vnderstand Onely thus much I aduertise the vnlearned that they must acquaint themselues with some fewe Mathematicall principles as to knowe what the Eleuation of the Pole meaneth how a squire line is to be drawne and such like which if they want a teacher they may sufficiently learne by themselues out of Records Castle his pathway and ground of Arts published in the English tongue for these tearmes could not be auoyded neither plainly described without much tediousnes We haue here added also examples and figures to euery kind that so the precepts might appeare more plaine and easie so that there is no plaine plat or wall howsoeuer it standeth or be placed either Declining Reclining or Inclining but by the helpe of this booke you may drawe a Diall vpon it If any man complaine of obscuritie he must knowe that Difficilia quae pulchra and yet small paines ouercommeth all The making of the Horologicall Cylindre and the Ring with some other Instruments we haue presently omitted partly for their curiositie in cutting and delineation and partly because if occasion serue we will entreate of these kindes of Horologicall Instruments by themselues together with the making of all kindes of plaine Dials in this booke prescribed by the way of Geometricall proportion In the meane while gentle Reader committing this booke to thy fauourable acceptation and thy selfe to the protection of the Almightie I end Tho. Fale To my louing kinsman Thomas Osborne THis booke which seuen yeares since was in a manner perfected as you knowe doth now vpon iust occasion present it selfe to the view of the world wherein you haue taken such paines for the triall of each example that I thinke none can finde any great fault but such as can see farre into other mens faults and forget their owne For after we found some precepts in Witekindus to be false we were enforced to trie and examine with great care each figure and example in the Sunne And therefore if any receiue benefite by this our trauell I would you should haue your due praise you deserue I haue altered some fewe things and added the making of the South and North Erect Declining Dials by the way of Geometricall proportion because those kinds be most in vse and I would the learner should haue his choise of the easiest way The grauer of the Figures was one M. Iod. Hondius who hath shewed himselfe an excellent workman in the great Globes set forth by M. Mullineux and the Mappes of England for M. Camdens booke and whether he hath performed like diligence in these I referre it to your selfe to iudge If any be desirous to haue the Instrument mentioned in the beginning of this booke for the triall of plats I hope you will helpe them to it for being of your owne inuention I know none so fit as your selfe to make it on which Instrument also it were conuenient to draw the Quadrant Horologicall that so it might serue for diuers vses I trust you will not be offended in that I leaue vnder our names this small monument vnto the world as a speaking witnesse of our thankefull hearts to this our Countrey and a testimonie of our affection towards the Arts Mathematicall Thus beseeching the Lord who hath endued you with extraordinarie knowledge in all Manuel Sciences to finish that good worke of his heauenly grace alreadie begun in you to his glorie and your owne comfort I take my leaue Commend me many times to your selfe all our good friends From London Ianuary 3. 1593. Yours assuredly T. F. Aduertisements to the Reader NOte alwaies that in euery Diall the one end of the Stile must be placed directly towards the North Pole and the other end towards the South Pole for about these two starres the whole heauens are moued they remayning immoueable The North Pole is a starre in the North part of the heauen being raised aboue the earth or our Horizon 52. degrees And this changeth his height if you goe Northward or Southward one degree in 60 miles but Estward or westward it altereth not The Eleuation of the Pole is the height of this starre aboue the earth Obserue also that the Substile is the line or place ouer which the Stile or Gnomon in your Diall directly hangeth The space betweene the Stile and Substile is the iust height thereof One line cutteth another squire-wise when they make right and equall angles The Contingent or touch line is that which is drawne by any poynt of another line or circle so that it toucheth the same and this line commonly in all Dials is drawne squire-wise to the Substile A quadrant is the fourth part of a circle The Meridian and twelue a clocke line are all one I call these lines parallele which are euery where of like distance one from another example whereof you may see in the Est and West Diall where all the houre lines be parallele You may make all kinds of plaine Dials vpon one stone if you prepare it first to be square like a Dye and then take off the eight corners and all the sharpe sides so shall you haue 25. plaine plats besides the base or foote whereon your Diall must stand If any be desirous to haue this Instrument readie made let him enquire at the Printers and he shall heare of them The making of an Instrument to finde out the situation of any plat or Diall and to place them already prepared CAP. I. FOr asmuch as it is necessary before you can drawe my Dial to know how your plat is already or ought afterward to be placed it shalbe expedient to shew the making and vse of an Instrument whereby you may examine and try all plain plats and place all dials being ready made and prepared Prouide therefore an halfe circle of Peare-trée Walnut-trée Bor or any other close grained and solide wood being well seasoned so that the alteration of the weather at any time may not make it change from the first proportion ther of Let it be perfectly tryed on both sides of an euen thickenesse halfe or thrée quarters of an inch thick or more if you will and sir or eight inches broad as you thinke good The edge or side A. B. must be very right Thē draw the Line C. D. thrée quarters of an inch equally distant from the side A. B. place one foot of your compasses in the centre E. which is the midst of the line C. D. and with the other draw halfe a circle from C. to A. deuide it into two equall partes or quadrants and laying your ruler vpon the centre E. and vpon this diuision drawe the line E. F. this done deuide eche of these quadrants into 90. equall degrées or partes which you may thus doe First deuide eche of them into thrée equall partes and euery of these into thrée other partes so shall you haue 9. diuisions in either quadrant whereof euery one shal represent ten degrées Againe part euery one of these into two and ech
of those into fiue if you can and so is eche quadrant diuided into 90. degrées Moreouer it were necessary if your Instrument were large inough to parte ech degrée into 60. minutes or at the least into 3. whereof ech parte may conteine 20. minutes This done fasten a thread wel wared in the centre E. with a plommet of leade on the end so that it may moue at frée libertie You may also if you will vpon this side of the quadrant between E. D. draw the diall whose delineation is taught in the 28. Chapter It were necessary to have here a little hole with a couer to put in your plâ—â—â—…et thread The â—omer â—â—â— of â—â—â—â— Instrument thus finished let the other be altogether liâ—e vnto it except that in stead of the the thread with the plâ—â—â—â—…t you must haue a plombrule made in this maner Prepare a péece of very good wood try it perfectly on both sides to an equal thicknes let it be about half an inch thick and twise so broad as the space betwéene the line C. D. of your instrument and the edge A. B. in the midst therof draw the right line G. H. and placing one foote of your compasses in the point G. with the other make a halfe circle according to the breadth of the ruler whereby you may cut the end round make the other end with a sharp point right in the end of the line G. H. as you sée in this figure Let the distance betwéen the point G. and the end H. be so much as is the semidiameter of the quadrant make by G. an hole so great that a ploÌ„met of lead hanging by a thread from the sharpe end may moue therein at libertie Make also an other round or square hole wherein you may place a néedle touched with the Loadstone as in the compasses or dyals you sée Finally make a little hole in the point or centre G. and with a broad headed naâ—e of brasse fasten it vpon the centre E. of your Instrument so as it may moue turne which way you wil and then your Instrument is finished Note that you may make your Instrument in forme of a quadrangle rightangled as Witekindê° teacheth cutting a round furrow without the circle and degrées made for the ploÌ„met to hang at libertie in so shall you néede but one side of your instrument to vse with a compasse or needle touched with the Loadstone for declinations But the form of the other whose making we haue taught seemeth more commnodious beholde the Figure The vse of this instruement CAP. 2. The vse of this instrument is in examining and placing the plat or dial In immoueble plats to know how they stand as if you would make a Diall vpon a wall first you must vnderstand whether the wall be erect or els recline or incline then whether it be direct East West North or South or els decline which you cannot know without the helpe of this Instrument Againe in moueable plats for the placing of them as if you haue made a South diall or any other kinde by this Instrument you shall easily and perfectly place them The triall of a plat for a Horizontall Diall IF your plat séeme to lye plaine making no angle with the horizon set the side or diameter A. B. of your Instrument vpon it and erect the plombrule right vp betwéene the two quadrants precisely ouer the lyne E. F. then if the thread with the plommet hanging at liberty fall directly vpon his line G. H. which way soeuer you turne your Instrument such a plat is saide to make no angle with the horizon and therefore the diall which is made vpon it is called a Horizontall diall In like maner may you place this kinde of dial being ready made parallele to the horizon and by the help of the néedle direct the stile towards the North pole The trying of plats for Erect Direct South North East and West Dials WHen the plat standeth vpright it maketh a right angle with the Horizon and is called Erect whereof some beholde one priucipall part of the world directly as the South North East or West other decline as the South and North toward the East or West of which kindes hereafter To examine an Erect plat apply the side or diameter A. B. of your Instrument vnto it the thread with the plommet on the foreside hanging at liberty If the thread fal vppon the line E. C. or E. D. the plat is Erect This done apply the said line or diameter A. B. to y â— plat your Instrument being placed equally distant to the Horizon and the plombrule vpon the line E. I. then if the néedle stand directly ouer his caracter the end touched with the Loadstone being next to the plat that plat is called a South Erect Direct In the North all the foresaid things are to be considered except onely that the end of the néedle touched with y â— loadstone is farthest from the plat These things knowen you may easily finde out the East and West Erect Direct if either you haue a line drawen squire wise to the caracter of the néedle or els if you place the plombrule ouer the line E. C. or E. D. And here note that the East and West are not saide to decline because the declination is accounted from the south and North to the direct East and West pointes The examining of plats for Declining Dials ALl such plats as beholde not some principall part of the world directly are called Declining The quantity of their declination is found out thus Apply the diameter A. B. of your Instrument to the plat remembring to hold it equally distant from the Horizon Then moue the plombrule vntill the néedle standeth right ouer the caracter and the point of the ruler which toucheth the degrées in the limb shall shew how many degrées and minutes it doth decline either toward the East if y â— plumb-rule lye in the quadrant C. E. F. or toward the west if in the quadrant D. E. F. The trying of such plats as recline IF the plat standeth not vpright but maketh an obtuse or blunt angle with the Horizon it is saide to recline The degrées of reclination are found out thus Apply the diameter A. B. of your Instrument to the plat the one end placed vpward the other downward theÌ„ moue the plomrule the thread with the ploÌ„met hauing frée course vntill the thread hang precisely ouer the line G. H. then the point of the ruler shall shew the degrées of reclination How Inclining plats are tried BUt if the angle which the plat maketh with the Horizon be acute or sharpe then it doth incline The quantity of inclination is thus knowen Apply the diameter A. B. of your instrument to the plat the thread with the ploÌ„met of the former side hanging at liberty and mark what degrée and minute the thrad shal cut for so much is the inclination The manner of trying those plats which recline and decline
vpon each diuision of the Equator and where it shall touch the Contingent line make markes This done draw the lines for the houres by those markes from the centre E. but those very fewe that is two nigh vnto A. and two by B. but prolong and extend them beyond the centre E. so that their contraries may bée made for in this kinde of Dials there bée but onely ten houres profitable that is 4 5 6 7 8 before noone and 4 5 6 7 8 after noone which shew but only in Sommer from the entring of the Sunne into ♈ vntill such tâ—ne as it entreth ♎ The Stile must bée fixed in the centre E. placed vpward directly ouer the lint E. C. with so great an angle as I. E. C. is Let the line C. D. bée placed vpward perpendicularly but so that it may not bée almost séene as afterward seruing to no vse because it is onely a line preparatiue Beholde the Figure A North Diall erect direct The making of the East and West Erect Dials CHAP. 6. IF you know the making of one of these you may easily make them both for they be very like differing onely in the naming of the houres for the one containeth houres for the forenoone and the other for the afternoone You must therefore on your plat make the quadrant of a circle A. B. C. which may afterward easilie bée put out as all the other lines must bée except the houre lines let the side A. B. be Perpendiculare B. C. Parallele to the horizon and let the arke beholde the South which being diuided into 90. degrées nomber therin the elenation of the Pole dounward from A. toward C. by the end of this number and by the Centre B draw a line so long as your plat will giue you leaue whose South ende shall behold precisely the Equinoctiall circle At which end draw a circle whose diameter shall bee almost the third part of the line Then draw another diameter or line in the centre squire wise to the other which shall shew the axtrée of the world and be the line for the 6. hour After ward at the cutward sides of the circle draw two contingent lines one beneath the other aboue so that they may be Parallele to the middle line Deuide each quarter of the circle into sixe equal partes Then place the ruler vpon the centre and eache of those markes or partes and where it toucheth the lines of contingence there make markes in them Afterward draw a line by those two markes which be next to the 6. houre in the lines of contingence which may be equallie distant from the line of the 6. houre In like maner doe with the rest so that you may haue in the East Diall two aboue the 6. houre the 4. and 5. in the morning and vnder it 7 8 9 10 11. In the West Diall like wise 7. and 8. in the euening aboue the 6. houre and vnder it 6 5 4 3 2 1. Neither of them doe shew the 12. houre because at that time the Sunne beames be Parallele to the plat Fixe the Stile in the centre of the circle right vp from the Plat so long as the Semidiameter of the circle is only shewing the houre with the very top or end thereof Yet it were more conuenient to haue it placed along ouer the line of the 6. houre being a plate of yron or some other metall being so broad as the Semidiamer of the circle is Behold the figures folowing The East diall Erect The West Diall erect Note that these fiue kinds of Dials before taught may be made vpon a stone cut square in forme of a die The making of a South Erect declining Diall which may be placed on any vpright wall whatsoeuer CAP. 7. IN all Declining Dials because the Stile doth not hang directly ouer the meridianline therefore you must first finde out and place the Substile which is the line ouer which the Stile directly hangeth and lik wise the line of the Stile which may bée both eastly and spéedily performed in this maner First by your instrument séeke out the Declination of the wall or plat whereupon you would make a diall which for example suppose I had found to be 50. degrées â— Therefore drawe the Horizontall line A. B. let the Meridian C. D. cut it squire wise in the point E. which may be in any place of the line A. B. and let the line F. G. cut the meridian squire-wise in the point C. which you may like wise take in what parte of the Meridian you thinke most conuenient Upon the center E. describe the quadrant of a circle from C. to A. if the declinatioÌ„ of your plat be West-ward or from C. toward B. if East-ward as in this example it is diuide it into 90. degrées and number in it from C. toward B. the Eleuation of the Equator 38. degrées and laying your ruler vpon the center E. and vpon the end of this number draw the line E. H. Againe account in the quadrant from C. toward B. the declination of the plat being 50. degrées and draw the line of Declination E. I. from E. to the end of this number Then take your compasses set one foote in the point C. extend the other vnto H. which is the intersection point of the line E. H. with the line C. G. and that same widnesse remayning place one foote in the centre E. and with the other marke the point 1. in the line E I. and from the point I. draw the line I. K. squire-wise to the Meridian E. C. placing K. at the intersection it maketh with E. C. Moreouer take with your compasses the iust length of the line I. K. and placing one foote in C. turne the other toward F. and make the point L. in the line C. F. drawe the Substile from E. by L. Let the line of Contingence bée drawne squire-wise to the Substile in the point L. This done take the distance betwéene the centre E. and the point K. and place it in this line of Contingence from the point L. vnto M. and make the point M. that the line E. M. may be made from E. vnto M. for the stile Measure with your compasses the least distance betwéene the point L. and the Stile and with the same widenes one foote remaining in L. turne the other toward E. and make the centre O. in the Substile vpon which describe the Equinoctiall circle Then placing your ruler vpon O. being the centre of the Equinoctiall circle and N. which is the point of intersection of the Meridian and Contingent marking where it cutteth the circumference for there you must begin to diuide it into 24. equall partes not withstanding those 12. are onely in vse which are next the contingent Finally place your ruler vpon the centre O. and vpon the seuerall diuision points of the Equator and where it toucheth the line of Contingence make markes by which from the center E. draw the
houre lines Place the Meridian perpendicularly vpon the wall the centre E. vpward the Stile pointing downeward Let the Stile hang directly ouer the Substile making an angle equall to E. M. L. The making of a North Erect Declining Diall CAP. 8. THe North Erect declining Dial differeth from the South onely herein that the centre is to be placed downeward the Stile pointing vpward to the North Pole and that the Meridian representeth the 12. houre at midnight and not at noone Therefore if the declination bée toward the East you must account the houre lines from that which is as it were the Meridian forthward 1 2 3 4 5 6 c. But if it decline toward the West number them backeward 11 10 9 8 c. omitting the first 3. which are before Sunne rising and after Sunne setting in our eleuation Let the line E. D. bée placed perpendicularly vpon the plat and the Stile point vpward to the North Pole Compare this figure with the former Another way to make the South Erect Declining Diall CAP. 9. ALbeit we haue plainely and perfectly shewed the making of the South and North erect Declining Dials in the two former Chapters yet to satisfie them that delight in variety here is also declared another way whereby you may make them namely by the helpe of Arithmetick and the Table of Sines which is placed in the end of this booke for this intent Therefore the Eleuation of the Pole being knowen and the Declination of your plat by your Instrument found out Multiply the Sine of the complement of the Eleuation by the Sine of the complement of the Declination diuide the product by the whole Sine which is 100000 and you shall haue a quotient Sine whose arke is the distance of the Stile from the Substile which distance kéep Then take the complement of this distance and the Elenation of the Pole and multiply the Sine of the lesser by the whole Sine parting the product by the Sine of the greater the quotient Sine which shall come of this diuision shall giue you an Arke whose complement is the distance of the line of the Substile from the Meridian which distance you shall likewise kéepe For better instruction herein consider the example Example of a South Diall declining 45. d. Eleuation of the Pole 52. d. FIrst I enter the Table of Sines for the Sine of the complement of the Eleuation which is 38. d. and I finde it to be 61566. Then I looke for the Sine of the complement of the Declination which is 45. d. and I finde that to be 70710. This done I multiply the one by the other and the product is 435333 1860. which I diuide by the whole Sine being 100000 wherof commeth a quotient 43533. With this quotient Sine I enter the Table and because I finde not the iust number I take that which is next either greater or lesse vnto it which you must alwaies remember to doe for so small a difference maketh no alteration and therfore I take in stead thereof 43523. whose Arke is 25 d. 48. m. which is the distance of the Stile from the substile Then I take the complement of this distance which is 64. d. 12. m. whose Sine is 90031. and the Eleuation of the Pole 52. d. whose Sine is 78801. and multiplying y e Sine of the lesser which is the Eleuation of the Pole by the whole 100000. the product is 7880100000. which I diuide by the Sine of the greater to wit the Sine of the complement of the distance of the Stile from y e Substile whose Sine is 90031 whereof commeth this quotient 87526 whose Arke is 61. d. 5. m. The complement of which arke is 28. d. 55. m. being the distance of the substile from the Meridian These distances being thus found out the drawing of the diall foloweth First draw a line Parallele to the Horizon A. B. out of whose middle point C. draw the Meridian line squire wise C. D. vpon the centre C. make the quadrant of a circle betwéene A. and D. Here vnderstand that generally in all kindes of declining Dials if the declination be towards the East you must draw the quadrant towards the West except in the South reclining declining and the North inclining Declining where the contrary is prescribed But if the declination be Westward the quadrant must be drawen Eastward Hereby you shall easily know on which side you ought alwaies to draw the quadrant and which way the figures following doe decline Your quadrant being made diuide it into 90. degrées number therein from D. the distance of the Substile from the Meridian which is 28. d. 55. m. Draw at the end of this number the line C. E. for the Substile Then from E. towards A. account the distance of the Stile from the Substile which is 25. d 48. m. and at the end hereof draw the line C. F. for the Stile Afterward by the point E. or in any place of the Substile draw the Contingent line G. H. so long as you can squirewise to the Substile Then take with your compasses the least distance betwéene E. and the Stile the one foote remaining in E. and the other extended in the Substile toward C. place at the pricke there made with the compasses I. vpon which pricke as a centre the same widenes of your compasses remaining draw a circle by E. which shall represent the equinoctiall or Equator Then lay the ruler vpon the point I. and the intersection whose marke is K. of the line of Contingence and the line C. D. which is alwaies drawen so that it may cut the other and where the ruler so placed shall touch the circle there make a marke and there begin to diuide it into 24. equall partes notwithstanding those 12. onely are to be vsed which doe beholde the contingent line Then lay the ruler vpon the centre I. and the Contingent line by euery diuision of the Equator and where it shall touch the line of Contingence there make markes by the which from the centre C. draw lines for the houres so many as shalbe necessary The line C. D. shall alwaies shew the 12. houre which must hang perpendicularly Number the residue of the lines in their place as they follow in order The line A. B. in such as doe decline is vnprofitable except it so chance that some houre line falleth in it Let the Stile be fixed in C. hanging directly ouer the Substile with so great an angle as E. C. F. is declining on neither side Note diligently the making of this declining Diall because in those which follow we meane not to repeate those things which héere haue béen taught And this one kinde well knowen all the other will séeme most easie For better vnderstanding hereof beholde the figure A South Erect declining Diall The making of a North Erect declining Diall another way CAP. 10. THe distance of the Stile from the Substile and of the Substile
Meridian or Substile being of any widenes make there the point or centre F. vpon which centre drawe the halfe Equator from G. by E. to H. Diuide the one half therof from E. to H. into 90. d. Account therein from the Meridian E. towards H. the declination of the plat 32. d. place the ruler vpon the centre F. and the end of this number and where it shall touch the Contingent line there make a marke by this marke you must draw a line squire wise to the Contingent line which shall be for the 12 hower And where the ruler shall touch the Equator there begin to diuide it into 12. equall partes by which lay the ruler from the centre F. making in the line of Contingence markes for the other hower lines all which shall cut the Contingent line squire-wise Note that sometime in diuiding of the Equator the two parts at both ends next to the Semidiameter G. H shall both of them make but one whole parte vnlesse you will make a whole circle for the Equator and diuide it into 24. partes Let the Stile be a small wyer standing right vp in the point E. being so long as the semidiameter of the Equator It may be also a plate of iron or brasse fastened in the Substile so broad as the Semidiameter is as in the East and West erect dialls c. Let the line A. B. be parallele to the Horizon Finish all other things as before A South reclining declining The third kinde If the Eleuation of the Meridian be lesse then the Eleuation of the Pole the making of this Diall i◠vnlike to both the other mentioned before yet the finding out of the distance of the Stile from the Substile is done like to the first kinde as by the example following may appeare Example of a South Diall Declining 45. d. Reclining 45. d. Eleuation of the Pole 52. d. First I multiply the Sine of the declination being 7071 by the Sine of the complement of the reclination which is likewise 70710 and the product 4999904100 I part by the whole Sine The quotient is 49999 whose arke is 30. d. The Complement of this arke is 60. d. which is the Complement to be repeated Then I increase the Sine of the Complement of the declination which is likewise 70710 by the whole Sine and the product thereof 7071000000 I diuide by the Sine of the Complement to be repeated 86602 the quotient Sine 81649 yéeldeth an arke 54. d. 44. m. which is the distance of the Meridian from the Horizon Afterward I multiply this Sine 81649 by the Sine of the Complement of the Reclination which is 70710 the product arising 5773400790 I part by the whole Sine the quotient is 57734. The arke whereof is 35. d. 16. m. the Eleuation of the Meridian which I compare with the Eleuation of the Pole being in our example 52. d. and finding the Meridian Eleuation to be least I substract it out of the Eleuation of the Pole there remaineth 16. d. 44. m. which is the difference kept This done I augment 86602 the Sine of the Complement to be repeated by 28791 the Sine of the difference kept and the product 2493358182 comming hereof I diuide by the whole Sine the quotient Sine 24933 yéeldeth an arke 14. d. 26. m. the distance of the Stile from the Substile Now comparing the Complement of this distance being 75. d. 34. m. with the Complement of the difference kept which is 73. d. 16. m. and séeing the Complement of the difference kept to be least I multiply 95765 the Sine thereof by the whole Sine and the product 9576500000 I diuide by 96843 the Sine of the complement of the distance and 98886 shalbe the quotient therof whose arke is 81. d. 27. m. The Complement of this arke is 8. d. 33. m. which is the distance of the Substile from the Meridian In the Delineation of this diall drawe first as before a line Parallele to the Horizon A B. extend another C. D. making right angles with the line A. B. Draw the Quadrant from A. to D. diuide it into 90. degrées In which account the distance of the Meridian from the Horizon from A. towards D. which is 54. d. 44. m. drawe at the ende of this number the Meridian line from the centre C. which shall shew the 12. hower Account from this toward D. the distance of the Substile from the Meridian which is 8. d. 33. m. at the end hereof extend from C. the line E. for the Substile From this number the distance of the Stile being 14. d. 26. m. toward D. if there be so much space if not account it from the Substile toward A. make at the end of this number the line C. F. for the Stile Let the line of Contingence cut the Substile squire-wise in what poynt you will Finish all other things as in the first of these thrée kindes of South reclining declining Dials In this kinde of reclining Dials whose Stile must bée placed from the centre C. vpward toward the Pole Artick if at any time you cannot draw to both ends of the Contingent line so many howre lines as shall be necessarie then prolong beyond the centre C. the lines opposite on the other side As if you would make the 8. houre line for the morning draw the 8. for the euening beyond the centre C. and you shall haue your desire Note that moreouer in this kinde contrarie to the other before if the plat decline toward the West as in this example it doth thē draw the quadrant towards the West c. But if the Declination be towards the East make the quadrant towards the East A South reclining declining The making of a North reclining declining Diall CAP. 15. The first kinde IN this kinde as in the South before first multiply the Sine of the Declination by the Sine of the Complement of the Reclination parting the product by the whole Sine The quotient Sine thereof shall yéelde an arke whose Complement shall be called the Complement repeated Then increase the Sine of the Complement of the Declination by the whole Sine diuide the product by the Sine of the Complement repeated the quotient Sine thereof will giue an arke which shall be the distance of the Meridian from the Horizon The same quotient Sine multiply by the Sine of the Complement of the reclination and the number arising part by the whole Sine the arke of this quotient is the Eleuation of the Meridian Now adde the Eleuation of the Pole to the Eleuation of the Meridian and the totall number or arke hereof wée will call the compounded arke And if the compounded arke be lesse then 90. degrées then multiply the Sine therof by the Sine of the Complement repeated diuiding the product by the whole Sine and hereof shall arise a quotient Sine whose arke shalbe the distance of the Stile frō the Substile Now compare
the inclination be greater then the Complement of the Eleuation of the Pole substract this lesser out of the other being greater and with the number remaining as if it were the Eleuation of the Pole make your diall like to an Horizontall This kinde likewise sheweth very few howers Example of this last kinde inclining 45. d. First I take 38. d. being the complement of the Eleuation of the Pale out of 45. d. the inclination of the plat and there remaineth 7. d. which I kéep for the Eleuation of the Pole For the delineation of this diall resort to the Horizontall Cap. 3. A North inclining Direct The making of the East and West inclining Dials CAP. 18. MUltiply the Sine of the Eleuation of the Pole by the Sine of the Inclination of the plat diuiding the product by the whole Sine the quotient arke shall be the distance of the Stile from the Substile Then compare the complement of this distance with the complement of the Eleuation of the Pole increasing the Sine of the lesser by the whole Sine part the product by the Sine of the greater where of shall come a Sine the Complement of whose arke shalbe the distance of the Substile from the Meridian It shall not be necessarie to shew any example hereof because the East and West reclining bée altogether like to this Wherefore resort thither for the working of your example for those distances in drawing this figure shall bée here obserued The delineation of an East Diall inclining 45. d. First drawe a line Parallele to the Horizon A. B. make the perpendiculare line C. D. squire-wise to the other Describe the quadrant from A. to D. number from A. toward D. 33. d. 52. m. the distance of the Substile from the Meridian and at the end hereof from C. draw the line E. for the Substile account from this 42. d. 9. m. drawing likewise at the end of this number the line G. for the Stile Let the Contingent line cut the Substile squire-wise Finish all things els as in the East reclining An East and West inclining The making of a South inclining declining Diall CAP. 19. FIrst multiplie the Sine of the Declination by the Sine of the complement of the inclination parting the product by the whole Sine The quotient Sine shall yéeld an arke whose complement shall bée named the complement repeated Then increase the Sine of the Complement of the Declination by the whole Sine and the product diuide by the Sine of the Complement repeated whereof shall come a Sine whose arke is the distance of the Meridian from the Horizon Afterward this Sine being multiplied by the Sine of the Complement of the inclination and the product parted by the whole Sine the arke of the quotient Sine shall bée the Eleuation of the Meridian Which arke you must adde to the Eleuation of the Pole And if the totall number bée lesse then 90. d. it shall bée named the Doubtfull arke But if it be greater then 90. d. take it from 180 and let the remainder be called the Doutfull arke This done augment the Sine of the Complement repeated by the Sine of the Doutfull arke the product arising thereof being diuided by the whole Sine the quotient arke shall be the distance of the Stile from the Substile Now compare the Complement of this distance with the Complement of the Doutful arke multiplying the Sine of the lesser by the whole Sine diuiding the product by the Sine of the greater the arke of the quotient Sine comming thereof shall bée the distance of the Substile from the Meridian But note if the doubtfull arke be found without subtraction from 180 which is if it bée lesse then 90 d. then you must subtract the distance of the Substile from the Meridian out of 180 and the number remaining shall be the true distance of the Meridian from the Substile Marke this likewise if the doubtfull arke be equall 90 degrées let the Complement repeated be the distance of the Stile from the Substile then shall there bée iust 90 d. for the space betwéene the Substile and the Meridian as before is taught in the North declining reclining whither you may resort for the working hereof Here it shall bée sufficient to shew two examples with the delineation of their figures the one where the doubtfull arke is subtracted from 180 d. and the other where there is no subtraction hereof because it is lesse then 90 degrées Example of a South Diall Inclining 45 degrees Declining 45 degrees Forasmuch as this is altogether like to the North reclining 45 d. declining 45 d. whither you may resort I wil omit the working of the former part of this exāple vntil I come to the finding out of the distance of the Substile from the Meridian The former part of this example you may finde to bée thus wrought in the North reclining declining 1 First the complement repeated 60 d. 2 Then the distance of the Meridian from the Horizon 54 d. 44 d. 3 Next the Eleuation of the Meridian 35 d. 16 m. 4 The compounded arke there which we call the doubtfull arke here 87 d. 16 m. 5 The distance of the Stile frō the Substile 59 d. 54 m. 6 Last the distance of the Substile from the Meridian 84 d. 33 m. But here as before is taught you must subtract this distance from 180 d. because the doubtfull arke was lesse then 90 d. and then the remainder 95 d. 27 m. shall bée the true distance of the Substile from the Meridian In the delineation of this diall first as before make a line paralele to the Horizon A. B. Draw another perpendicular C. D. cutting the former squire-wise Make two quadrants from A. by D to B. If the plat decline westward number the distance of the Meridian from the Horizon from A. toward D. c. But if the declination be Eastward as in this example it is then account this distance of the Meridian from the Horizon which is 54 d. 44 m. from B. toward D. drawing at the ende hereof from the centre C. the Meridian line which shall shew the 12 houre Account likewise from that toward A. 95 d. 27 m. the distance of the Substile from the Meridian making in like maner the line E. C. for the Substile From this line on which side you will number the distance of the Stile from the Substile being 59 d. 54 m. drawe by this the line G. representing the Stile Let the line of Contingence cut the Substile squire-wise in any point where you will Make the Equator begin the diuision thereof and draw the houre lines in all respects as in the North reclining 21 degrées 30 minutes declining 30 degrées Cap. 15. A South declining inclining Diall The secōd example of a South Diall Inclining 33. d. 40. m. Where the doutfull arke is subtracted frō 180. Declining 31. d. Where the doutfull arke is subtracted frō 180. First 51503
m. Distance of the Substile and the Meridian 6. d. 35. m. Distance of the Stile and Substile 4. d. 15. m. Eleuation of the Pole 52. d. Hetherto we haue taught the delineation of all kindes of Dials which are to be made vpon any plaine plat or superficies now followeth the garnishing of them with the 12. Signes and the howres vnequall How to draw the 12. Signes in all kindes of Dials before mentioned CAP. 22. FOr somuch as sometime the 12 signes of the Zodiake are placed in Sunne Dialls know in what signe y ◠Sunne is at any time which albeit any kinde will receiue yet most commonly the verticall directly opposite to y ◠South are garnished therewith Therefore in drawing the 12. Signes in these South and all other kindes of Dialls before mentioned doe thus Prepare a little Table of Iron Brasse or close grained wood in breadth 3. or 4. in length 5. or 6. inches Chose for the Diameter one of the shortest sides wherein draw vpon the centre A. halfe a circle to be deuided into two quadrants distinguished with a line drawen from the centre A. to the arke B. parte ech quadrant into 90. degrées The line A. B. is héere in place of the Equator shewing in the arke the beginning of Aries and Libra Moreouer how to finde the other Signes on both sides séeke in the Table of the declination of the Sunne from the Equinoctial circle which is afterward expressed First finde out the degrées of the distance in this Table of the beginning of Taurus from the Equator being 11. degrées 30. minutes Account this distance in the quadrant from the letter B. towards the left hand and at the end of this number draw a line from the centre A. which shall shew the beginning of Taurus and Virgo Account like wise the same distance on the other side from the line A. B. and make a line for the beginning of Pisces and Scorpius Againe in the 20. d. 12. m. from the line A. B. you shal haue the beginning of Gemeni Leo and so many degrées and minutes on the other side the beginning of Aquarius and Sagittarius To conclude on both sides in the 23 degrées 30 minutes there must bée on the one part Cancer and on the other Capricorne Afterward draw lines from the centre A by euery marke so long as your Table will receiue and at the end of these lines let the caracters of the 12 signes of the Zodiake bée fixed as in the figure following you may sée The vse of this Trigonall instrument in writing the 12 signes in Dialls YOur Diall being made and the Stile placed therein take your Trigonall instrument and set it vpon the Stile so that the whole Diameter thereof may stand plaine vpon the edge or vpper part the centre A. of your instrument alwaies remaining in one place of the Stile Let the line of ♋ bend vpward to the centre of your diall and the line of ♑ downe ward Then fasten a thred at the vppermost end of your trigonal in euery line of the signes so that you may direct it downward by the centre A. to the plat of your Diall and where the ende of the thred shall touch the Diall make a marke Then mouing the Trigonal on the right hand so that the thred may bée stretched on the left hand make there likewise a prick vpon the plat When you haue thus done 4 or 5 times vpon the one side of the diall that is on the left hand doe so likewise on the other side on the right hand These markes being thus made draw with your compasses or rather with a crooked ruler made according to those markes a line by them Doe thus with each one of the 7 lines of your Trigonal When you haue drawne al these lines being crooked except the middle line which is right and representeth the Equator then at the ends of them write the caracters of the 12 signes on this wise First on the right hand toward the East at the ende of the vpper line write or place ♑ At the second line downward ♒ At the third ♓ At the fourth ♈ At the fift ♉ at the sixt ♊ at the seuenth ♋ Then on the other side on the left hand toward the West at the ende of the nethermost line place ♋ At the second ♌ at the third ♠at the fourth ♎ at the fift ♠at the sixt ♠And finally againe at the vppermost set ♑ This done remember that in what place of the Stile the centre A. of your Trigonall was placed there fasten a small péece of yron or any such like thing which may shewe with the shadowe thereof the Signe which the Sunne shall be in at any time vnlesse the houre lines bée so short that where the small péece of yron should be placed you may cut the Stile that the ende thereof shall shew it But the first is the most conuenient way for the vse thereof You may in like manner with this Instrument drawe or place the 12 signes in Horizontal East West and all other kindes of Dials which before are recited because the difference is nothing but in placing the 12 signes at the ends of the lines the true doing where of you may easily perceiue by the course of the Sunne For in the South Erect when the Sunne occupieth Cancer then is the line of ♋ furthest distant from the centre of the Diall But in the Horizontall Diall the line of ♋ is next to the centre Few words shall suffice for this matter experience shall easilie teach you herein How to place the vnequall houres in a Horizontall Diall CAP. 23. FIrst you shall vnderstand that by an vnequall hower is ment the 12 part of the day whether it be short or long For when the Sunne is in the Equinoctiall circle the day hath 12 equall and like wise 12 vnequall houres But in winter solstice when the dayes be at the shortest and containeth with vs where the Pole is eleuated aboue the Horizon 52 degrées onely 7 houres 36 minutes then the vnequall houres be lesse For if you diuide these 7 houres 36 minutes by fractions into 12 you shall finde onely 38 minutes of an equall houre to make one vnequall houre But in the sommer solstice when the dayes bée at the longest and hath 16 houres 24 minutes then one houre with 24 minutes maketh one houre vnequall These bée like wise called the houres of the Planets and are placed in Dialls on this maner Your Diall being made and prepared draw vpon it the 12 signes of the Zodiake as you were taught before so large as your plat will giue leaue c. Note that alwaies the Meridian line or 12 equall houre is the 6 vnequall houre Marke likewise that when the Sunne entreth into the beginning of ♈ and ♎ both the equall and the vnequall houres be of like quantitie For the 7 equall houre in the morning is the first vnequall and the
the second marke in the Tropike of Cancer and the intersection of the line of the 5. hower with the Equator or line of Aries and Libra drawing like wise a line which shall shew the first howre in the East and the 11. howre in the West Diall make on this wise all the other vnequall howres namely the 10 9 8 and 7 in the West Diall And the 2 3 4 5 in the East Diall The making of an Horizontall Sphericall or hollow Diall CAP. 26. FIrst prepare your Sphere or plat perfectly hollow of what quantity you wil. Then with your compasses diuide the vpper brimme thereof into 4 equall partes marking it with the letters A. B. C. D. Afterward open your Compasses to the widenes of one Quadrant either A. C. or A. D. and with that widenesse one foote being placed in the point D. draw an obscure or light line from A. to B. This done set one foote of your Compasses in the point C and with the other you shall try whether the plat be perfectly Sphericall or not for if it be your Compasses will fall in the same line which you made before but if it be not perfect you may amend it And then draw this line manifest so that it may continue For it shall be the Meridian line shewing the 12 howre Againe place one foote in the point A. drawing with the other a light line from C. to D. then one foote being set in B. you may try with the other as before the truth of the line last made Now where these two lines cut eche other in the bottome of the plat place the letter E. Then diuiding the quadrant A. E. into 90. d. and accounting therein the Eleuation of the Pole from E. toward A. make y â— point F. by which the arke line of ♈ and ♎ representing the equinoctiall circle shall be drawen Afterward séeke out the greatest declination of the Sun from the Equator which you shall finde in the table of the declination of the Sunne which is 23. d. 30. m. Then account 23. d. 30. m. from F. toward E. making there a mark for the arke of Cancer Likewise from F. toward A. number the same distance for the arke line of Capricorne This done account from F. toward E. 20. d. 12. m. make there also a marke for the line of ♊ and ♌ And the like space from F. towards A. for the arke of â™’ and â™ To conclude number from F. towards E. 11. d. 30. m. making there also a marke for the â—ine of ♉ and â™ and so much from F. toward A. for ♓ and â™ When you haue thus made marks for al y â— arkes of the 12 Signes open your compasses to the Quadrant of the Spheare that is from A. to C. which widenes of the compasses remaining place one foote in the point F. in the arke of ♈ and ♎ in the Meridian and where the other foot shall touch the same Meridian towards B make the point G. which shall represent the Pole antarticâ— by which as it were from a centre draw a line from the point D. by F. to C. which shall be the line of Aries and Libra Then one foote of your compasses remaining in the point G. with the other draw lines from one side of the plat to the other by euery marke before made for the 12. Signes of the Zodiake The 12. Signes being thus finished procéede to the diuision of the equall howres on this manner Diuide y â— arke of the Equator into 12. equall partes beginning at D. by F. ending in C. Then open your Compasses to the quadraÌ„t of the plat and the same widenesse of them remaining place one foote on the first point of the diuision next C. in the Equator and if you haue diuided the Equator equally the other foote will touch the first part beyond F. towards D. by which from the centre G to the edge of the plat draw a line which shall shew the first howre afternoone This done remoue your compasses that widenesse remaining placing one foote in the second part from C. towards F. and the other foote touching the second part from F towards D. make a line as before from the centre G. to the brimme of the plat to shew the 2. howre afternoone In like manner finish all the other howre lines namely the 3 4 5 6 7 8 for the afternoone Then doe likewise on the other side for the howres in the forenoone namely the 11 10 9 8 7 6 5 and 4 drawing lines from the centre G. by euery diuision to the brimme of the plat c. The placing of the vnequall howres in this Diall When you will place the howres vnequal in this Sphericall Dial diuide the Tropick of Cancer and of Capricorne ech of them into 12. equall parts as before you did the Equator for the equall howres Then with the compasses ioyne eche thrée points of these thrée arkes answerable into one line or arke vntill you haue made 12. lines to shewe the 12. vnequall howres as in the figure following you may sée Whereof the Meridian or 12. vnequall howre shall alwaies be the 6. vnequall howre In placing the figures to the equall vnequall howres and the Caracters to the 12. Signes of the Zodiake the figure may sufficiently shewe notwithstanding you may place them where you will giuing to ech signe his proper Caracter and euery howre equall and vnequall their proper figures or names Fire the Stile in the centre G. standing vp so high as the brimme of the plat so that the vpper end may appeare as the centre of the circumference which you may try by placing a ruler vpon the points A. B. And againe vpon C. D. In like manner you may examine it with your Compasses but the former as practise wil teach you is the more conuenient way You may if you wil haue the Stile stand aboue the plat so that it may shew the equall howres aboue the edge of the Sphere and then fasten a knot of equall height with the plat which shall shew the motion of the Sunne in the 12. Signes and y â— vnequall houres which otherwise the end of the Stile should doo as in the figure following you may perceiue The Figure of an hollowe Horizontall Diall The making of a South Spherical erect direct Diall CAP. 27. YOu shall vnderstand that the making of this kind differeth almost nothing from the Horizontall except onely in the accounting the beginning of the Eleuation of the Pole drawing the houres vnequall First your Sphear or plat being prepared and parted into foure Quadrants as before in the Horizontall you were taught diuide the quadrant E. A. into 90 degrees Then number in it the Eleuation of the Pole from A. toward E. marking the ende of the number with F. Afterward open your compasses to the quadrant of the plat and the one foote placed in F. extend the other in the Meridian line towards B. making the