HOROLOGIOGRAPHIA NOCTVRNA.

OR LVNAR HOROLOGIOGRAPHIE.

Set forth and demonstrated (after a twofold manner) in the Horizontall Plane onely.

Vpon which (and all other by the same reason) may in a manner, as plainely and speedily bee discerned the t [...]mes of the Night by the Gnomonicall shadow, caused by the Moone, as the times of the Day upon any by the Sun: Serving as well in the day time for the Sunne.

By IOHN WYBERD.

Together with an Addition of certaine new and briefe Rules for the exact and most speedy mensuration of Circles and Spheres, and also Cylinders, both in solid and li­quid measure, by certaine plaine Scales onely, not hereto­fore published, but now set forth for the benefit of all those that have occasion to make use of such things.

‘Est natura hominum novitatis avida.’ Plin.

LONDON Printed by Tho. Cotes. 1639.

A DESCRIPTION OF THE HORIZONTALL LƲNAR DYALL.

THe making of this Dyall dependeth up­on the most [...] observation of the Moones Mediation of the Heaven, or comming to the Meridian, as the little Note or Table here following doth shew; and which Master Digges in his generall Prognostication, Mr. Hopton in his Concordancie of Yeares, and most others have and doe still chiefely observe and follow: Which observation or rule, although it seemeth not alwayes to hold very precise, by reason of the various and sundry mo­tions of the Moone, yet is it not so much amisse, or dissenting from the truth, but that the time of the night (the Moone shining) may be thereby sufficiently knowne, without any sensible errour to be regarded, as the afore named Authors (accounted good Mathematicians in their times, and which their workes doe still testifie) have in those bookes set downe without any stricter observations: And as I my selfe also have very often observed, when the Moone hath shined upon an [Page 2] Horizontall or other Sun-Dyall, by the shaddow of the Style or Gnomon, and comparing the same with other sufficient wayes, have found them to accord without any plainely per­ceptible difference: For having searched out the true time of the Moones mediating, or culminating of heaven, for any night, appointed in a place certaine (which is not very easily done) the true houre at any time of that night may be found, the Moone shining upon any true Sun-Dyall in the same place: Because the defect or excesse of the stylar shadow in time, in respect of the houre of 12. upon the Dyall, being de­ducted from, or added to the aforesayd time, giveth the true houre or time of that night: which thing although it be well knowne to many (as a common rule) yet unknowne to most men, for every man is not acquainted with the Moones sayd mediation, or hath knowledge artificially to get the times of the same, and none but such as have some insight into astrono­micall affaires, or perhaps knowing the same by some ordina­ry meanes (as many doe) yet cannot readily make subduction or addition of the sayd defect, or excesse (as occasion shall re­quire) unlesse the same doe chance to fall justly upon some [...] and entire time on the Dyall, at the time of observa­tion, and therefore it must needes be very convenient to have a Dyall, that shall even as readily (without any trouble) shew the houre of the night by the Moone, as the houre of the day by the Sunne: So that the time of the Moones comming to the Meridian (whatsoever time it be) is presupposed to stand in the Meridian line or line of North and South on the Dyall, in the place of the houre of 12. which time being fore-knowne for any night appointed: If the houre-lines be so drawne on the Plane (in a due order) that the time of the Moones comming to the Meridian, shall fall precisely in the sayd Me­ridian line, or line of North and South: I say then that these houre-lines being thus disposed, shall readily and precisely enough shew the houre of the same night, at any time thereof when it shall be required, if the Moone shineth on the Plane: yet it must not be expected that any Dyall should bee made (for continuance) to shew the houre of the night by the Moone alwayes so exactly as the houre of the day by the Sun, [Page 3] by reason of the various course and mo­tion of the Moone, in respect of the Sun, as before is sayd; but exactly enough for ordinary use: And hereupon is fra­med this Dyall, which here wee have in hand, according to this little Note or Table, hereto annexed as I sayd before: In the first columne whereof, are con­tained the dayes of the Moones age, reckoned from the time of her change, or conjunction with the Sunne: In the second is contained the time of her comming to the Meridian or South point, answering to each day of her age; for although the Moone being full South, shaddoweth alwayes upon the houre of 12. in the Dyall; yet doth she not alwayes come to the South at the houre of 12. and never, unlesse in the day of her conjunction or oppositi­on to the Sunne, and then at Mid-day in the one, and Mid-night in the other, or thereabouts; whereby it appeareth that for severall dayes of the Moone, there must be (as it were) severall Dy­als, so contrived (on one and the same Plane) that each of them may readily shew the times of that night, unto which it properly belon­geth: And therefore to proceede to our present purpose: you shall first prepare a square peece of fitting and well sea­soned wood, that will not warpe or bend, or of brasse, or o­ther metall, or of stone, according as you shall please, which (for the more conveniencie in use) had need to containe in breadth about 12. inches; the larger it is, the better: Now, because the Moone, in the day next after her change or con­junction, and likewise on the day next after her Full, or op­position to the Sunne, that is, she being one day, and sixteene dayes old, observeth the same (or much like) time in her

Age of the Moone.Her com­ming to the Meri­dian.
Dayes.H. M.
1161248
217136
318224
419312
520400
621448
722536
823624
924712
1025800
1126848
1227930
13281024
14291112
15301200

[Page 4] comming to the Meridian or Mid-heaven, and likewise being two dayes and seventeene dayes old, and so the rest in their order, (as you may observe in this Table) but contrary or opposite times of the day; the first happening after-noone, that is to say, betweene Noone or Mid-day and the Mid-night following, and the other in the morning or before Noone, that is, betweene Mid-night and the Mid-day following: You shall therefore upon your sayd Square or Plane, describe fifteene Concentrique circles, serving for the thirty dayes of the Moone (or Synodicall moneth) of equall and convenient distance one from another, drawing the outermost circle as large as conveniently you can: So that circle which is next to the Center, shall most fitly serve for one day, and sixteene dayes of the Moones age: the second for two dayes and seventeene dayes: the third for three dayes and eighteene dayes: the fourth for foure dayes and nineteene: the fifth for five dayes and twenty dayes, and so all the rest in their order, as the second figure doth shew (but for the three first dayes of the Moone, there is seldome any use of the three first circles next the Center, because it is most commonly the fourth day after the change, before she shineth in the Hori­zon) then upon a large sheete of paper or paist boord, draw the common houre-lines of the Horizontall Plane, (out at length) according to the elevation of the Pole; and for the more conveniencie in the making of this Dyall, it is best to divide each houre-space of the equinoctiall circle, by which you drew those houre-lines into five equall parts, and then marking them out upon the line of contingencie, you shall by those markes there made, draw out of the center of your houre-lines, obscure radiall lines at length, which will accor­dingly divide each houre into five parts, and so each part will containe twelve minutes of an houre, by which division you may readily and exactly set off on your Dyall any number of minuts set downe in the former Table, as pertaining to the houre of the Moones comming to the Meridian, as shall presently be shewed: this being done, you shall upon the Center of your houre-lines so drawne, describe fifteene ob­scure Circles, equall to those on your Plane, whereby you [Page] [Page]

Place this Figure next after page [...]

[Page] [Page 5] shall set downe the houres and their parts upon every Circle of your Plane, in their due position and distances one from another: All which things, this first figure doth demonstrate, which although it may seeme unto many to be needlesse, yet I have thought it convenient here to describe the same for the better satisfying of such as are not throughly experienced in these matters, and therefore doe desire plaine demonstrative instructions: these things being thus prepared, you must re­sort to the former Table, and there finde the time of the Moones comming to the Meridian or South point, for any day of her age: So I finde that the Moone being at the age of one day, or sixteene dayes, commeth to the aforesayd place at 48. minutes after Mid-day in the one, and Mid-night in the other: whereupon the Meridian or 12, a clocke line in the first figure, doth not then represent the houre of 12. but 48. minutes past the same, and the houre-line of 11. 48, minutes past 11. likewise the houre-line of 1. 48. minutes past 1. and so all the rest in their order: which being knowne, I set off the houres from the Meridian line after this manner: I take with my Compasses the distance betweene the houre of 12. in the Meridian line, and 48. minutes past the same, in the first circle on my houre-lines formerly drawne, being the next foure parts of the five, which are contained betweene the houre-lines of 12. and 1. or 12. and 11. (because, as I sayd before, each houre being divided into five parts, each of those parts, will containe twelve minutes, and therefore foure of them 48. minutes, as the first figure sheweth) then placing one foote of my Compasses in the Miridian line of the Plane upon the like circle; with the other I marke downe the houre of 12. towards the right hand: Also I take the distance be­tweene the houre of 12. (as before) and 48. minutes past the houre of 11. (being the next foure parts of the five, betweene the houre-lines of 11. and 10.) and setting one foote of my Compasses in the Meridian line of the Plane, with the other I marke downe the houre of 11. So I take 48. minutes or foure parts past the houre-lines of 10. 9. and 8. from the Meridian or 12. a clocke line of my houre-lines, to set downe the houres of 10. 9. and 8. from the Meridian line on the Plane; and [Page 6] so the rest on that side of the Meridian line: Then to placē the houre of 1. (and consequently the rest of the houres, which fall on the other side of the same line) I take the di­stance betweene the houre of 12. (as before) and twelve mi­nutes past the same, being the first of the five parts betweene the houre-linēs of 12. and 1. (because the houre of 1. falleth herē within twelve minutes of the Miridian) and with that distance I set downe the houre of 1. So I take twelve minutes or one part past the houre-lines, of 1. 2. 3. and 4. to set off the houres of 2. 3. 4. and 5. from the Meridian line on the Plane, and so all the other on that side of the samē line, as many as shall be needfull. Then to place the houres for two dayes and seventeēne dayēs of the Moone, I looke into the former Table, and there I finde the time of her comming to the Meridian, to be at 36. minutes past one of the clock, after­noone in the one, and after Mid-night or in the morning in the other: which time must here be supposed to stand in the Meridian line in the place of the houre of 12. and therefore the houre-line of 11. must needes signifie 36. minutes past 12. and the houre-linē of 1. 36. minutes, past 2. and so all other beforē and aftēr must signifie accordingly: wherefore placing one foote of my Compasses in the Meridian or 12. a clocke line (as before) on the second Circle of mine houre-lines, I extend the other unto 36. minutes past the same, being the three next parts of the five betweene the houre-lines of 12. and 11. Then setting one foote upon the Meridian line on the Plane in the like Circle, with the other I pricke downe the houre of 1. towards the right hand. So I take 36. minutes or 3. parts beyond the houre-lines of 11. 10. 9. and 8. &c. to set down the houres of 12. 11. 10. & 9 &c. from the Meridian line on the plane.̄ Then for the houres on the other side of this line, because that here the houre of 2. falleth within 24. minutes of the South point: I take 24. minutes or two parts from the Me­ridian or 12. a clocke line of my hourē-lines, and there with I set downe the houre of 2. on my Plane: In like manner I take 24. minutes or two parts beyond the houre-lines of 1. 2. 3. and 4. &c. to set of the houres of 3. 4. 5. and 6. &c. Then for threē dayes and eighteene dayes of the Moone; I [Page] [Page]

[figure]

[Page] [Page 7] finde by the former Table, that she then commeth to the South at 14. minutes past two of the clocke after­noone in the one, and in the morning in the other: wherefore I take two parts beyond the houre-lines of 12. 11. 10 9. &c. in the third Circle upon my houre­lines, and there with I set off the houres of 2. 1. 12. and 11. &c. from the Meridian line upon the like Circle towards the right hand: Then for the houres on the other side; because that here the houre of 2. falleth from the Meridian or South point, by 24. minutes of time, on the one side thereof, therefore the houre of three fal­leth from thence on the other side by 36. minutes: wherefore I take 36. minutes or three parts beyond the houre-lines of 12. 1. 2. and 3. &c. and therewith I set off the houres of 3. 4. 5. and 6. &c. Then for the fourth and nineteenth dayes of the Moone; I finde that she then commeth to the Meridian at 12. minutes past 3. of the clocke after-noone in the one, and in the mor­ning in the other: wherefore I take one part (or 12. minutes) beyond the houre-lines of 12. 11. 10. 9. &c. upon the fourth Circle of mine houre-lines, and there­with I set downe the houres of 3. 2. 1. 12, &c. on one side of the Meridian line upon the like circle: Then because the houre of 3. falleth here within 12. minutes of the Meridian on one side thereof, the houre of 4. will fall from thence on the other side by 48. minutes, and there­fore I take foure parts beyond the houre-lines of 12. 1. 2. and 3. &c and therewith I set off the houres of 4. 5. 6. and 7. &c. Lastly, to place the houres for the Moones age of five dayes, and twenty dayes, I looke in the afore­sayd Table; where I finde the time of her comming to the Meridian, answerable to those dayes, to be just at foure of the clocke after-noone in the one, and in the morning in the other; which houre being placed in the Meridian line on the fifth circle from the Center; the houres on both sides thereof, must be set off from thence, after the same [Page 8] manner, as the houres are on both sides of the houre of 12. when it standeth in the Meridian line, (and therefore they doe fall precisely upon the houre-lines for the Sun) because (the angles being here unequall) the same angles must still retaine the same places, otherwise great errours will ensue: All which things the second figure plainely sheweth: and in these five examples, are contained all the varieties of operations in this Dyall (in which I have beene somewhat the more tedious, to give the better contentment and satisfaction, to the more unlearned in these things) and therefore more examples would be altogether needelesse and superfluous, the rest being per­formed after the same manner: For the houres being noted downe in the five first Circles, (as wee have here shewed) the houres may be easily placed in all the other Circles, by the helpe of those onely without the former operation: For you may observe in the working (and as the former second figure sheweth) that the houre-lines or points of the sixth, and eleventh Circles, are in the same position (in respect of the Center) with the houre-lines of the first circle, and so the houre-lines of the seventh and twelfth circles, with those of the second, and those of the eighth and thirteenth, with those of the third, and those of the ninth and fourteenth, with those of the fourth, and likewise those of the tenth and fifteenth circles, with them of the fifth circle: Whereby it is evident, that five circles onely might be sufficient for this purpose, and then each circle should containe three of the circles in the former figure, which are thus matched together in respect of their houre-lines, but differing in the num­bers or figures belonging to the same, and hereupon each circle must serve for sixe severall dayes of the Moone: for the first circle from the center serveth for the 1, 16. 6, 21. 11, 26. dayes; (according as they are coupled rogether in the former figure) the second for the 2, 17. 7, 22. 12, 27. The third for the 3, 18. 8, 23. 13, 28. [Page] [Page]

[figure]

[Page] [Page 9] The fourth for the 4, 19. 9, 24. 14, 29. The fifth and last for the 5, 20. 10, 25. 15, 30. which way, although it be somewhat more compendious for the making of the Dyall, yet more confused for the use thereof to the un­skilfull, by reason of the manifold denominations of the circles and their houre-lines: for in the former figure each circle serveth onely for two dayes of the Moone, the one in her increase the other in her decrease, answe­ring each other, in respect of the houre and minute of the Moones comming to the Meridian, and therefore (in that respect) there will fall out 15. circles, and so the houre-lines of every circle, are but of one simple deno­mination; but in this latter way, each circle containing three of the former, serveth for sixe severall dayes of the Moone (as I sayd before) which doe answere one ano­ther, in respect of the number of minutes adhaering to the houre of the Moones sayd comming to the Meridian, whereby it happeneth that the houre-lines which must serve for those sixe dayes, doe concurre on the Plane, and therefore may very fitly be contracted into one and the same circle on the Plane, but then the same houre-lines will beare a threefold denomination, as may be plainely seene in this third and last figure, which I have thought fitting here to be set downe, for the better conceiving of this latter way, being indeede a more compendious and compleate way than the former, that so, whosoever shall make tryall of what is here delivered, may use that way which he shall best affect.

The houres in every Circle, are continued on both sides of the Meridian line, so farre as the houre-lines for the Sunne doe extend, that so the Dyall might serve generally for all times of the yeare; and though the houre of 12. falleth twice in some of them, yet may they both be use­full at one time of the yeare or other; for to place in such houres onely as shall happen to be of use, and neither more nor lesse, is a thing I conceive not to bee certainely [Page 10] done by reason of the uncertaine rising and setting of the Moone, and her uncertaine departure from the rayes of the Sunne.

Having noted downe the houres in every circle (as in the second figure) adde to each circle one or two inward circles, making one or two convenient spaces for the pla­cing in of little lines or strokes, for the houres and their parts (according to the usuall manner) and the figures belonging to them: but in the latter way you must adde to each circle, three other inward circles, making three severall spaces for the three rankes of figures belonging to every circle, (as you may see in the third and last fi­gure) because the houre-lines of every circle (as I sayd before) be here of a threefold denomination: and it is necessary for you so to order and contrive the circles on your plane, as that there may be left a convenient space betweene every severall Dyall or circle of houres, to distinguish betweene them, and not to mingle and con­found them one with another.

The parts of every houre necessary to be placed on the Dyall (though we have put none here, partly to avoyd tediousnesse in the worke, and some charge in cutting the figures, and partly because the are needelesse in this place) may be those which we have formerly used, or better it were for common use to have each houre divi­ded into some equall number of parts, as foure or eight parts, as is usually done in most Sun-dyals; for before we divided each houre into five parts, as being the fittest number for the more easie and exact making of the Dyall.

The outermost circle of all, belonging to the fifteenth day of the Moone or day of opposition, serveth aswell for the Sunne, the houre-lines thereof being rightly dis­posed for the Sunne. For the Moone, on the day of her coujunction with the Sunne, commeth to the Meridian much about the time that he doth, and in the day of her [Page 11] opposition to the Sunne, she commeth to the sayd place at the opposite time or thereabout, when the Sunne is in the North point of the Meridian circle, under the ear [...]h▪ or our Horizon, that is, at our Mid-night or 12. of the clocke (as the former Table sheweth) and then the same Dyall which serveth to shew the houre of the day by the Sunne, serveth likewise to shew the houre of the night by the Moone, though not alwayes so exactly, yet with­out any difference to be regarded in common use (as I have oftentimes observed) but at other times it cannot be so, because the time of the Moones aforesayd mediation or culmination, is not alwayes the same, but altereth on every day, and therefore that Dyall which should serve to shew the houres or times of any other night by the Moone, must (of necessitie) be altered, and the houte-lines bee otherwise ordered and disposed, or else why should not the Moone in any night when she shineth, shew the true houres thereof upon any true Sunne-Dyall by the stilar shadow, aswell as the Sunne sheweth the true houres of any day by the same; which thing, how farre it is from being so, I thinke there is scarcely no ordinary man that doth not know it; the rea­son thereof being (as I shewed before) because the Moone doth not alwayes observe the same times with the Sunne, in her rising, Southing, and setting.

These severall Dyals or circles of houres, may not onely be delineated upon the Horizontall Plane, to shew the time of the night by the Moone, but also upon all o­ther planes by the same reason and rule, (and therefore we have here entitled it, Lunar Horologiographie, that is, The Description of Dyals for the Moone) and most readi­ly upon the Equinoctiall Plane, by reason of the equality of the horariall angles: And in the direct Meridian and Polar Planes, where the Solar houre-lines are parallels, there also the Lunar will be parallels; and in stead of those fifteene concentricall circles formerly used, here must bee [Page 12] fifteene parallell right lines, of which the equinoctiall line of the Plane, may very fitly be one, which may (if you please) serve for the fifteenth day of the Moone, and so will serve continually for the Sunne by the reason aforesayd: So the seven Parallels falling under the sayd line, may then fitly serve for the seven dayes next enfuing the day of her change and Full, and the seven Paralells above the sayd line, for the seven dayes next before the Full, and the change next following: or you may begin at the uppermost parallell on the Plane, and account that for one day and sixteene dayes of the Moone, and so go­ing downewards, the lowest parallell will be for fifteene and thirty dayes, and so for the Sunne, and then the equi­noctiall line or middle parallell shall be for eight and 23. dayes, for you may begin with what parallell you will: then drawing the common houre-lines of these Planes, and dividing each hour [...] into five parts (as before) the houres for the Moone are set off from the houre-lines of 6. in the one and 12. in the other on both sides thereof upon their proper parallels, (as farre as the houre-lines for the Sunne doe extend) with as much facility as in any other Plane whatsoever, the Equinoctiall plane being excepted; so that you bee carefull to place the right houres in these planes: Having thus set downe the houres (and parts if you please) draw to each Parallell line another parallell including a convenient space be­tweene them, wherein to draw little lines or strokes for the houres and their parts, and to place the figures belon­ging to the houre-lines or strokes: But for that I shewed before, how this might bee performed by five circles in the Horizontall plane, so by the same reason it may here be performed by five parallells onely, for then each pa­rallell serveth for sixe dayes, and the houre-lines of each parallell are of a threefold denomination, and then you must draw to each parallell line, three other parallels, that so there may be three fitting spaces made for the pla­cing [Page 13] of three rowes of figures which belong to the houre­lines of every parallell, as was done by circles in the Ho­rizontall plane; and in the delineating of any of these Dyalls, it were convenient for you first to draw the com­mon (or Solar) houre-lines belonging to the plane, ob­scurely with the point of your compasse or such like thing upon your plane, by which you may easily discerne whe­ther you worke rightly or not: But to deliver any figure here concerning these last mentioned planes I thinke it to be needelesse, because if the working upon the former be rightly understood, the working upon these latter and likewise upon all other Planes may easily be understood by the same reason: And as for the stile belonging to to these last named Planes, it is necessary that the same be made full as broad as the Plane of the houre-lines, (or if it were a little broader in the top, it were not amisse) that so the shadow thereof may alwayes extend as farre as the parallell lines on the Plane; for though a straight round pin will serve in these Planes for a stile for the Sunne, yet it will not for the Moone, by reason of the varietie of Dyals on one and the selfe sam [...] Plane, all differing one from another: But indeed none other is so commodious for common use as the Horizontall Dyall, which may (most easily) be fitted for use two manner of wayes: For it may be either alwayes fixed abroad, like unto the common horizontall Sun-Dyall, and so be im­moveable, or else not fixed, but to be removed up and downe at pleasure, and then having a Magneticall Nee­dle placed in a Boxe after the usuall manner (whose Me­ridian line ought to be drawne therein, according to the deflection or variation of the Needle in the place of ob­servation) to be affixed to some side thereof, it may bee truely placed thereby, any night when it should be used, being holden or set precisely horizontall; or (for want of such a Needle) they that have an horizontall Sunne-Dyall about their house truely placed, may make a shift to use [Page 14] it well enough, by laying it flat upon that Dyall, and then applying one side the [...]eof to the side of the cocke or ftile of that Dyall, in such sort that the Meridian line of the one may be paralell to the Meridian line of the other. But indeed the most absolute way of all, were to have it made in brasse (which may be done by Mr. Elias Allen dwelling without Temple Ba [...]re, over against St. Clements Church, London, who maketh all sorts o [...] Mathematicall Instruments and also horizontall Sunne-Dyalls in brasse) and fixed alwayes upon a poast, or rather made upon a faire white stone, where the strokes for the houres and their parts and the figures belonging to them being done in blacke or other such notable colour, might be more perfectly discerned than in the other: So that then onely knowing the day of the Moone, (which may be knowne by any Almanacke) you have no more to doe, (the Moone shining on the Plane) but to looke out the circle which is appropriated to that day, and the shadow of the stile will presently give you the houre or time of the night, if your Dyall be rightly made and placed: And it would be very comely and convenient to have the stile to this Dyall made so, as it should touch the plane in those places onely where it is let into the same, that is, betweene the center and the circle next unto it, and againe a little about the outermost circle which is furthest from the center, that so the stroakes for the houres and their parts, and the figures which fall upon or very neere the Meridian line, might not be hidden and defaced by the stile.

But because houre-lines may be placed generally upon all planes (as I sayd before) to shew the houres of the night by the Moone; it would be an excellent way to have a Lunar Dyall drawne on glasse and placed in a window after the manner of those Sunne-Dyalls which are most accurately made by my loving friend Mr. Baptist Sutton, dwelling at the upper end of Chauncery Lane, neere Holborne (being the author of the ensuing worke [Page 15] or Addition) who likewise will be able to performe these as accurately as the other, if it shall be required of him: For there the plane of the Dyall being of a trans­parent matter, and intercepted (as a meane object) be­tweene the eye and the Moone, the houre-stroakes and figures, together with the shadow of the stile, may bee thereupon more perfectly and speedily discerned, than upon any other kinde of Plane whatsoever (and there­fore I thought it not amisse to give notice thereof) but it is well knowne that the shadow which is caused by the Moone, cannot be altogether so perfectly discerned as that which is caused by the Sunne, because the light of the Moone is not so perfect as the light of the Sunne, and therefore the time of the day may be somewhat more readily perceived on the Dyall by the stilar shadow, than the time of the night; yet it may be very easily dis­cerned thereby, especially when the Moone shineth out very bright.

And now, this our Horizontall Dyall I conceive (and I thinke, that any man of understanding will acknow­ledge) to be farre more easie and ready in use, than that Lunar Dyall which Mr. Fale hath long agoe described, in his booke of Solar Horologiographie, whose position must be in direct Paralellisme to the Equinoctiall circle of the Sphere, making the same angle (of inclination) with the Plane of the Horizon, which that doth, being the com­plement of the Latitude or Polar altitude, and therefore but few men know how to make use thereof in compa­rison of them that doe not know; and it must needes bee troublesome also to those that doe know how to place the same rightly, because they must stand and apply a Qua­drant together with a needle to it every night when they would use it, unlesse the same stand alwaies fixed abroad in its due position; and if it so doe, yet the unskilfull sort cannot well tell how to make use of it, by reason (it consisting of two severall parts or plates) of the in­ward [Page 16] moveable part thereof, turning about within the outmost plate, and upon which the houre-lines are drawne, whose Index, (or long tooth, as he termeth it) being fastned at the houre of 12. must be turned to the day of the Moone noted on the outermost or fixed part, and to the houre of the change (as he saith) accounting from 12. of the clocke; in which he hath not sufficiently expressed the meaning thereof, for such as are but meane­ly skilled in these things, to understand, and so (as I con­ceive) hath not well declared the making and use of the same. Vpon the outermost or fixed part, hee draweth a circle, which hee divideth into 30. parts for the thirty dayes of the Moone, after this manner: Now because (saith he) the Moone finisheth her course in 29. dayes, 12. houres, and 44. minutes, (that is, from the Sunne, being in a meane conjunction with him, till she be with him againe by the like conjunction) part or divide the aforesayd circle into 30. parts, so as 29. of them being equall, the thirtieth or last must not be so great as one of the other parts by ⅓, that is, it must containe ⅔ of one of them; by which account (if it were true) the Moone should finish her sayd course in 29. dayes, and 16. houres, (which make ⅔ of the naturall day) whereas the same is but 29. dayes, and 12. houres, or ½ of the day naturall, and about ¾ of an houre over, and therefore it doth not consequently follow, that the last part should containe ⅔ of one of the rest, but rather ½ onely: Indeed (for mine owne part) I must confesse, I never made tryall of this Dyall, and therefore can say the lesse of it, neither doe I know whether the same were of his owne devising or not; But sure I am that this our Horizontall Dyall is e­very way as exact as that, and serveth to a more generall use, it being of use and delight for all sorts of men, and more especially [...]uch as know not how to finde the houre of the night artificially by other wayes: for if they can but know how to get the true age of the Moone (which [Page 17] is easily done by an Almanacke, as I sayd before) they may as easily obtaine the time of the night by this Dyall (or the like made upon any other Plane, when the Moone shineth thereupon; and that sufficiently enough) as the time of the day by any Sunne-dyall when the Sunne shi­neth on the same: But if any list to make use of such a kind of Dyall, as that of Mr. Fales, lately mentioned, they may use another way to finde the time of the night more exactly thereby: For the houre-lines being drawne upon the moveable or turning plate or wheele (as before is sayd) which should now be so large as each houre may be distinctly divided into such a number of parts, as that you may guesse at any one minute thereupon, (which may conveniently 15. or 20. parts, for then each part will containe but foure or three prime minutes of time) If they can have a Table of the Moones comming to their Meridian artificially and exactly calculated for every day in the yeare, and so for every yeare severally (which in some yeares is to be found in one Almanacke or other, if trust may be given to them) then to make use of this Dyall in any night of the yeare when the Moone shineth, they must looke out that day in the sayd Table, and right against it, under its proper moneth is set the houre and minute of the Moones comming unto the Meridian for that day and place: then the Dyall being rightly placed if they bring that houre and minute noted on the inward or moveable part to the Meridian line noted on the out­termost or immoveable part, and so let the houre-lines in that position, the shadow of the stile shall shew the houres of that night exactly, without having any regard to the dayes of the Moones age, noted upon the upper­most part, as in the former, and therefore this must needes be a surer way than the former, for that depending upon the houre or indeed the houre and minute of the Moones change (in which the Almanackes doe so much differ) must needes cause an errour in the observation of the [Page 18] time: and neither this way nor the former, can be per­formed upon any Plane besides the Equinoctiall, by rea­ [...]on of the inequality of angles in all other Planes, whose houre-lines make angles of intersection.

And now in the conclusion of this worke, thus much I say; that if the best inventions and conceits of men be haunted by some Momaicall Spirit at one time or other, as it is certaine they alwayes have beene and still are: Then sure I am, and I must not otherwise expect but that this of mine (being so meane in comparison of many that have beene so haunted) will be in the same case; yet I may care the lesse, because the best of all have beene sub­ject to Momus his censures: But whosoever hee be, that shall carpe hereat, or evilly censure it; if he can finde out any other more exact way for this kinde of Horologio­graphie than that which I have conceited and here deli­vered (it having not beene done before by any, for ought that I doe know or could ever heare) as I doubt he cannot for the reasons formerly alleadged; my request to him is, that he would be pleased to bestow a little paines in brin­ging of the same into light, and then I desire, that for ever after, this may (as deservedly it might) lye hidden in oblivion and dakenesse: In the meane season I com­mit these my poore endeavours to the courteous and fa­vourable acceptation of the friendly Reader and practi­tioner, saying to him, (concerning this matter) somewhat in effect as I sayd before,

Vive, vale, si quid novistirectius ist is,
Extrahito in lucem; si non, his utere mecum.

AN ADDITION CON­CERNING THE MA­KING AND VSE OF SEVE­rall plaine Scales, for the exact and most speedy mensuration of Circles, Spheres, and Cylinders, and for Gauging of Vessels.

1. FIrst, a Scale for the taking of the dia­meter of any Circle, and thereby to finde the superficiall content in foote measure.

2. The second, a Scale for the taking of the Axis or diameter of any Sphere or Bullet, and thereby to finde out the solide content in inch measure: and if I had the true proportions of metals, I could have fitted a Scale for every se­verall metall, so that the Axis of any Sphere or Bullet, being taken by his proper Scale and cubed, the cube should be the weight of the Bullet or Sphere proposed.

3. The third, a Scale or line for the finding of [Page 20] the solid content of any Cylinder in foote mea­sure, and that as speedily as of any Paralellepipe­don, by two multiplications onely.

4. The fourth a line or scale for thē giving of the solid content of any Cylinder in wine gallons.

5. The fifth for the same in Ale Gallons, and these by two multiplications onely.

The length of each Scale severally as followeth.

1. First, the length of the Scale for taking of the diameter of a Circle is 1. 1283. foote, that is, one foote and 1283. parts of a foote divided into 10000. parts: This scale or line, and likewise all the rest, must be first divided into ten equall parts and each of those parts subdivided into ten equall parts (after the usuall manner) and so the whole line or scale will containe 100. equall parts; or you may conceive each of those last ten parts to be di­vided also into ten other parts, and then the whole line is supposed to containe 1000. equall parts; but indeed 100. parts will be sufficient: Then know­ing the length of every line or scale, you may take that in your Compasses, & turne it over upon a Ru­ler, as many times as you shall thinke to be fitting.

The length of the
  • 2. For the Axis of a Sphere, 1. 2405. inch.
  • 3. For Cylinders. 1. 0838. foot.
  • 4. For Wine measure. 6. 65. inches.
  • 5. For Ale measure. 7. 02. inches.

The use of these severall Scales briefely in their order.

By the first Scale or line, having taken the dia­meter [Page 21] of any Circle proposed (whethēr in Pave­ment, Seeling, or the like) if you square that dia­meter (the whole line representing but one foote) the same shall be the superficiall content of the circle in foote measure, as nearely as can be found by any other way whatsoever.

So if the diameter taken, be 4. 25. of the scale, the supernaturall content of the Circle will be 18. 0625. foote. The like may be done for inch measure.

2. By the second scale, having taken the Axis or diameter of any Sphere or Bullet proposed: if you cube that Axis; the same cube shal be the so­lid content of the Sphere or Bullet in inch mea­sure.

So the Axis of a Sphere being 8. 50. of his scale; the solid content will be found to be 614. 125000. cubicall inches: the like may be made for foote measure.

3. By the 3. 4. and 5. scales; if the diameters and length be taken by their proper scales, and the square of the diameter be multiplyed in the length, the product thereof shall be the solid con­tent in foote measure, Wine gallons or Ale gal­lons, according to the qualitie of the scale and measure.

So if the length of a Cylinder be 12. 00. by the third scale, and the diameter 1. 75. the solide content thereof will be found to be 16. 7500. cu­bique feete: the like for inch measure.

Rules for Gauging of Vessels.

It is generally holden (and I my selfe have found by severall trialls) that a wine Gallon con­teineth 231. cubicall inches, or very neare there­upon; and that an Ale Gallon conteineth 272¼ cubicall inches in liquour.

The 1. Rule.

This rule is thē best and certainest of all other, and the way to prove other rules by, because it is grounded upon good demonstration, but withall it is somewhat tedious: See Mr. Oughtreds booke of the Circles of proportion.

The Rule is thus.

Adde the ⅓ of the Circle at the head, to ⅔ of the Circle at the bongue in inches; the summe of this addition being multiplyed by the length in in­ches, giveth the solide content in cubique inches, which being divided by 231 (if wine measure) or 272¼. (if Ale measure) the quotient is the content in Gallons.

The readiest way for the finding of the ⅓ and [...] of the superficiall contents of circles at the head and bongue, is this.

1. As 1. is to 0.5237.

So is the square of the diameter at the bonguē to ⅔ of the circle at the bongue.

2. As 1. is to 0.2619.

So is the square of the diameter at the head, to [...] of the circle at the head.

These ⅔ and ⅓ added together, makē thē meane Circle, whose diameter may (not unfitly) be cal­led a meane diameter: and thus much for the first.

The 2. Rule.

1. How to finde the meane or equated diameter which is thus.

Multiply the difference of the Diameters by 7, and adde the product to the diameter at the head; the summe thereof is the equated diameter.

Example. [...]

2. To finde the Content of any Vessell in Gal­lons.

First finde the equatēd diametēr, and square it; Then first by inch measure.

As 294. (if Wine measure) or 346. 5. (if Ale measure) are to the length in inches: So is the square of the equated diameter, to the content in Gallons.

The reason of these two numbers, is the same with that of a Circle to its circumscribing square, that is, as 11. to 14. wherefore, if the cubique inches contained in a Gallon be augmented by 14. and the product divided by 11. the quotient will yeeld a number, which shall be the Divisor. Now for the triall of this rule: Suppose a vessell to be in length. 39. 9. inches, the head, bongue and equated diameter as before; the square of the equated diameter is 1105. 9. which multiplyed in the length, giveth 44125. 41. cubique inches, which divided by 294. (if Wine measure) giveth in the quotient 150. 08. Gallons of Wine: but by the scale ensuing, the sayd vessell would con­taine but 149⅓. So is the difference about ⅔ of a Gallon, which being so small, is not to be regar­ded in the Art of gauging.

The third way which I havē found out for the more speedy working herein, is by a scale or line of equall parts onely, having reference to none other line in the taking of the measures: yet (if you please) you may make use of Master Gunters line of numbers, or the Table of Logarithmes in the casting up of the contents: or you may worke by naturall or decimall Arithmetique, as speedi­ly, as ever hath beene shewed by any scale here­tofore published: neither am I ignorant of Master Oughtreds Ruler, where he useth two lines; the one of inches, and the other of unequall parts. But to come to the purpose: This scale or line, is the fourth in place formerly mentioned, the scale [Page 25]

[figure]

it selfe being 6. 65. inches, which length being taken with a paire of compasses from a line of inches (where the inch is divided into an 100. equall parts) may be turned over 6. or 7. times (or more or lesse, as you shall thinke to be most convenient) upon a rod or Ruler, having an hooke at one end there­of, according to the usuall man­ner, and then beginning right un­der the end of the sayd hooke, runne the divisions towards the other end, and set thereunto the figures, 1. 2. 3. 4. &c. from the hooke towards that end, and set them likewise backwards from thence towards the hooke, as this present figure sheweth: Or you may allow somewhat for the thickenesse of both the heads of the Vessell, from the place right under the hooke, if you shall think it fitting. Every such part of the Ru­ler must be divided into 100. e­quall parts; so will it be made fit for this purpose: You may (if you please) place the line for Ale mea­sure, and also the line of numbers thereupon, which may there serve for some use as occasion shall re­quire.

The use of this Gauging Ruler is thus.

First finde the equated diameter, as before. Then multiply the square of the equated diameter by the length of the vessell; the product is the content in wine Gallons.

Example.

[...]

Another Example.

[...] [Page 27] [...] Equated diame­ter: Or I might here take 26, be­cause the fraction approacheth nigh unto an unitie: for in this kinde of mixt numbers, when the last figure of the fraction towards the left hand exceedeth the number of 5. there (to a­voyd the fraction) you may adde an unitie to the whole part thereof, and so make it an absolute number, and when it wants of 5. (as in the last fraction) you may (if you please) reject the fracti­on (which will breed no sensible errour in the worke) and retaine the whole number onely, or you may cut off all the figures (if there be many) saving the last two or three towards the left hand, and so make it onely a centesimall or millesimall fraction: So the fraction of the last number afore­going, may be onely. 24, which here signifieth very neare ¼ of a Gallon.

The question in this last example, is as difficult as most that you shall meete with of this kind, and therefore if this be rightly understood, all other questions of the same nature may be easily under­stood.

Here I might have shewed the use of some o­ther scales for this purpose, and likewise the man­ner of taking the diameters of vessels at the head and bongne by this Ruler, but that this is a thing [Page 28] not unknowne to such as are exercised in gauging of Vessels, the same being fully shewed in bookes of gauging already published and therefore mine intention was not, here to set downe the whole Art of gauging, but briefely to shew the making and use of this gauging Ruler, which was never published before, although I could have set forth the same long before this time; and there­fore if any shall thinke good to make tryall of this or any of the rest which I have here delivered, let them speake of them according to what they shall finde in them, and not otherwise.

These two severall workes (friendly Reader) contained in this booke and so presented to thy view, being (each of them) but of a small quantity, and also as novelties, we have therefore thought it meete and commodious thus to connect them.

FJNJS.

ERRATA.

PAge 4. line 3. read, but at contrary. p. 5. l. 2. r. positions. l. 28. r. Meridian. p. 16. l. 29. read this his dyall. p. 17. l. 14. r. conve­niently be 15. or 20. l. 28. for let r. set. p. 21. l. 8. for supernaturall r. superficiall. l. 21. r. lengths.

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