HOROLOGIOGRAPHIA NOCTURNA. OR LUNAR HOROLOGIOGRAPHIE. Set forth and demonstrated (after a twofold manner) in the horizontal Plane only. Upon which (and all other by the same reason) may in a manner, as plainly and speedily be discerned the t●mes of the Night by the Gnomonicall shadow, caused by the Moon, as the times of the Day upon any by the Sun: Serving as well in the day time for the Sun. By JOHN WYBERD. Together with an Addition of certain new and brief Rules for the exact and most speedy mensuration of Circles and Spheres, and also Cylinders, both in solid and liquid measure, by certain plain Scales only, 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 horizontal LUNAR DIAL. Place this Figure next after page ●● The hours in every Circle, are continued on both sides of the Meridian line, so fare as the houre-lines for the Sun do extend, that so the Dial might serve generally for all times of the year; and though the hour of 12. falleth twice in some of them, yet may they both be useful at one time of the year or other; for to place in such hours only as shall happen to be of use, and neither more nor less, is a thing I conceive not to be certainly done by reason of the uncertain rising and setting of the Moon, and her uncertain departure from the rays of the Sun. Having noted down the hours in every circle (as in the second figure) add 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 hours and their parts (according to the usual manner) and the figures belonging to them: but in the latter way you must add to each circle, three other inward circles, making three several spaces for the three ranks 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 said 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 between every several Dial or circle of hours, to distinguish between them, and not to mingle and confound them one with another. The parts of every hour necessary to be placed on the Dial (though we have put none here, partly to avoid tediousness in the work, and some charge in cutting the figures, and partly because the are needless in this place) may be those which we have formerly used, or better it were for common use to have each hour divided into some equal number of parts, as four or eight parts, as is usually done in most Sun-dyals'; for before we divided each hour into five parts, as being the fittest number for the more easy and exact making of the Dial. The outermost circle of all, belonging to the fifteenth day of the Moon or day of opposition, serveth aswell for the Sun, the houre-lines thereof being rightly disposed for the Sun. For the Moon, on the day of her coujunction with the Sun, cometh to the Meridian much about the time that he doth, and in the day of her opposition to the Sun, she cometh to the said place at the opposite time or thereabout, when the Sun is in the North point of the Meridian circle, under the earth▪ or our Horizon, that is, at our Midnight or 12. of the clock (as the former Table showeth) and then the same Dial which serveth to show the hour of the day by the Sun, serveth likewise to show the hour of the night by the Moon, though not always 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 Moon's aforesaid mediation or culmination, is not always the same, but altereth on every day, and therefore that Dial which should serve to show the hours or times of any other night by the Moon, must (of necessity) be altered, and the houte-lines be otherwise ordered and disposed, or else why should not the Moon in any night when she shineth, show the true hours thereof upon any true Sunne-Dyall by the stilar shadow, aswell as the Sun showeth the true hours of any day by the same; which thing, how fare it is from being so, I think there is scarcely no ordinary man that doth not know it; the reason thereof being (as I shown before) because the Moon doth not always observe the same times with the Sun, in her rising, Southing, and setting. These several Dial's or circles of hours, may not only be delineated upon the horizontal Plane, to show the time of the night by the Moon, 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 Dial's for the Moon) and most readily upon the Equinoctial 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 fifteen concentrical circles formerly used, here must be fifteen parallel right lines, of which the equinoctial line of the Plane, may very fitly be one, which may (if you please) serve for the fifteenth day of the Moon, and so will serve continually for the Sun by the reason aforesaid: So the seven Parallels falling under the said line, may then fitly serve for the seven days next enfuing the day of her change and Full, and the seven Parallels above the said line, for the seven days next before the Full, and the change next following: or you may begin at the uppermost parallel on the Plane, and account that for one day and sixteen days of the Moon, and so going downwards, the lowest parallel will be for fifteen and thirty days, and so for the Sun, and then the equinoctial line or middle parallel shall be for eight and 23. days, for you may begin with what parallel you will: then drawing the common houre-lines of these Planes, and dividing each hour● into five parts (as before) the hours for the Moon 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 fare as the houre-lines for the Sun do extend) with as much facility as in any other Plane whatsoever, the Equinoctial plane being excepted; so that you be careful to place the right hours in these planes: Having thus set down the hours (and parts if you please) draw to each Parallel line another parallel including a convenient space between them, wherein to draw little lines or strokes for the hours and their parts, and to place the figures belonging to the houre-lines or strokes: But for that I shown before, how this might be performed by five circles in the horizontal plane, so by the same reason it may here be performed by five parallels only, for then each parallel serveth for six days, and the houre-lines of each parallel are of a threefold denomination, and then you must draw to each parallel line, three other parallels, that so there may be three fitting spaces made for the placing of three rows of figures which belong to the houre-lines of every parallel, as was done by circles in the horizontal plane; and in the delineating of any of these Dial's, it were convenient for you first to draw the common (or Solar) houre-lines belonging to the plane, obscurely with the point of your compass or such like thing upon your plane, by which you may easily discern whether you work rightly or not: But to deliver any figure here concerning these last mentioned planes I think it to be needless, 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 style 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 amiss) that so the shadow thereof may always extend as fare as the parallel lines on the Plane; for though a strait round pin will serve in these Planes for a style for the Sun, yet it will not for the Moon, by reason of the variety of Dial's on one and the self sam● Plane, all differing one from another: But indeed none other is so commodious for common use as the horizontal Dial, which may (most easily) be fitted for use two manner of ways: For it may be either always fixed abroad, like unto the common horizontal Sundial, and so be , or else not fixed, but to be removed up and down at pleasure, and then having a Magnetical Needle placed in a Box after the usual manner (whose Meridian line ought to be drawn therein, according to the deflection or variation of the Needle in the place of observation) to be affixed to some side thereof, it may be truly placed thereby, any night when it should be used, being holden or set precisely horizontal; or (for want of such a Needle) they that have an horizontal Sunne-Dyall about their house truly placed, may make a shift to use it well enough, by laying it flat upon that Dial, and then applying one side thereof to the side of the cock or ftile of that Dial, in such sort that the Meridian line of the one may be parallel to the Meridian line of the other. But indeed the most absolute way of all, were to have it made in brass (which may be done by Mr. Elias Allen dwelling without Temple Bar, over against St. Clement's Church, London, who maketh all sorts o● Mathematical Instruments and also horizontal Sunne-dyalls' in brass) and fixed always upon a post, or rather made upon a fair white stone, where the strokes for the hours and their parts and the figures belonging to them being done in black or other such notable colour, might be more perfectly discerned than in the other: So that then only knowing the day of the Moon, (which may be known by any Almanac) you have no more to do, (the Moon shining on the Plane) but to look out the circle which is appropriated to that day, and the shadow of the style will presently give you the hour or time of the night, if your Dial be rightly made and placed: And it would be very comely and convenient to have the style to this Dial made so, as it should touch the plane in those places only where it is let into the same, that is, between the centre and the circle next unto it, and again a little about the outermost circle which is furthest from the centre, that so the strokes for the hours and their parts, and the figures which fall upon or very near the Meridian line, might not be hidden and defaced by the style. But because houre-lines may be placed generally upon all planes (as I said before) to show the hours of the night by the Moon; it would be an excellent way to have a Lunar Dial drawn on glass 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 Chancery Lane, near Holborn (being the author of the ensuing work or Addition) who likewise will be able to perform these as accurately as the other, if it shall be required of him: For there the plane of the Dial being of a transparent matter, and intercepted (as a mean object) between the eye and the Moon, the houre-stroakes and figures, together with the shadow of the style, may be thereupon more perfectly and speedily discerned, than upon any other kind of Plane whatsoever (and therefore I thought it not amiss to give notice thereof) but it is well known that the shadow which is caused by the Moon, cannot be altogether so perfectly discerned as that which is caused by the Sun, because the light of the Moon is not so perfect as the light of the Sun, and therefore the time of the day may be somewhat more readily perceived on the Dial by the stilar shadow, than the time of the night; yet it may be very easily discerned thereby, especially when the Moon shineth out very bright. And now, this our horizontal Dial I conceive (and I think, that any man of understanding will acknowledge) to be fare more easy and ready in use, than that Lunar Dial which Mr. Fale hath long ago described, in his book of Solar Horologiographie, whose position must be in direct Paralellisme to the Equinoctial circle of the Sphere, making the same angle (of inclination) with the Plane of the Horizon, which that doth, being the compliment of the Latitude or Polar altitude, and therefore but few men know how to make use thereof in comparison of them that do not know; and it must needs be troublesome also to those that do 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, unless the same stand always fixed abroad in its due position; and if it so do, yet the unskilful sort cannot well tell how to make use of it, by reason (it consisting of two several parts or plates) of the inward movable part thereof, turning about within the outmost plate, and upon which the houre-lines are drawn, whose Index, (or long tooth, as he termeth it) being fastened at the hour of 12. must be turned to the day of the Moon noted on the outermost or fixed part, and to the hour of the change (as he saith) accounting from 12. of the clock; in which he hath not sufficiently expressed the meaning thereof, for such as are but meanly skilled in these things, to understand, and so (as I conceive) hath not well declared the making and use of the same. Upon the outermost or fixed part, he draweth a circle, which he divideth into 30. parts for the thirty days of the Moon, after this manner: Now because (saith he) the Moon finisheth her course in 29. days, 12. hours, and 44. minutes, (that is, from the Sun, being in a mean conjunction with him, till she be with him again by the like conjunction) part or divide the aforesaid circle into 30. parts, so as 29. of them being equal, the thirtieth or last must not be so great as one of the other parts by ⅓, that is, it must contain ⅔ of one of them; by which account (if it were true) the Moon should finish her said course in 29. days, and 16. hours, (which make ⅔ of the natural day) whereas the same is but 29. days, and 12. hours, or ½ of the day natural, and about ¾ of an hour over, and therefore it doth not consequently follow, that the last part should contain ⅔ of one of the rest, but rather ½ only: Indeed (for mine own part) I must confess, I never made trial of this Dial, and therefore can say the less of it, neither do I know whether the same were of his own devising or not; But sure I am that this our horizontal Dial is every way as exact as that, and serveth to a more general use, it being of use and delight for all sorts of men, and more especially ●uch as know not how to find the hour of the night artificially by other ways: for if they can but know how to get the true age of the Moon (which is easily done by an Almanac, as I said before) they may as easily obtain the time of the night by this Dial (or the like made upon any other Plane, when the Moon shineth thereupon; and that sufficiently enough) as the time of the day by any Sunne-dyall when the Sun shineth on the same: But if any list to make use of such a kind of Dial, as that of Mr. Fales, lately mentioned, they may use another way to find the time of the night more exactly thereby: For the houre-lines being drawn upon the movable or turning plate or wheel (as before is said) which should now be so large as each hour may be distinctly divided into such a number of parts, as that you may guess at any one minute thereupon, (which may conveniently 15. or 20. parts, for then each part will contain but four or three prime minutes of time) If they can have a Table of the Moons coming to their Meridian artificially and exactly calculated for every day in the year, and so for every year severally (which in some years is to be found in one Almanac or other, if trust may be given to them) then to make use of this Dial in any night of the year when the Moon shineth, they must look out that day in the said Table, and right against it, under its proper month is set the hour and minute of the Moons coming unto the Meridian for that day and place: then the Dial being rightly placed if they bring that hour and minute noted on the inward or movable part to the Meridian line noted on the outtermost or part, and so let the houre-lines in that position, the shadow of the style shall show the hours of that night exactly, without having any regard to the days of the Moon's age, noted upon the uppermost part, as in the former, and therefore this must needs be a surer way than the former, for that depending upon the hour or indeed the hour and minute of the Moon's change (in which the Almanacs do so much differ) must needs cause an error in the observation of the time: and neither this way nor the former, can be performed upon any Plane besides the Equinoctial, 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 work, 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 certain they always have been and still are: Then sure I am, and I must not otherwise expect but that this of mine (being so mean in comparison of many that have been so haunted) will be in the same case; yet I may care the less, because the best of all have been subject to Momus his censures: But whosoever he be, that shall carp hereat, or evilly censure it; if he can find out any other more exact way for this kind of Horologiographie than that which I have conceited and here delivered (it having not been done before by any, for aught that I do know or could ever hear) as I doubt he cannot for the reasons formerly alleged; my request to him is, that he would be pleased to bestow a little pains in bringing of the same into light, and then I desire, that for ever after, this may (as deservedly it might) lie hidden in oblivion and dakenesse: In the mean season I commit these my poor endeavours to the courteous and favourable acceptation of the friendly Reader and practitioner, saying to him, (concerning this matter) somewhat in effect as I said before, Vive, vale, si quid novistirectius ist is, Extrahito in lucem; si non, his utere mecum. AN ADDITION CONCERNING THE MAKING AND USE OF Several plain 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 find the superficial content in foot measure. 2. The second, a Scale for the taking of the Axis or diameter of any Sphere or Bullet, and thereby to find out the content in inch measure: and if I had the true proportions of metals, I could have fitted a Scale for every several metal, 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 the solid content of any Cylinder in foot measure, and that as speedily as of any Paralellepipedon, by two multiplications only. 4. The fourth a line or scale for them 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 only. 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. foot, that is, one foot and 1283. parts of a foot divided into 10000 parts: This scale or line, and likewise all the rest, must be first divided into ten equal parts and each of those parts subdivided into ten equal parts (after the usual manner) and so the whole line or scale will contain 100 equal 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 contain 1000 equal parts; but indeed 100 parts will be sufficient: Then knowing the length of every line or scale, you may take that in your Compasses, & turn it over upon a Ruler, as many times as you shall think 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 several Scales briefly in their order. By the first Scale or line, having taken the diameter of any Circle proposed (whethenr in Pavement, Ceiling, or the like) if you square that diameter (the whole line representing but one foot) the same shall be the superficial content of the circle in foot measure, as nearly as can be found by any other way whatsoever. So if the diameter taken, be 4. 25. of the scale, the supernatural content of the Circle will be 18. 0625. foot. 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 shall 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. cubical inches: the like may be made for foot 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 multiplied in the length, the product thereof shall be the solid content in foot measure, Wine gallons or Ale gallons, according to the quality 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 content thereof will be found to be 16. 7500. cubique feet: the like for inch measure. Rules for Gauging of Vessels. It is generally holden (and I myself have found by several trials) that a wine Gallon containeth 231. cubical inches, or very near thereupon; and that an Ale Gallon containeth 272¼ cubical inches in liquor. The 1. Rule. This rule is then best and certainest of all other, and the way to prove other rules by, because it is grounded upon good demonstration, but withal it is somewhat tedious: See Mr. Oughtreds book of the Circles of proportion. The Rule is thus. Add the ⅓ of the Circle at the head, to ⅔ of the Circle at the bongue in inches; the sum of this addition being multiplied by the length in inches, giveth the 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 superficial 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 bonguen 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, maken them mean Circle, whose diameter may (not unfitly) be called a mean diameter: and thus much for the first. The 2. Rule. 1. How to find the mean or equated diameter which is thus. Multiply the difference of the Diameters by 7, and add the product to the diameter at the head; the sum thereof is the equated diameter. Example. 2. To find the Content of any Vessel in Gallons. First find the equatend diametenr, 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 yield a number, which shall be the Divisor. Now for the trial of this rule: Suppose a vessel 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 multiplied 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 said vessel would contain 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 use of this Gauging Ruler is thus. First find the equated diameter, as before. Then multiply the square of the equated diameter by the length of the vessel; the product is the content in wine Gallons. Example. Another Example. Equated diameter: Or I might here take 26, because the fraction approacheth nigh unto an unity: for in this kind of mixed numbers, when the last figure of the fraction towards the left hand exceedeth the number of 5. there (to avoid the fraction) you may add an unity 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 error in the work) and retain the whole number only, 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 only a centesimall or millesimall fraction: So the fraction of the last number aforegoing, may be only. 24, which here signifieth very near ¼ of a Gallon. The question in this last example, is as difficult as most that you shall meet 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 showed 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 not unknown to such as are exercised in gauging of Vessels, the same being fully showed in books of gauging already published and therefore mine intention was not, here to set down the whole Art of gauging, but briefly to show 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 think good to make trial of this or any of the rest which I have here delivered, let them speak of them according to what they shall find in them, and not otherwise. These two several works (friendly Reader) contained in this book and so presented to thy view, being (each of them) but of a small quantity, and also as novelties, we have therefore thought it meet 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 dial. p. 17. l. 14. r. conveniently be 15. or 20. l. 28. for let r. set. p. 21. l. 8. for supernatural r. superficial. l. 21. r. lengths.