Baculum familliare, catholicon siue generale A booke of the making and vse of a staffe, newly inuented by the author, called the familiar staffe. As well for that it may be made vsually and familiarlie to walke with, as for that it performeth the geometrical mensurations of all altituded, longitudes, latitudes, distances and profundities: as many myles of, as the eye may well see and discerne: most speedily, exactly and familiarly without any maner of arithmeticall calculation, easily to be learned and practised, euen by the vnlettered. Newlie compiled, and at this time published for the speciall helpe of shooting in great ordinance, and other millitarie seruices, and may as well be imployed by the ingenious, for measuring of land, and to a number of other good purposes, both geometricall and astronomicall: by Iohn Blagraue ...

Heere beginneth the Booke of the readie , eadie , and pleasant vse of this new Instrument , called the FAMILIAR STAFFE .

CHAPTER . I.

What moued the Author at this time to publish so much of this Instrument and his vse , as he now setteth forth .

IT was my good hap to be at the mansion place of my most honorable fauorer the right Ho. Sir Frances Knolles knight , called Greyes Court in the Countie of Oxenford in Summer last , where the right excellent and most noble Lorde , Robert Deuorax Earle of Essex , his grandson beeing expected that day , it pleased his Honor to passe the time , or rather as it might be iudged , to stirre vp by his example the couragious minded knights and Gentlemen his sonnes , naturally apt inough of themselues to patrizate , imitate , or rather to excéede in all such magnanimous exercises , there to contend with the right worshipfull and valorous Gentleman , Sir William Knolles knight , his sonne & heire , in shooting with a small péece of ordinance at a marke , which péece was there ready on her carriage , appointed at that time together with another great péece , not long before the Spanish kings , called a Saker , which the sayde sir William to his high deserued commendations , then lately had brought home from the winning of the Groyne in Spaine , & many other smal shot there also set readie on the leads of the house , with trains of gun pouder to be shot off , to welcome the said noble Earle : sending forth amidde the regions of the aire the excéeding ioy that was there taken of the safe and happie arriuall of his noblenesse , from the then late desperate voiage performed into Portingale .

At this time after his H. and his sayd sonne and heyre had each of them shot , I being at hand , was demanded a question or two of getting the distance of the marke wherto they shot . And the sayde Sir William Knolles was also verie desirous and inquisitiue of me , in what time himselfe might learne skill sufficient for that purpose . Of which so iust and wished occasion I was right glad , and the rather when I considered with my selfe , how these dangerous times threaten to set our great ordinance mightily on worke , and how needfull & appertinent it is to the shooting in them certaynly and speedily , to get the distance of the marke they shoote at , as well for annoying of the enemie , as sparing of shootes spent in wast . So that I was in manner assured , that no Treatise was like to be more acceptable vnto his H. ( next vnto bookes of sincere religion ) then such as should tend towards the defence and safe keeping of this his natiue Countrie . Wherein it is wel knowen , euen to any that least know him , how forward his H. hath alwais bin and continueth euerie waie whatsoeuer . That olde age and graie hayres cannot yet daunt or holde him backe from the face of that enemie that should inuade the same , or offer violence or hurt to the person of our most gracious soueraign Ladie and Queene Elizabeth , whome God graunt long to raigne ouer vs to his glorie . Considering also what no small want of some one perfect meane , Generall for all these actions yet remained after so great a number of both Latine & English authors , writing of so sundrie waies to attaine Altitudes , Longitudes , Latitudes , Distances and Profundities , some by the Quadrate , some by the Trigon , some by the Crosse Staffe , some by the Cyrste , some by the Quadrante , some by the bare bare rule or Squyre , some by plaine stickes and stations , some one waie some another . And amongst them all , no one instrument sufficiently apt for all purposes , neither yet to doe any of these feates in all pointes , or almost in anie point of himselfe , without the continuall & readie vse of the fiue partes of Arithmetike . Which in the vnlearned Gunner is not alwayes to be had : nor hauing it , easie for him to performe , especiallie in such busie times , when the buzzing of dangerous businesse amongst the multitude , shall bring the best learned and skilfull man out of his numbers : besides the number of preceptes so toile some , the manifolde absurdities admitted , so loathsome . Upon al these iust occasions I was in maner forcibly drawen at this time to bend the fabrication and vse of this so noble instrument wholie vpon these causes , which I had for three or foure yeeres before determined to haue published in a more ample sorte , almost as generall for a number of matters of Geometrie , as my Iewel is for matters of Attronomie , Cosmographie and Nauigation , which I yet meane to doe , but that I dare make no more promises in print , vntill I haue finished the second part of my Iewell , so often since required at at my hand , being fiue yeres past : which yet this busie world suffereth me not to bring forth , although I contend to loose no manner of time .

Chap 2.

Of the imperfections of the Crosse staffe called by Gemma Frisius , Baculus Geometricus , and how much this Familiar staffe exceedeth it and all other Instrumentes hitherto deuised to like purposes , both for sufficiency and facillity .

FOr that I haue bene acquainted with diuerse willing wits desirous of knowledge , wanting the rudiments of Geometry , whereby they might be enabled to make choise of such instruments as might be subiect to fewest errors and absurdities , to haue bene marueilously in loue with the crosse staffe and that altogether , because it yeldeth his vse with that facillity , though but in matters at hand . For which cause , I thought good euen of zeale and good will to all such willinge young practisers , to waste this Cap. for their good , to assure them how weake and to small purpose the crosse staffe is , in respect to be imployed in any weighty seruice , scarce doing any thing well , and that not much aboue a bowe shute of , whereas this my familliar staffe shall performe them no lesse exacte at a mile , 2. or 3. distante , if the marke bee suche that the eie may cary it strongly .

There haue bene from time to time besids the crosse staffe diuerse other instruments , deuised for these kindes of seruisable mesurations , as in the Cap. before I mentioned : of which the Geometricall quadrate was thought to be the best , as it seemeth to me by G. Frisius , who often vpbraydeth the same quadrate with his staffe , when he had in as much as mighte be doen , reduced the crosse staffe to all yerfection , letting it then to lacke no commendations , saying euen at the first entraunce to the vse of it , lib. de radio astro . & Geomet . cap. 5. Dimensionibus longitudinum altit . latit . & distantiarum antecellit radius reliqua instrumenta ad similem vsum excogitata facillitatem habens longe maiorem & copiam . But by G. Frisius good sauour , I see no causa why it should carry any of those commendations , more then for the facillity in vse , and for this , wil aske no better iudge then him selfe . For in taking of an altitude , which is simply the best thing it can doe , if the staffe be not directed leuell with the horrizon , then cannot the crosse bee parallell to the vpright , and therefore breedeth error as him selfe confesseth in the same 5. Cap. saying : Vnum a paucis notatum intollerabiles inducit errores . Si quidem Radius in dimensionibus per directam lineam , & quasi ad normam tendere debet versus lineam quam metiri statuimus , siue ea sit longitudinis fiue latitudinis , what can a man aske more then direct consession , yet after he sayeth againe by way of auoidance in the same Cap. Neque vereri de bes paruum a norma deflexum qui nullum inducere potest errorem sensu perceptibilem . But by his fauour againe though a litle holding from the leuell , can breede no great error in the altitude or latitude . Yet that very smal error , there committed : shall growe to somewhat in the longitude or distaunce : being he teacheth no other way in manner , to get a distance but by the altit . or latit . of some thing at th extreame of the distance first obtayned , multiplyed into the length . Which in a long distance will multiply that insensible error to become intollerable as he termeth it . But what should we talke of longe distances , when as he maketh a prouiso , we shall deale with none by these wordes in his 5. Cap. or the like in effect . Nihili esse quantum distes a re mensuranda , verum opus est distantia non admodum longa . And then were wee as good to be without his staffe in my opinion , as to entertaine him on such streight conditions . But now to remedy those errors in altitudes , he sayeth in one place you may sette the staffe leuell by a thredd and plummet aplied to the crosse . In erectis quidem appenso perpendiculo ▪ Yet in another place he thinketh that , too combersome , saying thus . Qua in re , sufficit rudius oculi indicium ac examen . As for latitudes transuerse : remedy he coulde finde none , saying : In transuersis vero , visui credere oportet . Yet for all these things he could not holde but conclude towards the ende of his first practises . Cap. 2. Itaque nulla in parte superatur ascala Geomet . verum multis modis superat , quin ipse radius , scala quo que quaedam est geometrica , tanto praestantior quanto maiorem prebet vsum , he should haue said facil orem vsum and then he had sayd somewhat , for taking away his facillity , you take away his chiefe goodnes . The quadrate , the plaine stationes which stickes , the bare rule or squire , being wel handled , will do much more , as wel in great as small distances , onely they want the like facillitie in vse . Yea and G. Frisus him selfe for all his great bostes before let fall was driuen ere he ended his booke to seeke another waye for his matters in maner quadrate wise , by hanging his crosse Staffe , as it were by the haire of the head , with his armes abroade , and then is his so well boasted facillitye quite gone : Besides that , the longest parte of your goodly instrumente is brought then to halfe the length of the crosse , and a small length of the staffe , which in a staffe of 5. foote length will bée but 15. inches , and in a staffe of 9. or 10. foote , which no mans height can possibly reach to vse in that manner without a ladder , the longest part will be little aboue 2. foote , and of that length though the facillity remained , a man might as easelye wilde a quadrate . And now considering that halfe the crosse and 3. quarters of the staffes length , is by this meanes abiect and to no vse , who would carry all that wood about with him , except the weather were cold . Therefore to conclude , let no man be led away with the facillity of the Crosse staffe , or of any instrument , rather let him thinke no pains too great that produceth an exacte truth . And where as G. Frisius sayeth , that his staffe is quaedam scala geometrica , I say that my Staffe is not quaedam , but summa scala geometrica , that be is nobilissimum trigonum geometricum . For what may be doen by Triangles in Geometry , whole volumes do testifie , and my selfe in another treatise of this staffe at some other time will partely manifest . And I say that he shal be quoddam quadratum Geometricum and quidam radius Geometricus , and performe the vse of his Radius more effectually then it performeth the quadrates vse . What should I say , it is Baculum Catholicon siue generalissimum , and shal recompence the tractable facillity of the crosse staffe , with his familiar palpaple vse , as well in his performance of these mensurations , as his daily vsage for an ordinary and familiar walking staffe . For which cause I haue named him Baculum Familliare , the Familliar staffe .

Chap 3.

Of the framing and fashioning of this noble instrument , called the Familiar staffe .

THis staffe consisteth of two seuerall partes , or rather two seuerall staues , the one I call the standerd staffe , the other the running staffe . Both in manner like , very plaine to conceaue : being each but as it were , two streight rulers iointed together , to open and shutte euen like an ordinary paire of compasses .

The running staffe represented in this figure by E. D. F. is the verie like to the standard , being also but the like two legs or limmes D. E. and D. F. ioynted at D. each made of thrée rules or narrowe boordes of foure foote length and better , and of breadth and thicknesse , conuenient to fill the hollownes of the standard staffe , hollow as the former , not eight square , but foure square . Herein it differeth , that at the point G. of the side D. E. twentie inches from D. the parte G. F. shall bee to take off and on with helpe of a square socket or some screwe , made in the end G. of the parte T. G. to be taken off , when it is to be vsed as the Gunners quadrant , or to be set on at E. to inlarge the side D. E. as occasion shal serue . Also at the point G. there must be ioynted another light foure square hollowe ruler , viz. G. H. equall in length to G. F. which ( the instrument shut together ) must fall into the channels of G. F. and E. I. This square ruler G. H. I call the Graduator , because hee yeeldeth degrees . The centre of this graduators ioynt G. shall be euen with the middest of the breadth , and his length shal be such , that taking D. I. in the side D. E. iust equall to D. G. and the running Staffe opened exactly to a square angle , as here you see , that the extreame of the graduator , viz. H. which I will hence forth cal his Apex , may but iustly touch the point I. making there a right angled Aequicrurall triangle . And let the graduator haue at his Apex H. some deuise with a socket or payre of chéekes , or else annexed to some such running bolt , as before in the standard carrieth the sightes , and a screw pin to fasten him in anie parte of the side .

A Supporter .

Your instrument thus prepared neatly in all pointes , as a workman can better of himselfe tell how , then if I shoulde write much more . You shal diuide each legge of either of these staues into as many inches as they will containe , beginning from the centres A. and D. and euerie inch , into eight partes , which partes shall signifie feete , paces , perches , pike lengths , or anie other kinde of measure that you shall vse : so shall the fiue soote length of the legs A. B. and B. C. of the standarde , containe each 480. equall partes , and the sides D. E. and D. F. of the running Staffe as many like partes as it may containe , all which to be subdiuided againe , each into foure equall partes , and set numbers vnto them , encreasing by tens , each sorte of diuision drawen to his seuerall space limbe-like , as vsually workemen can doe full well . Thus is your instrument fully finished , sauing for his degrees , which in the next Chapter I will shew .

Other necessaries there are appertinent , as a threed and plommet for the running Staffe , or els in stead thereof ( which is much better both for vse and carriage ) some pretie rule of mettall , equall in length to D. G. heauy towardes the lower end , mouing pliant , sometimes on the centre D , and somtimes on a pinne set on the hanging side of the staffe , thereby at anie time to set him perpendicular to the Horizon . A copartner at all times to helpe , for that the instrument is great , a couple of supporters , if you will , which neede not be curious , they may be made of two stiffe stickes three or foure foote long , nayled together about three or foure inches from the vpper ende , so that they may open and shut vpon the nayle , making a forke aboue to rest the staffe in , as in this figure you see , or any other deuise you like better . But if anie man desire to haue this Familiar Staffe made in a lesse or more slender proportion then this before described , thereby to be more neate and fit for a dayly walking staffe . Then let him haue no running staffe at all , but set the graduator in the standard it selfe , and haue a small thyrd foure square ruler , with a centre hole , in all respects like the one side of the running Staffe , loose , to vse at pleasure . For so shall it be sufficient enough for anie purpose , onely the running Staffe helpeth to doe all things with more speede and facilitie , which two standards also made in this sorte may as well performe . For the one may serue in steade of the standard , the other as the running Staffe .

Cap. 4.

How you shall in a singular sorte set degrees , on the leuell side of the running staffe , and also on his Graduator , together with the points of the gunners quadrant .

HAuing had the inuention and vse of a geometricall instrument not much vnlike this my Familiar staffe , nere these 7. yeares , but of much smaller size then my good wil desired , because I could neuer conclude with my selfe , how to compas conueniently without comber , the degrées of the circle thereon : neither yet what foot or rest to cary him on , in vsing him , vntill now this suddeine occasion ministred by my honorable frends in the 1. Chap. mentioned , did new sett a sharpe edge on my dull witts : yea although I conferred sondry times with diuerse mathematically geuen about the same . As for the foote or reste which I coulde neuer deuise but very great and more combersome then the staffe it selfe , requiring a spare body to cary it : Now I meane that spare body shall supplye the vse or stead thereof : as heareafter shall appeare , but for the graduacion you shall thus after a singular sorte supply .

The running Staffe framed , as in the last Chap. I wil call the side D E ( whereon the graduators apex must run to and fro ) the leuel side , because in al questions for the most part it must be carried leuell with the horrizon . The side D F I will call the hanging side , because in euery leuell the plum line must hang directty by it : the piece G F being taken from the side D F I will call the iointe piece , this knowen : you shall on some plain boorde of two foete bredth draw a ground line , vz. M F then on some point thereof , vz. D erecte the perpend : D K of 2. foote length at the least : Wherein you shall sette the pointe I. xx . inches iuste from D , and likewise G as much from D , in the groundline D F , then on D with the quantity D K , describe the semy circle M K L and on G with the quantity O I , describe the semy circle N I F. This doen deuide the semy circle M K L into 180. degrees , and euerye degree into sixe partes at the least , with blinde notes : you shall also on the centre D with the quantity D I describe the quadrante I G , which you shall deuide into 12. equall partes , which are called the 12. pointes of the gunners quadrante , and euery of those 12. partes , againe you shall subdiuide into other 12. partes , which are called the minutes of a gunners quadrante , so haue you 144. partes .

Thus is your ground plot laide , whereby to set on all your graduations . Wherefore you shall now bring your runninge Staffe prepared as in the last Chap. & opening it to a square angle , ( which is doen when the apex of the graduator is fixed to the pointe I of the leuell side ) place him now on this figure his centre D , on the point D of this figure , and so consequently I vpon I , G vpon G , F vpon F &c.

The tipe of graduating this instrument , commended by the Author , to the ingenious matthematicall minded gentleman , Master Auditor Hill .

The vppermost side of the graduator you shall deuide into 90 degréees , by a rule laide from D on euery diuision of the quadrante K L , and the vndermoste side into the 144 partes of the gunners quadrante , by the quadrante I G in like manner : So is your graduator furnished with his partes , yf you draw certaine parallell lines , limbe like as the manner is , and adde but numbers to each of them : but now to set graduation in the leuell side D E you shall kéepe the hanging side D F , sure fixed on the groundlyne M F keeping his former place , & bring the leuell side euen with it , shutting in the graduator close out of sight : then shall you open him againe till his fiduciall line doe cut one degrée aboue L of the semicircle M K L , and there lifte vp the graduator til his apex doe touch the leuel side . Marke that touch point , for one degrée : then open the leuell side vnto 2. degrées aboue L , and there bring the graduators apex againe to touche , marke that touche pointe in the leuel side , for 2. degrées , and so doe from degrée to degrée of the whole semicircle M K L , marking still the touch points in the leuell side , and you shall finde that the apex will touch that leuell side euer in the semicircle N I F but when you are once paste 10. or 15. degrées , you shall make notes in like manner for euery subdiuision of eache degrée , and let these degrees be placed either in the vpper or lower flatte of the leuell side , it is no great matter which , and numbred from E ending at D with 180. degres , for note , that the euen partes mentioned in the last Chap. must be set on the inner or shutting flats of both sides of this running Staffe .

Chap 5.

How by this Familiar Staffe to trie whether a peece of ground be leuell , whereon to plant your peece of ordinance .

I Perceiued by that small practise I sawe in shooting , mentioned Of leuelling . in the first Chapter , that it is needfull to place a peece of Ordinance to be shot , on a leuell plot of ground , that one wheele of theyr carriage goe not higher then another , least in her recoile it make her shoote awrie : first sticke some woodden pin in the ground , and resting the centre of your running staffe , ( set at the square angle ) theron : lifting vp the hanging side , by helpe of a threed and plommet or plum rule , vntill the leuell side be exactly placed leuell with the Horizon : then shall you from that woodden pin extend a threed or line , euen by that leuell side of the Staffe so placed , and with another pinne also thrust into the ground , there fasten it , then keeping still the centre of your staffe on his first pinne , turne about the leuel side somewhat wide from the line you haue strained between the two pins , and there in the very like manner place another threed or line extended from the said first pin by the leuell side of the Staffe , and let the same be holden stiffe out with a third pinne : now laying your eie nere the ground , by these two lines or threeds so extended , you shal see whether any part thereof be higher then the leuell , to bee pared awaie , or lower , to bee filled vp E. A. N. is the running Staffe A. the first pin K. the second , I. the third A. K. and A. I. the two threds or lines extended leuell with the Horizon P. the cie leuelling by the threeds , O. an hillocke to be pared awaie .

Chap. 6.

How by this Familliar Staffe to mount a peece of ordinance by pointes of the Gunners quadrate .

HAuing by the last chap. leuelled the ground , whereon your Of mount●… ordinance is to be planted , next followeth to know how to mount your peece vnto any point desired , which is most easie : For your running Staffe set at this squere , pulling awaie the ioynt peece of the hanging side , so is that side the shorter by more then halfe . Then putting his leuell side into the peece vp to the verie apex of the graduator , there let it bee holden euen and leuell , with the bottome or lowest side of the concauitie

A peece leuelled at point blanke . of the peece , then lifting vp or weighing downe the peece till the threed and plummet , or plumme rule , hanged out of the centre doe rest euen with the fiduciall line of the hanging side , ther is your peece scituated leuel with the Horizon neither mounted nor embased anie point or minute , but euen at point blanke , as they call it . After this , if the peece be eleuated neuer so little aboue that leuell , then doeth your thred and plummet or plum rule , shew on your gunners scale ( appointed in the fourth Chapter , on the inner side of the graduator ) to what point or minute the peece is eleuated for to shoote at randon , as they call it , yea , and if need be , it sheweth you on the vpper scale of the graduator , the same randon

A peece mounted to shoote at randon . by degrées of the circle , which for anie thing I can see , might be applied to this purpose as wel as the gunners points .

Chap 7.

By what meanes a certaine table is to bee made , thereby to knowe how farr any peece will shoote at randon , beinge mounted to any poinct of the gunners quadrante .

LEt no man thinke that I pretend to shewe the arte of shooting in great ordinance , being in deede a matter that I neuer tooke occasion so much as to thinke of , before this time , but for that matter , do aduise euery man to repair vnto Tartaglia , which is lately englished by M. Cyprian Lucar , & published . Who hath set down diuerse singular conceites & obseruances about the same , only to the end to sharpen your tast for the fruit of this my worke following . I thought good to present you with this instance out of Tartaglia , which in the next Chapter I meane also to applie to my Staffe . He giueth but a glance in his first booke , 1. Colloquie , that anie one peece being mounted from point to point , and minute to minute of the gunners quadrate , and the randomes or distances in paces of that peece taken at euerie seuerall mounting , and noted in a table ( being carefully dealt in ) would serue to know the randoms of any other péece likewise eleuated from point to point : if you do but know anie one shoot at anie one point eleuated of that other peece . For looke what proportion the shoot of any point of the first , beareth vnto any other point of the same peece . The like shall the randomes of anie two like pointes of the second beare one to another .

As for example : If the first péece shoote fortie paces at the first point , fiftie at the second , sixtie at the third , &c. Then if you shoote one shoote in another péece , which at the first point happily shooteth but thirtie fiue paces , and that by this one shoote knowne of this second péece , you would before hand know how farre he should shoote being eleuated to the third point . In this case you must by the rule of three ( saith Tartaglia ) seeke out a number in that proportion to thirtie fiue , as sixtie is to fortie , which you shall finde 52. ½ . paces : and so much shall this second péece shoote , eleuated to the third point , if that Instaunce of Tartagliaes be true in it selfe . Although many secret accidents besides may much alter it , as that the pouder at each shoot be like good & like much , the pellet of like waight , the péece of one temper , and such like . For Tartaglia writeth amongst many other experiments singular well by him discussed , which I am not any way to meddle with , that a péece being cold , shooteth not so farre at the first shoote , as with like charge hee doth at the second or third being then temperatly hote : And after when she is ouer hote with shooting , she beginneth to shoote shorter againe : and sheweth the reasons thereof .

Chap. 8.

Hauing made a table of randoms to some one peece according to the precepts in the last Chapter . How by this familiar staffe , to make the same table serue for any other peece without any arithmetycall calculation .

TRuely this inuention is very new : for it came into my Of prop●●tion . head but euen as I was writing the last chapter , where you are taught Arithmetically to performe the same . But my familiar staffe will not haue you troubled with numbers in such daungerous times . Wherefore hauing your table made by some one péece exquisitly shot in , and one shoote giuen of some other péece at some one certaine point or minute perfectly made . So haue you alwaies , as in the last Chapter is shewed three numbers giuen : two out of your table : and the third is the shoote of the péece in action . You shall seeke the one of your two table numbers ( it is no matter which ) in the right legge of the standerd staffe , and thereto by helpe of the mouing sight pin , place the centre of the running staffe , set at his square angle , or any other lesse angle it is not materiall what : and direct the leuell side vnto the centre of the standerd : There hold him till ye haue pulled too or thrust out the left legge of the standerd , so that it cut in the hanging side of the running staffe your other table number . There wrest the standerd fast at that angle by his centre skrew . Lastly , seeke in the said right legge of the standerd the number of paces of the shoote giuen , and thither by helpe of the said sight pin , remoue the centre of your running staffe , keeping his former angle , and his said leuell side , directly still with the centre of the standerd , and questionlesse the left legge of the standerd shall there cut off in the hanging side of the running staffe , the iust number of paces desired .

For example , it is admitted in the last Chapter , that the shoote of a peece eleuated vnto the first point was thirtie fiue paces , by which I would know how farre that peece would shoote , being mounted at the third point : I seeke in the Table there mentioned for the same first point , there according to the last chapter I finde fortye paces , and also for the

third point I finde sixtie paces , which had , I seeke the biggest of those table numbers , viz. 60. on the right legge of the standerd : it endeth at B there I place the centre of the running staffe , being set at a venture at the angle C B A and apply his leuell side B A euen with the centre A of the standerd , and there on his hanging side B C I seeke the other table number , that is fortie , at C. thither I bring the left legge of the standerd to cut , and there locke him fast to kéepe the angle C A B. That done I seeke the number of paces of the shoote giuen , that is to say thirtie fiue , on the said right legge of the standerd , that is to say at E and thither I remoue the centre of the running staffe his leuell side , keeping still the centre A and in both the staues their angles before set C A B & A B C vnstirred , and there doe I sée the left legge of the standerd to cut off in the running staffe at D fiftie two ½ paces , the Random of this second péece at the third point desired : in all respectes the same which in the last Chapter you found by Arithmetike . So that vpon the matter you haue now learned the rule of thrée by Geometry , and is demonstrated in Eucl. lib. 6. Propo. 10.

Chap. 9.

If a Wall or Tower were to be scaled , and that you may come vnto the base of it without daunger , How by this familiar staffe spedily to get the height thereof , thereby to make your scaling ladders according .

IT hapneth often that it is thought more conuenient to win Of altit a towne or fort by scaling with ladders and such like , then to batter it with ordinaunce . In such a case where the walles may be come to , without daunger , it is so easie and common to get the height by any instrument , that I could scarse spare it a roome , but that it may serue as a ground , or first introduction to the rest . This my familliar staffe as in the 2. chap. I saide , may be vsed in most cases , eyther as himselfe , or as the quadrante or circle , or as the quadrate , or as the crosse staffe , or as the gunners quadrant : and in this case indifferent to them all . For if you take your running staffe set at his square angle , and apply the leuell side to your eye , lifting vp the centre till the line and plummet out of the centre do hange iustly on the 45. deg. or 6. gunners poinct of the graduator , which are both in one streight line , what vpright soeuer you sée , then euen with the leuell side the height thereof is equall to the distannce from you . In so much that when at any time you shall by this instrument or any other finde the altitude of the sunne 45. deg. if then you runne and measure the shaddow of that tower or wall , the same shall be equall to the height therof , as most aucthors affirme , but in very déede it shall be lesse then the height by so much as one quarter of a degrée commeth to , as in the treatise of my new Astronomicall staffe not yet extant shall appeare : in the meane time take the shaddow at 44 ¾ degrées high , and the same shall be your desire .

But now , if you will doe it crossestaffe wise , then set the extreme of the leuell side of the running staffe to your eye carrying it square to the vpright , as néere as you can , the hanging side vpwards and parallell to the wall , and go in or out so , till you may sée the toppe of the vpright , euen with the toppe of the hanging side , and there shall you finde the distaunce to the

wall equall to the height thereof , as before . And if you place the wing in the middest of the hanging side , and by that sée the toppe from the extreme of the leuel side , then is the distance to the vpright double to the height , if at a fourth part from the centre , then is the distance 4. times the height , &c. For example in this figure the running staffe set at his square angle , and carried square to the wall as you sée : if you go in or out till you might see the toppe P of the tower R P euen by the extreames E and F there shall the distance from your standing to the tower be equall to P S , then adding thereto your height viz. R S , you haue the height desired . And if you chuse your station so that you sée P by the extreame E of the leuel side and the wing H : and that H be one 4 part of D F from D , then is E S foure times the height P S , because D H is foure times in D E : in like manner H being set at halfe or a third part , &c.

Chap. 10.

To performe the last cap. Where you dare not come neere the base of the tower for daunger of shot or let by reason of some deepe mote or ditch .

I Will first in this Chap. shewe 〈…〉 by this familiar Of altitu staffe to do this feate after 〈…〉 mer almost of the Crosse-staffe , which many 〈…〉 ell , and in the next chap. after his owne fashion , a 〈…〉 may as well be applied to a wall or vpright approchable .

Take your running staffe set at his square angle : and place the wing of his hanging side neere about the middest thereof , or as occasion shall serue : fixed : then applying your eye to the extreame of the leuell side , directed right against the wall or tower in manner of thel last chap. chusing you a station somewhat farre from the wal , where from th extreame of the leuell side you may sée the toppe of the wall , by the sayd wing before fixed : which done , then shall you place the running sight of the leuell side from his extreame towards the Centre , halfe or a quarter , or iust so much as the sayde wing before fixed in the hanging side is placed from the Centre of the staffe , and there let this wing also be fixed . Then chuse you a second station ( going in towards the wall ) carrying the instrument plum as before , till you may againe see the toppe thereof by both these fixed wings . Lastly , measure the distance betweene both your stations for the same shall be eyther the whole , the halfe , or quarter of the height of the wall you seeke , according as you did set the last wing from th extreame of the leuell side , eyther the whole , the halfe , or quarter the length of the first wing from the Centre , adding thereto when you haue doone the height of your eye aboue the base of the vpright .

But here I can no longer delay , but warne you of two things in this working , both which , G. Frisius halfe wineketh at in the vse of his Crosse Staffe , because he would haue it commended forsooth for facillity . But I haue euer detested that facillity that should produce any absurdity . The one is , that the hanging side of our instrument be parallel to the wal , the other , that your eye in both stations be sett in one leuell , that is to say , no higher aboue the base in the one station , then in the other , both which are fowle faults to be admitted , if the vpright should be far of : yet are easely salued with a little paines . And I earnestly exhort euery practiser in these actions , to defy that ease , that should shame him selfe & bringe his arte in question : a notable faulte amongst moste of our land measurers in these daies , I meane those that measure by platt , who partly by want of skill in Geometry , partly by want of perseuerance and knowledge in other sciences and faculties , wherwith a perfect surueior ought to bee adorned and furnished : and chiefly by want of industry , paines and diligence , doe bring them selues and a most excellent Science into disdaine and obloquy , when as seldome two of them can produce one measure or like plat of one self ground , and that which more is , scarce one of them shal agre with him selfe . I meane produce at his second measurement either the same platt or the same measure which he did at the first . But God willing when so euer I shall goe in hand to write againe of this instrument , I shall sett downe moste certaine salues for euery sore in those cases . In the meane time , to retourne vnto the two errors , that might accreaue to this matter we haue in hand : they are easely salued with no pains at all in respect : because the greatnes of the Staffe requireth an assistaunte or partner at the further end : who shal discharge you thereof . The first is easie remedied by a plum line , or rather a plum rule mentioned in the third Chapter , applied to the hanging side , as in the second Chapter was saide , which your partner may easely guide whiles he stayeth theend for you , especially hauing an halberd pitched in the ground to help him rest his hand steddy . The second as easy salued by a spare halberd , or a staffe pitched somewhat farther in towards your vpright then your second station shall be : which halberd shall haue a bright marke viz. Q placed on it , euen with your eie at the first station , by which marke Q you and your partner may easely direct the leuel side of your instrument at both stations of one height . Note that whatsoeuer is before written of altitudes , the same doth G. Frisius , Chapter seuenth de Rad. Geo. conuert to the latitudes or distaunces betwéen two markes , towers or trées , willing you to beare the crosse aside , and not vpright , and to take care that you stand square to the latitude as néere as you can , saying , a litle awry will doe but a litle harme . You may not doubt do it as well by this Familiar Staffe , as by the Crosse Staffe : but I will not bid you to do so much as a little harme , leste you doe a litle more , and then all starke naught . I meane to teach you a better way in my 21. Chapter .

Chap. 11.

How by this Familiar Staffe to performe the last Chapter another way , more exacte for long distaunces , the more safelye to keepe you out of daunger of the shotte of the forte , whiles you are in action .

HItherto we haue but as it were borrowed the precepts of the Crosse Staffe to fitt the fancy of some , who I hope will not deny but that this my Familliar Staffe performeth Of altitude . them with no lesse facillity , and no great alteration : yet as in the last Chapter I sayd , my earnest care of exacte trothes will not suffer me to aduise you to relye vpon them , for anye altitude aboue a bowe shoote of , as in the second Chapter I touched , for many causes too long here to recite . But in case the vpright be far from you , whose height you seeke , then shall the proper and naturall working of this my Familliar Staffe serue your turne much better in this manner . You shall first by helpe of two stationes as in the fiftéenth , seuentéenth or twenty Chapter following is taught , get the distaunce from you to the base of the wall or tower , viz. howe many féete , yards , paces , or other measure , it is from your first station : those reckon on the leuell side of your runninge Staffe from the centre , and thereto place the wing fixed : that one , set that wing to your eie ( placed iust ouer your station ) directing the centre of your Staffe to the wall , and let your partener kéepe the hanging side plumne by the plum rule , and with al , be reddy with his hand to moue the wing of the hanging side , by direction of your eie , so much aboue the centre till your selfe may from the sayd winge at your eie , by this second wing sée the toppe of the wall or tower . Then sée what euen parts are contained betwéene the centre and this second wing on the hanging side , for so many féete high is the toppe of the tower aboue the leuell of your eie .

For example , admitte you had by the fiftéenth , seuentéenth or twenty Chapter following , found the distance from the station N in this figure , vnto the poincte of the towre leuel with your ese viz. S. to be an hundreth pace or fiue hundreth foote , all is one , but that in getting the altitude of any thing , the rekoning had néede to be kept in féete , though for distances or longitudes , paces , perches , pike-lengthes , or any other may suffice : those hundred paces I reckon on the leuell side of the Staffe , they end at I. where I place the wing . Then directing the centre of my Staffe , viz. D. to the towre or wal , I cause my partner to lifte vp the wing of the hanging side , vntill it come directly betwéene I and the towre top , viz. at H then I looke on the Staffe what euen partes I finde betwéen the sighte H and the centre D , admit I finde eight . Therefore I conclude , that wall or tower to be eight paces highe , which is forty foote , and in this working you shall take helpe if néede bée of the fifte or sixe notes of the fiftéenth Chapter following .

Chap. 12.

How you shall know by this familiar staffe , the depth vnder the iust leuell of your eye , of the base of any tower vnaprochable when the same base is to be seene .

SUch may be the aduantage of the ground whereon wee make our stations , that the leuell of our eye may be much Of profunditie . aboue the base , and then are we not satisfied for the height of the vpright , if it be vnaprochable : wherefore when you haue by the last Chapter gotten the height of the wall or towre aboue the leuell of your eye : note then some marke on the wall , euen with that leuell : and so may you as easily and by the selfe same meanes get the depth of the base vnder the leuell , as in the last Chapter you got the height of the toppe aboue the leuell . There is no difference in the worke , but that you must turne the extreame F of the hanging side of the staffe dounewards , and set the wing thereof iustly betwéene the wing I , and R the base of the towre , that is to say at X as in the last Chapter you did set it at H betweene I and the top of the towre P , and the partes of the staffe betweene the centre D and the wing at X shall be your desire . Which added to the former height P S maketh vp the full height from the toppe to the base , that is P R.

But where the ground hath no great aduantage of the vpright , I would neuer wish you to make two workes of one , for if it be leuell with the base of the towre , it is a small matter to lay your selfe downe and worke the last Chapter close by the ground : if it be lower then the base , then place the leuell of your eye no more aboue it , then that it may direct to the base : such like small matters he that could not of himselfe prouide for , I would not haue him allowed for an executioner of these seruices .

Note , that if you list not in this working to turne the hanging side of your staffe downewards , or that the ground will not admit it to sinke so low as the leuell of your eye marked on the towre , you may worke it as well and easily , kéeping the hanging side vpwards , in such maner as in the twentie sixe Chapter following is taught : and then must you kéepe the centre of the staffe ouer the station N and direct the extreme E of the leuell side towardes the towre or vpright , as by the bare inspection of the triangle I V O of the figure of the same twentie sixe Chapter : you may easilye conceaue . The quantitie I. V. of the staffe , shewing the depth of the point C vnder X the leuell of the eye in that figure as here the quantitie D X sheweth the depth of the point R vnder the point S leuell with the eye in this figure .

Chap. 13.

To knowe the length of the scaling ladder to reach ouer the ditch to the toppe of the wall or tower .

THe height of the wall or tower together with the distance thereof from your station first had by the 11. and 15. chapters and helpe of the 12. then measure from that station directly towardes the tower till you come at the out side of the ditch where the foote of the ladder must stande , take that measure out of the whole distance , keepe the remaine , and then as in the 30. chap. shall be shewed , prooue with your leuell whether the footing of the ladder be no higher or lower then the base of the wall , if it be higher , then take it out of the height , if lower , adde it thereto , and keepe that number also . Nowe shall you reckon the first number kept on the leuell side of your staffe , set at his square angle , and the second number kept on the hanging side , and there make notes then applying the ioynctpeise or any part of the standerd betweene those notes you may thereon tell with a sticke as they say , howe many foote long your ladder shall he .

For example in the figure of the 11. chap. T is the footing of the ladder , M the station , M T measured and taken out of M R leaueth R T the first number kept , this point T is so far vnder the leuell of the eye , as W T or S R commeth to , therefore adde it to P S , so haue you R S your second number kept , and those two numbers reckoned on the seuerall sides of the running staffe as is sayd , and the ioynctpeise layde betweene them yeildeth you the Hypothenusa P T which must needes be the length of the scaling ladder desired .

Chap. 14.

How at any station either by the standerd or running staffe the angle of station or position betweene any two markes or places is to be taken two seuerall wayes .

I Am not ignorant that an angle of position in Geography Of tal angles . is the angle comprehended betweene the visuall line directed vnto any place appointed , and the meridian line of your being . But if we call the angle made by two lines issuing from one place or station vnto other two places , an angle of position ( though happily more aptly to be termed an angle of station ) the matter is not great , being it is the angle of position or placing of the one place from the other in respect of your station . This angle shall most casely by this familiar staffe two waies be taken , the first easie and familiar to

conceaue , the second more easie and familiar to be performed .

For the first way suppose P your place of station and N and T the two places or markes whose angle of station or position you seeke . Let your partner and you get ech of you your supporter mentioned in the 3. chap. on which two supporters , you shall so rest the one legge of your staffe , viz. A C. ( his centre iust ouer your station marke , viz. ouer P that you may by the sight pinnes , or pegges of that legge sée the one of your places , vz. N : there looke that leg of your staffe lye fast on his rest , leauing that to your partners charge by his steddy holding of his supporter both with hand and knee . That legge so setled euen with the mark N , you shall gentlye open the other legge A B lifting it vp and downe withall , vntill by the two toppes of the sight pinnes of that legge A B you may see the other mark T , and there with your centre screw pinne , locke your staffe fast at that angle T A N : for the same is the angle of station or position desired . And if you take this angle by the running staffe in this manner , then doth the graduators apex also shew you the degrees which that angle contayneth on the leuell side of the staffe . But for your supporters , it is not materiall to make such reckoning of them as to be choise about them : for two stickes pulled out of an hedge , knit together with a point towardes the one ende may serue for a shift . Or if a Captayne haue but his halberd , let him sticke it fast in the ground vpright , and with his garter tye the one ende of the legge of the staffe thereto , he may then vse the other at his pleasure without helpe . Or sometimes he may rest him to a tree , or on the very barrell of the Cannon . In these cases I would haue no man tyed to precepts , but be ready to supply as occasion shall minister .

Now for the second waie , let year station be P. and let L. & T. be the two places or markes , whose angle of position you séeke . Sticke your dagger or anie stick vpright in the station marke P. in the ground , and thereon rest the centre , viz. A. of the standard or running staffe . Then applie your eie vnto the extreame of his one legge , viz. to B. and let your partner apply his eie to the extreame of the other leg , viz. to C. each of you opening his leg by little and little so wide , till your selfe see the mark T. by the sight pins or pegs of the leg

A. B. & your partner sée the marke L. by the sights of the legge A. C. & there wreast fast your Staffe at that angle C A. B. for the same is equall to the angle T. A. L. by Eucly . lib. 1. propos . 15. which is the angle of position betwéene the marks T. and L. desired . And if you performed it by the running staffe , then shall the graduators aper , as before among the degrees or graduation of the leuell side , shew you also what that angle is , and how many degrées of the circle it containeth . Yea , your partner and you may as well and more speedily doe it without anie dagger or rest , but that a rest may happilie guide the centre of the staffe iust ouer the marke . Note also , that in taking the angle in this manner by the running staffe , let the leuell side be first directed to his marke , and let him that directeth it , pull the apex of the graduator to and fro , till his partner finde the hanging side opened euen with the other marke .

Chap. 15.

How ( in manner of the first and plainest meanes , mentioned in the last Chapter , to take the angle of position ) to get the most exact distance of a Castle or Fort from you , yea though the same Fort be two or three miles off or more , whereby you may know how to place your maine battel as neere as may be without danger of shot from the Fort , and also in what space you may march to the same when you will .

ALL this while we haue about altitudes reckoned vppon feete or paces at the greatest , but now shall we for longitudes Of longitude or distance . or distances , deale ( & that as certainly ) with paces , perches , pike lengths , or miles , which commeth neere the substance of our pretence , and shall be farre more easie then the premises .

First come to the place where the ground serueth you best to place your Canon , there make a marke for your first statition , then send some spare bodie a conuenient distance off , that waie , which you finde the ground fittest , so it be not directlie backwards or forwards , to set you vp another mark for your second station . Which done , you shall with your standard staffe after the first manner of the last Chapter , take the angle of position betweene your second station , and some one pinacle or other notable marke of the Castle or forte , thereat locke your staffe by helpe of the centre screwe at that angle that you may carry him safely without sagging , vnto your second station . This done , you shall goe to the other station , measuring the distance betweene with a wyre chaine , morice pikes , or how you will , but most exactly , be sure . Those perches or pike lengths you shal reckon on that leg of your stanstard staffe , which you before directed to your station , by the euen parts and numbers theron set : and to the end of that rexkoning place , the running bolt or sight of that legge , and there fixe him by help of his screw pin . Then place your staffe again at this second station on his supporters , so that this fixed sight pin be directly ouer the marke of the second station , and the centre end directed towards the first station , which your partner shall support , and lifte vp the other legge withall , putting to and fro the running fight of that legge by your commandement and direction , vntill that your selfe doe finde the foresayd marke , hole or pinacle , directly euen with the knops or tops of both the running sight pins . And then looke what number of partes you finde there shewed in that further legge by the second sight pin : so many paces , perches , or pike lengths is that marke or pinacle from your first station .

gunnery diagram

P. the first station where you woulde place your Canon K. or rather N. the second station . T. a marke in the tower to bee battered . R. and S the two supporters , A B C the standard staffe placed on his supporters , his centre A at the first station placed ouer the marke P , his one legge A C directed to the second station at K his other leg A B to the marke T in the tower . T A C , the angle of position taken at the station P. Admit the distance betweene the stations P and K , to be fortie perches or pike lengths that number fortie I seeke in the legge A C , it endeth at N , there I set the running sight N fixed , which at this second station K , I place iust ouer K , directing the centre A to P ( the angle of position B A C vnstirred ) M. the running sight of the other legge , set directly , betweene the pinacle T , and the sight N : so shall the number of partes comprehended betweene A and M on the leg A C , shew you the exact distance from the first station A , vnto the pinacle , in such measure as you measured between your stations P and K.

Many things might be noted , which in halfe a daies practise will be easier found , then though I shoulde write many nights .

1 First , the greater distance that your two stations are in sunder , except they be vnreasonable much further then the marke : the more certaine is your working .

2 The sharper that the angle is made betweene the legges of the Staffe , as for example , F A K in this second figure or the blunter , as G A K : The greater distance of the stations is required : otherwise the point of Crossing either at F or G , will hardly appeare .

4. If you meane to get an exact distance , you had néede ( yea by your best position ) let the distance betweene your stations be no lesse then one eight part of the distance to your marke as neare as you can imagin . Otherwise you shall hardly get the true point of crossing , as you may perceiue at H : or at the least let it be neuer lesse then one twelfe parte : either of which are easie to be had in a small ground , and will serue for a great distance : for fortie pearches is but a reasonable distance for two stations , and are to be found commonly in a small close , and yet that is the eight part of a myle of a thousand pace , and it is the twelfth part of your common longest vsuall myles .

5 Other small conceites are to be noted as if the distance of the stations in the last example were so small , that in account on the legge A C of your staffe it falleth out so neare the handle , that the running sight N might not be brought thereto : then may you set your sight N at double that number , and when you haue done , take halfe the number found on the legge A B betweene A and the sight M for youre distance desired , or if you set him at thrise or foure times , and in the end take a third part or quarter of that you finde , all commeth to one passe . Yea if the distance be very short , you may reckon euery tenne but for one , and then if you r●●ct one cyphare from euery number your staffe is readie figured to your contentinent .

6 One thing I had almost forgotten : for as in rekoning the distance of your stations on the legge A C you shall euer be rather led to encrease your scale , as in the fift note I shewed , especially , for short distances or longitudes , as they call them : So contrary wise for long distances , when as the mark desired is a myle or two from you , except your stations bee made much the larger , you shall be driuen to place halfe , or a third , or a quarter of your stationary distance betwéene A and N : and then take the double , treble , or quadruple of that you finde betweene A and M , for your desire , as in steade of the fortie perches betwéene P and K to haue set twentie or ten euen partes betwéene A and N. Yea , or if your stations had béene fortie seuen : ( here because fortie seuen is not easily parted into a quarter because of the fraction ) you might first worke by a quarter of the euen number , that is to say of fortie , and then worke by the seuen by it selfe , and adde the two productes , as if by ten you found an hundreth perches , you must take foure hundreth for those : and then working by the odde seuen , you shall get seuentie more to bee added to foure hundreth , so is your whole distance foure hundreth and seuentie .

Also you must prouide to haue two bright markes flickering ouer both your stations till you haue done , that you bee assured iustly to take your leuell .

Chap. 16.

Of the Geometricall ground , and familar proofe thereof , wheron the whole working by this familliar Staffe dependeth .

AS I haue thought it very requisite to shew the grounde platte of these precepts in hand , so it were in vaine for mée here to iterate any expositions or diffinitions of vsuall termes Geometricall , since they are now a dayes very common , and are of Euclide and diuerse other recited , and of me in my Mathematicall Iewell 1. booke sufficiently declared . Understand therefore that if in any triangle you drawe a line parallell to any one side , the same line shal cut of a triangle like , & equiangled to the former . For example within the triangle A B C let there bee

drawen the line D E parallell to C B I say that the triangle A D E is equiangled to the triangle A B C , that is to say , the angle E is equall to the match angle B , and the angle D to the angle C , and the angle A of the one , to the angle A of the other , for the angle A is common to both , & also the triangle A D F , shall be like to the triangle A B C , that is to say , what proportion the sides of A D E beare one vnto another , the like proportion doe the sides of A B C beare one to another . For Familiar proofe of the first , open your compasses at auenture , and with one scantlet on the centres B and E , describe two seuerall arches cutting the seuerall sides , encluding the same angles B and E , as you see F G and H I , and those two arches you shall finde by your compasse to be iust equall the one to the other , and therefore of necessity the angles F and B subtended by those arches are equall : in like manner may you proue the angle D to be equal vnto the angle C , and being the angle A common to both , therefore the triangles are equiangled , if you desire more artifyciall proofe , repaire to Euclide lib. 1. propos . 29. and lib. 6. propos . 5. 6. and 7. Likewise for Familiar proofe of the second , deuide any one side of the triangle A B C into some nomber of euen parts , admiste the side B C into ten equall parts , then deuide the match side of the other triangle into the like number of parts , viz. D E into ten equall parts also , then measure with your compasse how many of those parts of B C are contayned in the side A B of the triangle A B C , and you shall be sure to finde the like number of the parts of D E in the match side A E of the triangle A D E , and as many parts of B C as are in A C , so many parts of D E are in A D : therefore are they saide to be like and proportionall . This Familiar proofe I haue thought beste for my Familiar Staffe : for artificial proofe séeke Euclide , lib. 6. propo . 4. 5. 6. and 7. Euen so in the figure of the last Chapter at the second station K , the leg A B of your standerd Staffe doth cut the maine triangle T K P or rather T N A by the line M A parallell to the syde

T A , making within the iurisdiction of the Staffe , the triangle N M A equiangled , and like to N T A. Therefore being that N A is appointed so many euen partes as K P containeth euen perches , it followeth of necessity , that what euen parte you finde betwéene M A , there must also be so many euen perches in T A , which is the longitude or distance desired . Note that the letter A wanteth in this figure at the station K.

Note also that if in the former figure you drawe the line O P parallell to A C , and R S parallell to A B , they shall make a litle triangle in the bely of A B C , viz. K L M equiangled , and like to A B , yea and euery triangle that you can picke out in the same figure is equiangled , and like to A B C , and therefore each of them to other . Thus haue I opened you a great breach , which if you throughly entre and possesse , you may be able alwaies to atchieue these maistres without booke at all times of neede .

Chap. 17.

How to performe the fifteenth Chapter with more facillity by meanes of the second manner of taking the angle of position mentioned in the 14. chap.

LEt no man be amazed at this working for it is all one in Of longit●… or distan●… substance with the 15. Chapter , but oppositely performed , which in diuerse partes of the Mathematickes produceth the same troth as the direct way doth . For many times Oppositorum eadem est ratio , if I shall familiarly shewe you the difference it may be compared vnto a cupple of men going together towardes one place , the one with his face forwardes , the other backwardes , the matter is no more difficult , therefore marke it well . Let P and K be your two stations , & T the tower whose distance you séeke from

your first station P. You shall therefore at P with your standerd staffe after the second manner of the 14. chap. take the angle of Position betweene T and your second station K , or rather L directly ouer it , as in this figure you sée C A B , and locke fast your staffe at that angle of position , for it is the opposite angle of T A L , and equall vnto it by Eucl. lib. 1. propos . 15. as in the 14. chap. was shewed . Then repayre vnto your second station K , measuring the exact distaunce betwéene your stations with some wyer cheyne or moryce pykes , and according to that measure place the running sight of that leg of the staffe , which at P was directed to K , viz. at L. This sight L there fixed , you shal now place directly ouer your second station , by resting it on your dagger or some sticke stuck into the ground , and let your partner ( applying the centre of the staffe to his eye ) direct the same legge againe to the first station P by helpe of the sight pegges , as here you see . And then your selfe shall mooue too and fro the running sight of the other legge vntill you may place it so that by it you may see the tower T , euen with the sight before fixed at L , viz. at O , by the visuall line O L T. To conclude then , I say , that the euen part of the staffe cut by the sight O , shall shew you the exact distance of the tower T from your first station P. The certainty hereof may well be prooued by the last chap. for the angle L A O is all one with the angle N A M because the staff is fast lockt to that angle , and therefore equall to T A L being but the opposite angle of N A M the angle A L O being also opposite to T L A , is therefore equall vnto it by Euclyde lib. 1. propos . 15. and when two angles of any tryangle are equall vnto two angles of another tryangle , the thirde angles can not chuse but bee equall by Eucl. lib. 1. propos . 26. then séeing the tryangle L A O is equiangled to L A T therefore of necessitie they must be like , and their sides proportionall by Eucl. lib 6. Prop. 4. and A T bereath that proportion to A L as O A doth to A L of the tryangle O A L , as if within the tryangle A T L you did set the tryangle A L O you should easily conceaue . Or if you turne the figure vpside downe , then shall the working seems all one with that of the fiftenth Chapter , the Angle A M N being equall to A L O.

Chap. 18.

In case that a Castle or fort were digged out of some rocke , or scituate in some valley betweene two hilles , admitting but some narrow comming vnto it , and therefore enforcing your two stations to be one directly behind another . How yet by this familiar staffe you shall attaine the distance of the same from you .

FIrst come as neare the wall as you can without danger , Of longitu or distance so that it be not ouer neare , and take your running staffe set at his square angle , and both the winges placed on the hanging side . Apply the extreame of his leuel side to your eye , carrying him as leuell as you can , and there looke where aboute you may place the vpper wing to see the toppe of the wall , but yet at some euen number of fiues or tennes be sure because of after reckoning . The vpper wing so placed to remaine fixed , then let your partner and you together settle your staffe a litle further or neare ( his hanging side kept plumbe ) till you may from the extreame of the leuell side , see the highest part of the wall or tower euen with the said fixed wing . Marke that station on the ground . Then goe backe a good quantitie , and there chuse another station , doing in the very same manner with the other wing , placing him also fixed at some euen ten or fiue . Then measure exactly the distance betwéene those two stations : For looke so many times as the euen partes or distance betweene the two winges , are contained amongst the euen partes from the centre of the staffe to the vpper wing : so many times is the measurement betweene your two stations contained in the whole length betwéene your furthest station and the wall .

As for example , admitte that the distance betwéene the stations M and N were twentie pearches , and that at the inner station N you set the one wing , to wit L at two hundreth perches from D the centre of the staffe , and there fixed . And at M the outer station , you set the other wing , that is to say H at an hundreth and fiftie partes . Your stations M and N so chosen , that at N you see the toppe of the towre , to wit P , by the visuall line E L P , and at M , by the visuall line E H P. The number of euen partes ( by taking an hundreth and fiftie out of two hundreth ) I finde fiftie , betweene the winges L and H. Now I conclude because L H that is to say fiftie , is foure times contained in L D : two hundreth therefore foure times the distance of M N that is , foure times twentie perch is the true distance from M the outermost station vnto the towre , to wit , the length of M R.

Another way is thus , get the altitude of the towre top aboue the leuell of your eye , that is to say of P S by the ninth or tenth Chapter , which had , reckon the same on the hanging side of your running staffe , and thereto set the wing fixed , admit at H. Then choose you a station as farre from the towre as you thinke good , admit at N , there direct your staffe against the towre as before , kéeping the station N directly vnder your eye , and your eye no higher leuell then S , then moue the wing of the leuell side , that is I to and fro , till you may by both the sightes I and H , see the top of the towre that is to say P. Then looke how many euen partes are betweene T and D , for so many paces is the distance from your station at N to the towre .

Note that if there be no wall or towre high inough for the exact working of this Chapter farrinough off : you may make a shift to it , by two markes of the wall in latitude , that is to say in the length of the wall : for that the working by the altitude and latitude is al one , as in the end of the tenth Chapter was noted , so you can direct your staffe square thereto : but if you happen not to direct him square , you misse so much of your distance to the wall as maketh vp the square : as for example . If T P were a wall , and that aiming at the square , you should direct your staffe to the marke W thinking the square to be there , I say you shall in stead of the distance E W , get the distance E S , such is the certaintie of your crosse staffe working , which you can not auoid because of necessity , as in the second Chapter was said In transuersis visni oredere oportet .

Chap. 19.

How you shall peerforme the 15 , Chapter , where the distance of the fort or castle is verie far off , and the ground being vneuen with hils , dales and rockes , hath no one leuell plaine sufficient to make two stations for so great a distance .

IF some valley happen betwéene your first station , and that place where you woulde willingly , according to the Of longitu or distance third note of the 15 Chapter . Plant

your seconde station , as here you sée in this figure described , a déep bottome betwéen the stations P and K. In this case you shal by a third station made on the plaine , whereon the first station is , viz. at Q. and help of the first , get the distance of the farthest station K , beyond the sayd vallie , in such sorte , as in the 15. or 17. Chapter is taught , or as in the next Chap. shal be shewed . And so shall you haue the distance of your 2. long stations P and K , as exactly as though they were in one plaine to bée measured with a line . And by this meanes , though the valley be neuer so déepe betwéene your two maine stations P and K , it shall not hinder you , but that you may at them procéede to get the most exact distance to the forte or tower , in all respects as in the 15. or 17. Chap. was done , euen as though the ground had bene all one planne .

Chap. 20.

If in a night you haue secretlie gotten with your armie neere anie forte , and that you woulde with more speede then in the 15. or 17. Chapter is shewed , know the distance whether you are neere inough to plant your ordinance for batterie .

NOw commeth in the readie vse of the running staffe , for Of 〈◊〉 or 〈◊〉 which cause I so named him . And in this Chapter resteth the swéete vse of this instrument , therefore marke it well . This matter resteth wholie vppon the diligent furtherance of many helpers both of men , and horses also , if you will , according to the prouerbe , Fit cito per multas praeda petita manus . There is no more cunning in this , then was in the fiftéene Chapter : rather lesse . But that you must haue diuerse to execute it : that is to saie , a couple ( with horses if you will ) to speed them to the second station , there by helpe of the runninge staffe , to take the angle of position betwéene the first station , and some turret of the forte , whiles your selfe and your partner are as busie at the first station with your standarde staffe , taking the position angle between

the same turret and the second station , which wyll most speedely bee done by the seconde meanes of the 14. Chapter , and fie vpon restes or supporters nowe we are in hast . The whiles also let two other speedilie running with a wier chaine , get the exact measure betweene the two stations : or if the forte be far off , or the ground vnleuell , it will not be amisse to get the distance between those two stations by a thirde station , in manner of the last Chapter . Which distance either way most exactly gotten , let him that keepeth the first station reckon it on one of the legges of the same standard staffe , it is no matter , which ( for now we be in hast , wee must not be too curious in precepts ) and to the end of that reckoning , let him place the running bolt or sight , fixed with helpe of his screwe . And if by this time his partener bee not come from his second station , then let him take a nagge and gallop to meet him , taking speciall care that either of them locke their staues fast at the angles of position before taken , least they should start with this hastie carriage . Now then when they are met , if he that came from the second station , doe but clap the centre of the running staffe on the sight pin of the standard before fixed , guiding it so that his one side cut the centre of the standard , extending his other side crosse the standards other legge . Looke at that crossing what partes you finde , for the partes on the standard are the distance from your first station to the forte , and the partes of the running staffe , are the distance of the second station , to the same fort desired , which is so much more then the standard could doe of himselfe , besides the speed , yet for all your hast , the notes of the 15. Chapter must be regarded . And thus much farther , that you enlarge the leuell side of your running staffe with the ioynt peece of the hanging side taken off , if cause so require .

For example : admit C A B to be the angle of the position , taken by the standard at the first station , and D E A the angle of position , taken by the running staffe at the second station , and that on the one leg A B of the standard , the point H , reckoned from A , expresie the distance between the two stations mesured : there shall the

running bolte or sight pin be set , and thereon the centre E , of the running staffe A E D his one side , lying euen with the standards legge A B , and cutting his centre A , so doth the other E D cut off in the legge A C at D the distance of the tower from the first station . And in the point D of the side . E D of the running staffe cut off by the standards leg A C , sheweth the distance of the tower from the second station .

Chap. 21.

If you shall see two fortes of the enemies within viewe , and woulde know how farre they are in sonder , and whether ther may be passage for an army betweene them without danger of shatte from those fortes . Or to get the length and breadth of any Forte a far off , thereby to gather of what receite the same forte is . Or to get the width of a riuer fronting any fort , keeping your selfe a farre off without daunger of shotte .

FIrst you shall by the fiftéenth , seuentéenth , nineteenth , or Of lati last Chapter , get the seuerall distances of the same fortes from your station appoincted , seeke the one distance in the one legge , the other distaunce in the other legge of your standerd Staffe , and to each sett the running sighte pins fixed , then pitching againe at the same station , take with your standerd Staffe the angle of position between those fortes by the fourtéenth Chapter , and there wreste him faste to keepe that angle sure . Lastly place the centre of the running Staffe on one of the said fixed fight pinnes , applying also one of his sides vnto the other sighte pin , and the number of that side of the running Staffe , there touching that other sight pin is the distaunce betwene the two forts desired . Or you might apply the ioincte piece or any parte of the running Staffe betwéene the sight pinnes , but that it is not so easy to rekon as from the centre it is .

In like manner may you get the distaunce betweene two trées or two towers in one forte , and thereby get the length or bredth of the same forte , and be able by that meanes to descrie of what receit the same is . Also the bredth of any riuer by taking two markes , as trées , bushes , or buildings on each side of the riuer one . But you are by this neuer the neare , to know the distance betweene two shippes on the sea , as other writers and those no small ones , do teach you by a like precepte arithmeticall , except those shippes lie at ancor that they stirre not , yet in the twenty foure Chapter following , I shall satisfie you for that .

This is another maner of working for latitudes then that which the Crosse Staffe yieldeth : the manner whereof I noted vnto you in the end of the tenth Chapter .

Chap. 22.

If in a fort or hauen on the sea coast , or abroad on the plaines on the sea banckes , you shall see anie ships a farre off sayling towardes you , or any armie approching by lande . Howe you shall alwaies be prouided in such speciall places , that in a moment almost and with small helpe , you shall know how farre they are from you , and by that meanes speedily finde when they shall be commen within the random or pointe blancke of your shot .

IN such dangerous times when any assault of an army by Of lo or dist land or of ships by sea is expected against any fort or hauen , you shall appoinct in the same hauen or fort two certaine towers farthest distant , in stead of your two stations . Their exact distaunce you shall alwayes haue in a reddinesse gotten by the last chap. Let one of these towers be called the first station the other the second . In this first tower you shall haue alwayes your standerd readie placed by some kind of steadfast supporter , his one legge directly on the other tower or station , not to be easely wrested aside from that position , the other leg next the enemy at liberty . In the second tower let the running staffe be alwaies readily placed in like manner , his one side stedfastly on the first station , his other side next the enemie at liberty . Your instruments thus exactly placed , alwayes readie at your two stations , and the certaine distaunce betwéene them foreknowen , your worke is at any time almost performed ere you begin . Let your selfe at the first station , and some practizd body at the second , guide the loose legs of your instrumentes directly still vpon the mayne toppe of some principall shippe , or formost Auncient of the army , and let a third man within a little after he shall perceaue both your eyes layde to your instruments with a trumpet or horne , giue a short blast : and immediatly vppon the instant of the blast , let both of you locke fast your instruments at those angles , which angles had and taken both at one instant of the blast giuen . Let each of the obseruers come from their towers and bring their instrumentes to méete together as speedily as they can , and clapping one vppon another in such manner , as in the 20. chap. was done , you shall there immediatly desery how farre that shippe or army was off at the blast giuing .

But because it may be long ere two can come out of the toppes of towers to meete : besides that , because it is harde bringing such an instrument downe stayers , or letting it downe with a rope for feare of sagging or slipping of the angles taken . Therefore to remedie this , let him that obserueth in the first tower , haue a spare running staffe , besides the standerd staffe wherewith he obserueth : And let him that giueth the blast , bee placed néere about the middest betwéene these two station towers . And when the blast is giuen let him in the second tower that obserueth with the running staff , looke what degrée of the graduation on the leuell side of his staffe , the graduators Apex doth shew , and report it with a loude voyce to this middle man : And let him report it againe to the obseruer in the first tower or station , who hauing the sayde spare running staffe shall immediatly set it by the same degrée and minute reported vnto the very same angle that the running staffe at the second tower is at , and therewith worke in all respects as before euen as though the other running staff had beene brought to him .

But if any man will obiect , what if there bee not two towers in the hauen , then I say it is likely there is but one Church , and that it is a small matter in such daungerous times to make scaffoldes with boordes on housen toppes for such good purposes .

Also in the very like spéedie manner , you may worke with a cople of stations readie pitched on the sea bankes : withall you must euer haue regarde to the notes of the 15. chap.

Chap. 23.

If an army on the land , or a Nauie on the sea , shall be as farre off as you may ken making towards your Fort. To know by helpe of this Familiar staffe : How fast their gate is , and in what time they shall according to that gate , come within reach of your shot .

THis matter very little differeth from the last chap. For your two staues being readie planted in their towers or Of m●… in long●… stations as there is shewed . First take the distance of the army or Nauy , as farre as you can possibly ken them , at a blast or sound giuen by the middleman , whose charge shall further be for this purpose to tourne vp a mynute glasse or two , so soone as he hath giuen his blast , and to kéepe them running . Then after a quarter of an howre or 15. mynutes or more or lesse time as you will , and as the occasion requireth , prepare your selues to take the distance of that nauy or army at another short blast giuen in the very same maner as before . Now hauing gotten the distance of the shippe or army this seconde time : & also vpon report of the middle man how many mynutes were passed betweene his two blastes giuen , you may easely know by the difference of the two distances taken , how much they be come nearer at this second blast then they were at the first , for so much do they saile or come on in so many mynutes , and according to that rate you may easily cast how much they sayle in an howre , and consequently howe many howres or mynutes it will be , if holding on their way they approch you , and in how many mynutes they will be within the randome or poinct blancke of any great piece , and rather then to be deceaued least the winde or state of the seas should alter , you may make more tryalls ere they come neere that .

But in stead of mynute glasses , which as they saye , they vse at the sea , I should like better of a clocke or watch that should turne the hand quite round about the dyall euery houre to shew the exact mynute I haue séene such readie made .

Chap. 24.

If standing on the sea bancks , you see your ship of war at the sea pursuing another ship of the enimy , to know how far by help of this Familliar Staffe , & how much the one getteth of the other in sayling , whether he be like to ouertake the enimy , and in what time .

THis matter differeth litle from the working of the last Of motion both in longitude and latitude . Chapter , onely it asketh more helpe . For you had néed to haue at the first towre or station thrée standerd staues , and foure obseruors , and at the second tower or station two running staues , and two obseruors all ready pitched and placed , as in the two & twenty Chapter was taught , in such sort , that one paire , that is to say , one standerd Staffe , and one running Staffe doe wholy attend vpon your ship , the other payr vppon the enemies shippe , and the odde standard Staffe to attend them both , by helpe of two obseruors , to kéepe alwayes the angle of position betweene the two shippes , and al of them to locke fast their angles at the instante of a blast giuen , and then by the two and twenty Chapter to get the distaunce of ether shippe from you , and by the one and twenty , and helpe of the angle of position , the distaunce of either ship from other at the time of the blaste . Then after a quarter of an howre or certaine minutes compleate , they must al to worke agayn by warning of a second blaste , as well for the distances of eche shippe from you , as of one of them from the other . Then comparing the differences of ech kinde together , you haue by the one ( that is to say ) by their seuerall distances from your station in that number of minutes , as were betwéene the two blastes geuen , the certainty of each of their gates , in so much time by the last Chapter , and by the two seuerall distances of ech shippe from other at both times , you may by taking the bigger out of the lesser , know how much the one shippe hath ether gotten or loste of the other , and according to that rate of time , cast how soone the one shall ouertake the other , if the wind and state of the seas alter not , or they alter not theyr course . For which cause you shall make some more trialles in the very like manner as oft as you shall thinke good .

Chap. 25.

Your selfe planted on the toppe of an high rocke , clift , or tower , by the sea side . To knowe by this Familliar Staffe howe deepe the leuell of the water is vnder you .

IT is most common vppon the sea coaste to haue highe rocky Of pro●…dity . cliftes . If therefore you woulde from the top of anye such knowe how déepe directly vnder you , that the leuell of the water is , you shall espy some marke in the bottome of the sea bancks or next clifte , euen with the edge of the water the nearest vnto you that you can espy . But if there be none neare inough , then let some ship be lette purposely at ancor nere vnto you , the distaunce of which ship , you shal get by two pretty stationes , such as the toppe of the rocke may yielde by the fiftéenth or seuenteenth Chapter . Or if the rocke or clifte bee so stiepe and sharpe , that it yield you not station inough on the toppe , see then if you can discene to some lower part of the rocke for a second station , or any way by any rule in this booke , helpe your selfe to the distaunce of the shippe from your station on the hill toppe . Which had , take your standerd staffe , and let him at a true square angle by helpe of your running Staffe : there locke or wreste him faste that he start not from his square , Then place him so , that his one legge bee leuell or parallell to the horrizon , the other perpendiculer sette by a plumme line , his centre ouer your station . Your standerd so placed , then your partner and you directing the leuell legge towards the shippe or marke : you shall between you moue the running sighte pinnes of both legges to and fro in such sort , till by them you see the saide marke or shippe where she lieth at ancor , there wreste the sight pinnes fast . Then sette the centre of the running Staffe on the sight pin of the leuell legge , directing his one side to the middle or centre of the other sight pin , his other side euen with the centre of the standerd . There locke the running Staffe fast at that angle , and marke what number of the running Staffe is there cut off by the centre of the sighte pin . For if that be equall to the distaunce of the shippe or marke before gotten , then doth that sighte pinne shew your desire , if otherwise then moue the running Staffe fast lockt at the said angle to and fro , the centre of the standerde by helpe of the sighte pinne whercan hee rideth , vntill there be cutte off in the saide side of the runninge Staffe , the exacte distaunce of the said shippe or marke before found . And then shal the pointe of cutting shewe you on the standerd the very height of your eie aboue the leuell of the water desired .

This Chapter seemeth more painefull at the first shewe , then it wil be when it is rightly vnderstoode , and that you haue made experience thereof by an example or two the best is , it is needefull to bee doen but once for al , in anye one place .

Chap. 26.

If a Gunner keepe a block house , or haue a piece or two of Ordinance planted on the toppe of some very high clifte by the sea side . How by this Familliar Staffe he him selfe without any helpe at all , shall most easily and speedily in a moment get the distaunce of any ship at the sea , making towards him or passing along , and that most exacte , for so far as the randome of any great piece will extend .

TRuely this Chapter on such cliftes and places on the sea Of longitude or distance from an high . coste , which are very high aboue the water ( as many such there are ) is the most necessarie and ready for a gunne of all the rest . But if it be not high aboue the sea , it is least worth : And the higher , so much it is the better for this purpose , and also for the Gunner , as it should seeme vnto me by Tartaglia who saith in his first booke , second Colloquy , that a peece either mounted or embased from the leuel of the Horizon shooteth with more force and further , then it wil , being shot leuell . The chiefe substance of our practise in this , consisteth in the exact finding of the leuell of the water vnder your station on the clifte toppe : For which cause I promised the last Chapter . Whereas others haue left it very absurdly to be done with a line and plummet of lead let down from the clift toppe : as though euery clift or any clift almost would admit such palpable facillitie .

Well , to the purpose . In such a set place you shall haue alwaies your station ready prepared , with the depth of the leuell of the water knowne by helpe of the last Chapter : and there your standard setled at his square angle , and alwaies ready pitched in maner of the last Chapter , on some such rest that he may speedely be turned which way soeuer any shippe commeth , keeping him selfe still plumbe and leuell , the sight pinne of the perpendiculer side , fixed fast with his scrue at the euen part , answering the hight of your station aboue the water , your standard staffe thus alwaies set in a readinesse , your worke is done in manner ere you beginne . For so soone as you espye any shippe making neare to your coste , direct the extreame of the leuell legge of the standard to the shippe , and clap on the centre of your running staffe , to ride on the fired sight pinne of the hanging legge , and there lifting vp or downe the one side of the running staffe close by the said leuell legge directed to the shippe , vntill by the sight pegges of that side of the running staffe you see the shippe . Then shall the euen part of that side of the running staffe , cut by the leuell legge of the standerd , be the distaunce of the shippe desired , al which by this figure you may perceaue .

A the station on the clifte N VI , the standerd Staffe alwaies ready placed thereon his leuel legge V N directed to the shippe G approching , I the sight of the standerds hanging leg , whereon the centre of the running Staffe is placed , whose one side I N , directed close by the standerds legge V N to the bottome of the shippe , G is cutte off by V N at N. Thereby I conclude that the euen parts betweene I and N sheweth the distaunce from your eie to the ship viz. I G desired .

Note that the other side of the running Staffe is to no vse in this practise . And one thing more I thought good to warne you off , that in placing of your sight pin I , you haue a care of the rising or falling of the leuell of the water by reason of the tides . For which cause , you had neede to haue some speciall markes purposely sette in the bottome of the next clifte or sea bancks , by which you may at any time gather how much the water is risen , or fallen , and according to that rising or falling you must fixe the sighte put I higher or lower when you begin your worke .

Note that this Chapter and the last also , mighte as well haue bene performed in manner of the twelfth Chapter , by turning the extreame of the hanging side of the staffe downewards if the place doe admitte , and happily that course maye séeme the more familiar , and propper way for profundities although both come to one passe .

Chap. 27.

If a man were prisoner with the enemie , how being in the top of a tower on the leads , or out of his prison window , hee might by this Familliar Staffe know the depth to the ground , to see if he were able with anie deuice to let himselfe downe without danger .

FOr this purpose , yea , or almost anie precept of altitudes , an instrument of ten inches long , is as good as one of ten foot , Of profundity . and such a one a man might priuily haue conueyed vnto him , and easily wilde it in a chamber . You shall out at a windowe by the eightéenth Chapter , or from the toppe of the leads , by the fiftéenth or seuentéeth chapter , get the direct distance from you of some tower next yours , which suppose were XC , whose base C you may sée out at your windowe , viz. IX , then place your instrument plum and leuell towardes that tower XC , in such sort as was done in the last Chapter . But contrariwise to the last Chapter , place that distance IX , gotten on the leuell side at O fixed . Then putting vp or downe the sight pin of the hanging side , viz. I , till by it and the sight pin

O , you may sée the base of that tower , viz. C , by the vsuall line IOC. There I saie , shall the sight pin I shew you the deapth of the tower XC , viz. from x the leuell of your eis , vnto C the base , and so high from the ground you may presume that your selse are in that roome where you are prisoner . Let your selfe downe and you can , sauing your necke peece .

Happily this Chapter were more easily performed by turning the hanging side of the Staffe downwards , according to the note in the end of the last Chapter , because the instrument is small , and may easily rest in the one end .

Chap. 28.

If afort or tower stand vpon an high hil how by this Familiar staffe , to know the ioynt and heights both of the hill and tower .

TO helpe vs for want of a figure , you shall admit that Y Of 〈◊〉 and 〈◊〉 of 〈◊〉 were the top of the hill , and base of the tower , and PY the the tower standing thereon . Which granted . The first thing you shall doe , get the distante from your standing , viz. N , vnto the point S leuell with your eie , directly vnder the base of the

tower , by the eightéenth Chapter . But if the hil and tower be farre off , then if by the fiftéenth or seuentéenth Chapter you get the distance IY , and by discretion take somwhat lesse then that for the distance IS , a little error in that longitude wil not hurt vs for the altitude . This distance IS anie waie gotten , you shall reckon the same on the leuell side of your running Staffe ED directed to the hill , and there set the one wing , viz. I , and from it direct your vsuall line to the towers base , viz. to Y , and set the other wing on the hanging side directly betwéen I and Y at V. I saie the number at V shewed by that wing , is the height of the hill desired , viz. of YS , and if from I you direct your vsuall line againe to the top of the tower on the hill , viz. to P. Then shal the wing on the hanging side cut at H , where agayne you shal haue the whole height both of tower and hill viz. of PS , and the distance betwéene H and V sheweth the height of the tower PY seuerall .

Chap. 29.

If being at the sea , you would cast ancor as neere some fort or harbour , as you might be free from reach of their shot , how by this Familiar Staffe you shall exactlie get the distance thereof , of the distance of anie other ship from your ship , being both fleeting at once vppon the wilde sea .

THis is the most curious matter which we had to deale withall , and as sleightly dealt in by other writers , whose whole deuice hetherto , hath béene to looke from the top of the ship wherein they are , vnto the bottome of the other ship , performing it after the same reason that in my 26. Chapter is shewed . For they appoint the knowen length of the mast of their ship , in stead of the knowen height of the clift in that 26 Chapter . And to make the matter seeme of more account , they call this a distance gotten at one station . A goodly thing : as who saith that the square angle , which they imagine at the bottome of the maste , and the length of the mast knowen , is not in all respects a second station , as it were readie , made to theyr hand . Let me alwaies haue a reentangled triangle to deale with , and I will neuer aske you but one such station , for all that I haue before written . But now looke yet neerer vnto the matter , and though the ground of this their working is vnfallible , yet see to how small purpose , and in manner absurd , theyr precept is in this . For if ( as in the fourth note of the foureteenth Chapter I shewed ) the second ship bee distant aboue ten or twelue masts length , their working is of small account , euen on plaine ground : but then consider the tottering of the ship on the water , they shall be forced for want of steddy taking of the angle euen totalliter errare . For which causes I cannot content my selfe to deliuer this matter so sleightlie , as that I thinke it to anie purpose to be done in anie ship , but rather by helpe of two shippes , or in a calme one ship and help of the cockbote . Let both those ships bee grapled or linked together with a strong rope or cable , and let sailers and sternes men , keep the ship with side winds , and labouring the ruthers or stearnes at the full length of the rope , facing the fort , harborow , or other ship , whose distance you seeke , and at the two ends of those two ships farthest distant , let the standard staffe

Heere should stand the picture that is in the 27. Chapter .

in the one , and the running staffe , in the other , bee placed with two obseruors to each staffe , to take the angle of position , after the second manner of the foureteenth Chapter , betweene the sayde forte and his fellow obseruors , in the other ship sodenly at a blast giuen , as was done in the 22. Chapter , there locking fast their instruments , and hasting by haling in the ships to bring them together , they shall descrie the distance to the forte desired , in such sort as in the 20. or 22. Chapter was done , or without haling the shippes together by reporting the angle taken one to another , and help of a spare running staffe , as in the end of the said 22. Chapter is shewed . For the length of the cable and both ships knowen , yeldeth the distance betweene your two stations .

And for the more spéedy and sure taking of those angles , let each paire of obseruors hang a verie white cloth vnder the centre of their instruments . In this figure H and G are the two ships linked together with a cable rope , and F is a ship at sea , whose distance they séeke .

Note that if a man be so straight driuen , that he hath no helpe but one bare ship , then let him doe it in the verie lyke manner , placing his obseruors at both endes of the ship , as far of as may be , which shall performe his desire : much more certayne then from the top of the mast . And if anie man woulde doe it from the mast , then let him take the angle downe to the bottome of the ship with a sea Astrolabe , and after set his running staffe to the same angle , & his standard staffe to a square angle , and then performe it in manner of the siue and twenteth Chapter .

Chap. 30.

How by this familiar staffe to carry the leuel of one place to any other , necessarie for such as shal vndermine afort , to know alwaies how deepe they are : or for such as would trie whether waters may bee brought from one place to fortisie another .

THis matter is verie easie , requiring more diligence then skill . For if you set the leuell side of your staffe leuel with the Horizon , by helpe of a plumme line , and hauing a couple of assistants to carie two poles before you , with bright marks sliding vp and downe on them . Then all the matter consisteth in the diligent noting of the rising or falling of the ground , by helpe of those moueable marks carrior from place to place on those poles , vntill you come to your waies end : and then shal you compare them together , whether is the greater of all the risings or all the fallings , each added seuerally together into a grosse summe : For if they be equall , then the leuell at the end is equall to the leuell at the beginning : if vnequall , them difference sheweth the difference of the rising or sinking accordingly .

And if you should carrie the leuelmany miles , to the intent to lead water in a conduite , then for the fall thereof , you must haue also a regarde of the roundnesse of the massie globe of the earth and water . Of which I shall at some other time more at large signifie .

Chap. 31.

How by helpe of this familliar Staffe , you shall carrie a mine vnder the ground , and sett barrells of gunpowder directlye vnder any towre or thiefe place of any castle or forte .

THis is no rare matter neither harde to performe . First gette the exacte distaunce to the same towre from the place where you meane to begin your mine , by the fiftéenth , seuentéenth , or twenty Chapter . Then sincke your selfe into the ground at the mouth of the mine , as much vnder as you think méete , and there by two plumlines from aboue pitched directly vppon the middle of the towre , sette the leuell side of your running Staffe vnder ground directly vppon the towre , by which direction you shall cary your mine streight till you come almost there . And if you be hindred that you can not digge streight in any place , by meanes of some rocke make a square , retourne by direction of your Staffe , till you are past the same rocke , and you must of necessity when you come almost there , make two or three square retournes out of the way , and still bring your selfe to your direct way againe , to the end to stay the force of the powder for issuing directly backe out of the ouen or caue closed vp , thereby hindring his exploite . So kéeping your note booke certainly of your goings aside out of the direct way , you may by the like square angles retourne againe iust as much vnto the same , and then procéed direct againe . And also keeping notes how you goe either shallow or deep , in manner of the last Chapter , you shal at the last both knowe when you are gone so far as the distance first taken aboue ground amounted to : and also how deepe or shallow you are from the bottome of the towre to be blowen vp .

Chap. 32.

How a Captaine may by this familiar staffe , sett in platte or mappe any prouince of the enemies countrey .

THis matter is all ready handled of many writers to be don by the circle , quadrante , or crosse Staffe , but specially by the circle , and is in our Englishe tongue published by diuerse namely , Master Digges , William Boorne , Master L●●●r , and others , vnto whom I therefore refer you for the circumstaunce , because they shall not bee idle the whiles . Onely thus much I thoughte good to note vnto you , that look what angles of position they take by theyr cyrcle , the same may you and your partner more speedily take by the second manner of the foreteenth Chapter , and your running Staffe , and note the degrées of euery angle or position in a booke or tables as they doe . And when you haue those angles noted , and would reduce them into mappe , if you can not otherwise more readily doe it , then take paines in such manner as they teach , by helpe of that small cyrcle , which they call , and fitly a protuactor , in the mean while till I may haue a wished time to write of this my Instrument more at large . Then will I teache you to lay a side your detractor , and shewe you more knacks then I dare at this time to name or make promise of for my owne quiet sake , leaste I should be by some importimacyes interrupted from the seconde part of my Iewell , which I woulde moste gladly bring forth with as conuenient spéede as may bee .