended ouer the paper and then by the scale with which you protracted your lines of deuiation examine how many pases or yards that point of intersection is distant frō the point where your worke began which representeth the point of your first entery into the Myne for that compared with the fundamentall distance or length of the Horizontall line informes you if you be past or not yet come vnder the proposed Forte Therefore in these cases you were best first of all to limit vpon your paper with your scale and compasse the direct length of the fundamentall or Horizontal line and so in your protracting may you call them backe if they séeme to run beyond the Forte Then in the former Chapters be you taught to know how far vnder the Forte you be whereby you may ascend néerer or descend further from the superficies of the earth as the cause shal require Certainely most exact and excellent is this kind of working for conueying of mines and of no smal importance for the due placing of Fornaces of powder to blow vp Forts Castels Townes or such like whether they bee situate high hpon an hill or low in a valey which for all purposes in these and such like cases vnder ground you shall find the Topographicall Glasse to be most requisite CHAP. XCIIII Of the building of a Citty and of the situation
thereof IN our discourse of Topography the building and situation of Citties houses and such like is right necessary to bee remembred but for Citties of defence they require a long discourse for their situation as well in respect of their walles c. to defend as of Turrets Mounts c. to plant ordinauce in and vpon to offend onely therefore touching health let your cittie bee planted by a faire and portable riuer farre from marshes and fenny places for the vapours rising thence be vnholsome and in as barren and fruitlesse a place yet dry and firme as you may for in short time the compost and scauengers durt will soone make the conterminating soyle batfull and fertill as may be seene by London which of it selfe according to the nature of the soyle stands but in a dry and barren place though it be forced ranke by the abundance of compost Sandy ground is right necessary for the plantation of a citty and for the plat ground hereof let it not bee altogether very leuell and plaine but haue pleasant ascents and rising bankes which will cause the citty to bee more pleasant to the eye healthfull to the body and fitter for warlike defence as it may be séene by old Rome which now lyeth ruinate there were seuen such hilles in the head of the citty stood mount Saturnall towards the middest of the citty were two other mounts called Palatine and Quirinal vpon the left hand of the cittie was the mount Esquiline vpon the right hand Caelian and towards the end of the citty were two other mounts called Viminall and Auentine all which mounts much beautified the citty and thereon were many sports acted where also was and would be in other citties fit places to erect pyramides or other such citty ornaments Touching the stréets there should be foure maine stréetes lying into the 4. Cardinals of the world that is one runing North and South the other East and West crossing each other about which crossing should the Forum or common market place stand So was the citty Alexandria builded and these streetes would be spacious and broad so shall the minde blowing from any quarter come in and passe through the whole body of the said citty and thereby purge the same of all corrupt and ill vapours such like that commonly occupy citties For the citties be â—â—â—y vnholsome and apt to breede infections where the stréetes bee close shutting out the open and pure aire which sure is an imperfectioÌ„ much to be lamented in London would héedfully bee regarded in the new plantation in Ireland And as you haue diuided the citty â—nto 4. quarters so may you appoint other collaterall stréetes which will also receiue the collaterall windes whereby any aire stirring the Cittie shall haue benefite thereof Certainly most excellent right pleasant and necessary would it bee to see a Cittie thus builded for our citties at first commonly were villages or such like and so increased and augmented as the people multiplied whereby there be a confused number of houses ranged and thrust together without forme or regular fashion and now not to be reformed vnlesse it were all built anew CHAP. XCV Of the situation and building of a Mannor house in the country HE that will build himselfe a house in the countrey should haue a speciall regard that it tâ—e pleasant delightfull necessary in all respects because hee commonly spendeth a third part of his life therein yet this Prouiso would be had that hee proportion his house according to the quantity of the ground that he hath to lay thereunto insomuch that there would bee such a proportion betwixt the house and the ground or the ground and the house that a wise man building and a wise man also viewing the edifices might iudge of the quantity of his land or viewing the land might coniecture of the proportion of the house for a faire house without land such cittie follies that are often built out of London are neither commendable nor necessary and therefore they haue begot themselues a nick-name or by-name as Mocke-begger And in this point as Pliny reporteth in his 6. Chapter booke 18. of his naturall Histories there were two men liuing at one time who much halted herein to wit Lord Lucullus Q. Scaeuola for Scaeuola had faire lands without a competent house and Lucullus had a competent house without lands in which regard he was checked by the Censors as many Londoners may for swéeping more floures then he plowed lands Touching the situation of your house the best opinion now is vpon a hill or hill side hauing before the same a plaine Champion countrey for such grounds be dry and holsome if the aire be good for men thereby are made of a liuely spirit Pliny would not haue a house situate néere vnto a fenny and dormant water or ouer against the course or streame of a running water Homer saith the aire and mists rising from great riuers before the the Sunne rise are vnholsome howbeit you shall finde it pleasant and necessary to haue a cleare riuer fluant and running at a reasonable distance from your house for besides the pleasure you shall finde it necessary for vaults and such like that carry filth from your house to empt themselues into In any case situate your house distant from marshes fennes plashy and foggy grounds which are vtter enemies to health And in the politicke situation of an house diuers wise and honest men haue much laboured to bee sarre from wrangling and turbulent neighbours which they hold as great an inconuenience as want of holsome aire and for that part of the heauen that the face and open side of your house should behold you must haue regard vnto the nature of the country and quality of the winde issuing from that part of the heauens Pliny would haue you sittuate your house in a hoat country into the North and in a cold countrey to affront the South but in temperate regions to lye open into the East With vs in England the principall coast for a house to lye open into is Eastwards as well for health as in Sommer for the auoyding of the extremity of heate of the mid-day and afternoons Sunne which indéed is troublesome and vncomfortable according vnto Aristotle 2. Meteor cap. 6. and also according vnto Magirus l. 6. c. 9 d. 13. The east wind with his collaterals is moderately warme and dry and the holsomest of all much exhilarating the mind and making the body apt for any action whereas the South wind doth diminish the strength of the body minde filling the head with rheumes cathars and such like destroying the stomacke and by the frequent blowing thereof it doth not onely putrifie the bodies of liuing creatures but also it corrupteth and putrifieth the fruits whereby also quotidian feuers pestilences and other contagious sicknesse rise Now in building a house much arte is required Pliny reporteth builded a house in Cape Misenum as hee had
fortified a Campe that C. Martius who had béene seuen times Consull of Rome right skilfully that when Sylla surnamed Foelix saw it said that the rest in comparison of him were blinde béetles knowing neither how to build or incampe When therefore you minde to build a house with your Scale and compasse lay downe the ground plat according vnto your proportion ordering your sellerage larder and all houses of office in as necessary forme as to you shall séeme most conuenient appointing places for great staires priuate staires houses of office chimnies c. that shall be most requisite for vse and least annoying or defacing the house or any of the principall lights chambers or roomes then according to your ground plat drawe the forefront or face side backe-side ends and gabell ends with all returnes iutteyes soyle péeces windowes c. euen as you determine to haue it made but draw it not as commonly these Painters do proportions of houses by the eye but lay it downe by your Scale and compasse that by the application thereof at any time you may know how many foote or inches any returne any gable end any story or window is in length or bredth which you shall be taught to do haply in some other place thus vpon seuerall papers set out euery seuerall part of your house whereby your selfe or the architector may informe the mechanical Carpenter of the length of euery seuerall péece of timber all things else required about the house as the number of boords for flooring and dooring the quantity of glasse and tile with the quantity of séeling rough casting pauing other such like whereby you may giue order to the Glasier for the bredth and length of your glasse to the Tiler for tile to the Plaisterer for lime to the Sawyer for boords procéeding no one thing staying for the finishing of another thereby proportion your house according to your purse Now for the addition of more delight vnto your house vpon the South side thereof set out a faire square garden beautified with bowers walkes and such like as your gardener can best deuise adioyning vnto which let there be a fine orchard planted with trées but if your clymate be hote as Spaine c. plant your garden in the North but for England the South is best vnlesse for some trées that naturally desire the shade let there be no oxe-stall dormant and filthy water stable or other thing that may bréed noysome smelles néere vnto your gaâ—den make the alleys drie for which I could teach you diuers deuises which here is no place for and plant the trées in your orchard after a Chequer forme that standing at any trée all the rest be in right line with you which forme is called a Quinqunx within your house make your staires large not with these monnell posts but with foure steps and a halfe pace a faire light answering to euery halfe pace Let the chambers be of a conuenient height ouer head and sufficient light albeit the chamber you lodge in would not be ouer light not yet a ground chamber inclining rather to cold then heat for by meanes of heat in sléepe we may procure a swoune because the heate of the body beeing become internall and cold externall this inclosing heat and that cold will striue let the place therefore be temperate and frée from noyse for sleepe is a a cessation of the common senses which béeing occupied troubled with noyse hindereth sléepe moreouer kéepe the beames of the moone from your bed for it is hurtfull to the sight to haue the moone shine vpon your eyes sléeping Touching the plats and formes of houses some affect the quadrant building with a square court inclosed in the middest like to the Colledges or as the Royall Exchange which indéed in respect of the columnes and arches making the vnder walkes is more stately againe some affect the Romane H. some other formes but that must bee partly referred vnto the pleasure of him that bestoweth the cost and for my part I intend not at this time to lay forth the diuersitie of plats and how they should be taken or laid downe by scale and compasse for that haply I shall open the same in another péece of worke more proper CHAP. XCVI Of the sinking of a Well and of the conueying of water in pipes IF you desire to find a place where digging a pit you may also find water fit to maintaine a well or pumpe you must ss Iean Liebault writeth earely in the morning your face into the East looke close by the ground if then you espy any vapour like to a little cloud rise out of the ground there if you dig is water to be found or if such vapoâ—rs rise in a dry and faire season also if you dig trenches foure or fiue foote déepe throwing therein wooll that is cleane and dry couering the same with leaues hearbes or such like if then this wool hauing lyen for a certaine space still remaine dry there is no water thereabouts to be found but if it be little wet or greatly wet there is little or great store of water to be found according as the wool was in wetnesse Also water is to be found vnder these insuing herbes Yarrow or Nose bleed Veruaine wild peniroyall Venus haire Cammomill Dogs tooth foxtaile trifoly Cinkefoile Millefoile Coliander or as some say where aboundance of gréene Ferne doth plentifully grow or as L. saith where any other gréene hearbs naturally flourish and abound without setting Your springs thus found they of longest continuance be which are in a gray or red grauelly rocke or ground in a blackish sandy clayie or red stony ground especially being mixed with stones and grauell Now for the pipes for the conueyance of water lead is good earth is better but wood of fir Alder or pine or such other wood that hath rosen in it is best such they vse now in conueying of waters to houses from the new water mil in Westminster they must be bored through with long agores first with a lesse one theÌ„ with a bigger any boughes or knotty péeces wil serue so they bée large when the poles so bored haue not ground to lye straight vpon but lye vneuen rising and falling there be crooked péeces of wood like elbowes prouided of purpose which are also bored through being let a foote at either end into the other two poles it ioyneth together so are all the poles that be ioyned one to another made to go into the end of one another a foote or more in manner as they péece bag-pipes or such like the hole in the end of the one pole receiuing the hollow end of the other pole into the same being alwaies for a foote déepe wider then the rest of the bore which you must ioyne together with good cement as you be taught before to do CHAP. XCVII A briefe discourse how to draw the platforme of any kind of building or any other thing