THE DESCRIPTION AND USE OF THE double horizontal Dial.  
TO THE MOST NOBLE, AND HOPEFUL GENTLEMAN Sr. WILLIAM HOWARD KNIGHT OF THE BATH, AND SON TO THE RIGHT HONOURABLE AND ILLUSTRIOUS LORD, THOMAS EARL OF ARUNDEL AND SURREY, EARL MARSHAL OF ENGLAND, etc.  
LONDON, Printed by M. FLESHER. MDCXXXII.   

The description, and use of the double horizontal dial.  
THere are upon the Plate two several Dial's. That which is outermost, is an ordinary dyal, divided into hours and quarters, & every quarter into three parts which are five minutes apiece: so that the whole hour is understood to contain 60. minutes. And for this Dial the shadow of the upper obliqne, or slanting edge of the style, or cock, doth serve.  
The other dyal, which is within, is the projection of the upper Hemisphere, upon the plain of the Horizon: the Horizon itself is understood to be the innermost circle of the limb: and is divided on both sides from the points of East and West into degrees, noted with 10.20.30. etc. as fare as need requireth: And the centre of the Instrument is the Zenith, or Vertical point.  
Within the Horizon the middle strait line pointing North and South, upon which the style standeth is the Meridian, or twelve a clock line: and the other short arching lines on both sides of it, are the hour lines, distinguished accordingly by their figures: and are divided into quarters by the smaller lines drawn between them: every quarter containing 15. minutes.  
The two arches which cross the hour lines, meeting on both sides in the points of intersection of the six a clock lines with the horizon, are the two semicircles of the Ecliptic or annual circle of the sun: the upper of which arches serveth for the Summer half year; and the lower for the winter half year: and are therefore divided into 365. days: which are also distinguished into twelve months with longer lines, having their names set down: and into tenths and fifts with shorter lines: and the rest of the days with pricks as may plainly be seen in the dial.  
And this is for the ready finding out of the place of the Sun every day: and also for the showing of the Sun's yearly motion because by this motion the sun goeth round about the heavens in the compass of a year, making the four parts, or seasons thereof, namely the Spring in that quarter of the Ecliptic which begins at the intersection on the East side of the dial, & is therefore called the Vernal intersection. Then the Summer in that quarter of the Ecliptic. which beginneth at the intersection with the Meridian in the highest point next the Zenith. After that Autumn in that quarter of the Ecliptic which beginneth at the intersection on the West side of the dial, and is therefore called the Autumnal intersection: and lastly the Winter in that quarter of the Ecleptic, which beginneth at the intersection with the Meridian in the lowest point next the Horizon.  
But besides this yearly motion, the Sun hath a diurnal or daily motion, whereby it maketh day and night, with all the diversities and inaequalities thereof: which is expressed by those other circle's drawn cross the hour lines; the middlemost whereof, being grosser than the rest meeting with the Ecliptic in the points of the Vernal, and Autumnal intersections, is the Equinoctial: and the rest on both sides of it are called the parallels, or diurnal arches of the sun, the two outermost whereof are the Tropics, because in them the sun hath his furthest digression or Declination from the Equinoctial, which is degrees 23. ½: and thence beginneth again to return towards the Equinoctial. The upper of the two Tropics in this our Northern hemisphere is the Tropic of Cancer and the sun being in it, is highest into the North, making the longest day of Summer: And the lower next the horizon is the Tropic of Capricorn; and the sun being in it is lowest into the South, making the shortest day of winter.  
Between the two Tropics and the Equinoctial, infinite such parallel circles are understood to be contained: for the Sun, in what point soever of the Ecliptic it is carried, describeth by his lation a circle parallel to the Equinoctial: yet those parallels which are in the instrument, though drawn but to every second degree of declination, may be sufficient to direct the eye in magining and tracing out through every day of the whole year in the Ecliptic, a proper circle which may be the diurnal arch of the sun for that day. For upon the right estimation of that imaginary parallel doth the manifold use of this instrument especially rely: because the true place of the sun all that day is in some part or point of that circle. Wherefore for the better conceiving and bearing in mind thereof, every fift parallel is herein made a little grosser than the rest.  
For this inner dial serveth the shadow of the upright edge of the style; which I therefore call the upright shadow.  
And thus by the eye and view only to behold and comprehend the course of the sun, throughout the whole year both for his annual and diurnal motion, may be the first use of this instrument.  

TWO use. To find the declination of the sun every day.  
Look the day of the month proposed in the Ecliptic, and mark how many degrees the prick showing that day, is distant from the Equinoctial, either on the Summer or winter side. viz. North or South.  
Example 1. What will the declination of the sun be upon the eleventh day of August? Look the eleventh day of August, & you shall find it in the sixth circle above the Equinoctial: Now because each parallel standeth (as hath been said before) for two degrees, the sun shall that day decline Northwards 12. degrees.  
Example 2. What declination hath the Sun upon the 24. day of March? Look the 24. day of March, and you shall find it between the second & third northern parallels, as it were an half and one fift part of that distance from the second: Reckon therefore 4. degrees for the two circles, and one degree for the half space: So shall the Sun's declination be five degrees, and about one fift part of a degree northward that same day.  
Example 3. What declination hath the Sun upon the 13. day of November? Look the 13. day of Novemb. and you shall find it below the Aequinoctial ten parallels, and about one quarter which is 20. degrees and an half southward. So much is the declination. And according to these examples judge of all the rest.   

III. Use. To find the diurnal arch, or circle of the sun's course every day.  
The sun every day by his motion (as hath been said) describeth a circle parallel to the Equinoctial, which is either one of the circles in the dial, or somewhere between two of them. First therefore seek the day of the month; and if it fall upon one of those parallels; that is the circle of the Sun's course that same day: But if it fall between any two of the parallels, imagine in your in inde, and estimate with your eye, another parallel through that point between those two parallels keeping still the same distance from each of them  
As in the first of the three former examples, The circle of the Sun's course upon the 11. of August, shall be the very sixth circle above the Equinoctial toward the centre.  
In example 2. The circle of the sun's course upon the 24. of March shall be an imaginary circle between the lecond and third parallels, still keeping an half of that space, and one fift part more of the rest, from the second.  
In example 3. The circle of the Sun's course upon the 13. of Novemb: shall be an imaginary circle between the tenth and eleventh parallels below the Equinoctial, still keeping one quarter of that space from the tenth.   

FOUR Use. To find the rising and setting of the sun every day.  
Seek out (as was last showed) the imaginary circle or parallel of the sun's course for that day, and mark the point where it meeteth with the horizon, both on the East and West sides, for that is the very point of the Sun's rising, and setting that same day, and the hour lines which are on both sides or it, by proportioning the distance reasonably, according to 15. minutes for the quarter of the hour, will show the hour of the Sun's rising on the East side, & the Sun's setting on the West side.   

V use. To know the reason and manner of the Intreasing and decreasing of the days & nights throughout the whole year:  
When the Sun is in the Equinoctial, it riseth and setteth at 6. a clock, for in the instrument the intersection of the Equinoctial, and the Ecliptic with the Horizon is in the six a clock circle on both sides. But if the sun be out of the Equinoctial declining toward the North, the intersections of the parallel of the sun with the horizon is before six in the morning, and after 6. in the evening: and the diurnal arch greater than 12. hours; and so much more great, the greater the northern declination is. Again, if the sun be declining toward the South, the intersections of the parallel of the Sun, with the horizon▪ is after six in the morning and before six in the evening: and the diurnal arch lesser than 12. hours; and by so much lesser, the greater the southern declination is.  
And in those places of the Ecliptic in which the Sun most speedily changeth his declination, the length also of the day is most altered: and where the Ecliptic goeth most parallel to the Equinoctial changing the declination, but little altered. As for example, when the sun is near unto the Equinoctial on both sides, the day's increase and also decrease suddenly and apace; because in those places the Ecliptic inclineth to the Equinoctial in a manner like a straight line, making sensible declination. Again when the sun is near his greatest declination, as in the height of Summer, and the depth of winter, the days keep for a good time, as it were, at one stay, because in these places the Ectiptic is in a manner parallel to the Equinoctial, the length of the day also is but little scarce altering the declination: And because in those two times of the year, the Sun standeth as it were still at one declination, they are called the summer solstice, and winter solstice. And in the mean space the nearer every place is to the Equinoctial, the greater is the diversity of days.  
Wherefore we may hereby plainly see that the common received opinion, that in every month the days do equally increase, is erroveous.  
Also we may see that in parallels equally distant from the Equinoctial, the day on the one side is equal to the night on the other side.   

VI Use. To find how fare the sun riseth, and setteth from the true East and west points, which is called the suns. Amplitude ortive; and occasive.  
Seek out (as was showed in III. use) the imaginary circle, or parallel of the sun's course, and the points of that circle in the horizon, on the East and West sides cutteth the degree of the Amplitude ortive, and occasive.   

VII. Use. To find the length of every day and night.  
Double the hour of the Sun's setting, and you shall have the length of the day; and double the hour of the Sun's rising, and you shall have the length of the night.   

VIII. Use. To find the true place of the sun upon the dial, that is, the point of the instrument which answereth to the place of the sun in the heavens at any time. which is the very ground of all the questions following.  
If the dial be fixed upon a post: Look what a clock it is by the outward dial, that is, look what hour and part of hour the shadow of the slanting edge of the style showeth in the outward limb. Then behold the shadow of the upright edge, and mark what point thereof is upon that very hour, and part in the inner dial among the parallels, that point is the true place of the Sun at the same instant.  
If the dial be not fixed, and you have a Meridian line noted in any window where the Sun shineth: place the Meridian of your dial upon the Meridian line given, so that the top of the style may point into the North and so the dial is as it were fixed, wherefore by the former rule you may find the place of the sun upon it.  
If the dial be not fixed, neither you have a Meridian line but you know the true hour of the day exactly: hold the dyal even and parallel to the horizon, moving it till the slanting edge of the style cast his shadow justly upon the time or hour given: for then the dial is truly placed, as upon a post. Seek therefore what point of the upright shadow falleth upon that very hour, and there is the place of the Sun.  
But if your dial be lose, and you know neither the Meridian nor the time of the day. Frist, by the day of the month in the Ecliptic find the sun's parallel, or diurnal arch for that day, then holding the dial level to the horizon, move it every way until the slanting shadow of the style in the outward limb, and the upright shadow in the sun's diurnal arch, both show the very same hour and minute, for that very point of the sun's parallel, which the upright shadow cutteth, is the true place of the Sun on the dyal at that present.  
But note that by reason of the thickness of the style, and the bluntness of the angle of the upright edge, the Sun cannot come unto that edge for some space before and after noon. And so during the time that the sun shineth not on that upright edge, the place of the Sun in the dial cannot be found. Wherefore they that make this kind of double dial, are to be careful to file the upright edge of the style as thin & sharp as possible may be.  
That which hath here been taught concerning the finding out the sun's true place in the dyal, ought perfectly to be understood, that it may be readily, and dexterously practised, for upon the true performance thereof dependeth all that followeth.   

IX. Use. To find the hour of the day.  
If the dial be fastened upon a post: the hour by the outward dial, or limb is known of every one: & the upright shadow in the sun's parallel, or diurnal arch will also show the very same hour.  
But if the dial be lose, either hold it or set it parallel to the horizon, with the style pointing into the North and move it gently every way until the hour shown in both dial's exactly agreeth, or which is all one, find out the true place of the sun upon the dial, as was taught in the former question, for that point among the hour lines showeth the hour of the day.   

X. Use. To find out the Meridian, and other points of the compass.  
First you must seek the true hour of the day (by the last question) for in that situation the Meridian of the dial standeth directly North and South: and the East pointeth into the East, and the west into the west, and the rest of the points may be given by allowing degr: 11. ¼ unto every point of the compass.   

XI. Use. To find out the Azumith of the sun, that is the distance of the Vertical circle, in which the sun is at that present, from the Meridian.  
Set your dial upon any plain or flat which is parallel to the horizon, with the Meridian pointing directly North and South, as was last showed: then follow with your eye the upright shadow in a straight line, till it cutteth the horizon: for the degree in which the point of intersection is, shall show how fare the suns Azumith is distant from the East and west points, and the compliment thereof unto 90. shall give the distance thereof from the Meridian.   

XII Use. To find out the Declination of any Wall upon which the sun shineth, that it, how fare that wall swerveth from the North or South, either Eastward or Westward.  
Take a board having one straight edge, & a line strike perpendicular upon it; apply the straight edge unto the wall at what time the sun shineth upon it, holding the board parallel to the horizon: Set the dyal thereon, & move it gently every way, until the same hour and minute be showed in both dials: and so let it stand: then if the dyal have one of the sides parallel to the Meridian, strike a line along that side upon the board, crossing the perpendicular, or else with a bodkin make a point upon the board, at each end of the Meridian, and taking away the instrument from the board, and the board from the wall, lay a ruler to those two points, & draw a line crossing the perpendicular: for the angle which that line maketh with the perpendicular, is the angle of the declination of the wall. And if it be a right angle, the wall is exactly East or west: But if that line be parallel to the perpendicular, the wall is direct North or South without any declination at all,  
You may also find out the declination of a wall, if the dial be fixed on a post not very fare from that wall; in this manner. Your board being applied to the wall, as was showed, hang up a thread with a plummet, so that the shadow of the thread may upon the board cross the perpendicular line: make two pricks in the shadow & run instantly to the dial and look the horizontal distance of the suns Azumith, or upright shadow from the Meridian. Then through the two pricks draw a line crossing the perpendicular: and upon the point of the intersection, make a circle equal to the horizon of your instrument, in which circle you shall from the line through the two pricks measure the horizontal distance of the upright shadow, or Azumith from the Meridian, that way toward which the Meridian is: draw a line out of the centre, to the end of that arch measured: and the angle which this last line maketh with the perpendicular, shall be equal to the declination of the wall.   

XIII. Use. How to place the dial upon a post without any other direction but itself.  
Set the dial upon the post, with the style into the North, as ne'er as you can guess: then move it this way and that way, till the same hour and minute be showed, both in the outward & inward dials, by the several shadows, as hath been already taught, for then the dyal standeth in its truest situation; wherefore let it be nailed down in that very place.   

XIIII. Use. To find the height of the Sun at high noon every day.  
Seek out the diurnal arch or parallel of the sun's course, for that day (by use III) and with a pair of compasses setting one foot in the centre, & the other in the point of intersection of that parllel with the Meridian, apply that same distance, unto the samidiameter divided, for that measure shall therein show the degree of the sun's altitude above the horizon that day at high noon.   

XV. Use. To find the height of the sun at any hour or time of the day.  
Seek out the diurnal arch, or parallel of the sun's course for that day: and mark what point of it is in the very hour & minute proposed. And with a pair of compasses, setting one foot in the centre, and the other in that point of the parallel, apply the same distance unto the semidiameter divided: for that measure shall show the degree of the sun's altitude above the horizon at that time.  
And by this means you may find the height of the sun above the horizon at every hour through out the whole year for the making of rings and cylinders and other instruments which are used to show the hour of the day.   

XVI. Use The height of the sun being given to find out the hour, or what it is a clock.  
This is the converse of the former; seek therefore in the semidiameter divided the height of the sun given. And with a pair of compasses setting one foot in the centre and the other at that height, apply the same distance, unto the diurnal arch, or parallel of the sun for that day: for that point of the diurnal arch, upon which that same distance shall light, is the true place of the sun upon the dyal; and showeth among the hour lines, the true time of the day.   

XVII. Use. Considerations for the use of the instrument in the night.  
In such questions as concern the night, or the time before sun rising, and after sun setting, the instrument representeth the lower hemisphere, wherein the southern pole is elevated. And therefore the parallels which are above the Equinoctial toward the centre, shall be for the southern, or winter parallels: and those beneath the Equinoctial, for the Northern or Summer parallels; and the East shall be accounted for West, and the west for East; altogether contrary to that which was before, when the instrument represented the upper hemisphere.   

XVIII. Use. To find how many degrees the sun is under the horizon at any time of the night.  
Seek the declination of the sun for the day proposed (by use II.) And at the same declination on the contrary side imagine a parallel for the Sun that night: and mark what point of it is in the very hour & minute proposed: And with a pair of compasses, setting one foot in the centre, and the other in that point of the parallel, apply that same distance unto the semidiameter divided: for that measure shall show the degree of the sun's depression below the horizon at that time.   

XIX. Use. To find out the length of the Crepusculum, or twilight, every day.  
Seek the declination of the sun for the day proposed (by use II.) And at the same declination on the contrary side imagine a parallel for the sun that night. And with a pair of compasses setting one foot in the centre, and the other at 72. degrees upon the semidiameter divided, apply that same distance, unto the sun's nocturnal parallel: for that point of the parallel, upon which that same distance shall light, sheweth among the hour lines, the beginning of the twilight in the morning, or the end of the twilight in the evening.   

XX. Use. If the day of the month be not known, to find it out by the dial.  
For the working of this question, either the dial must be fixed rightly on a post, or else you must have a true Meridian line drawn in some window where the sun shineth, wherefore supposing the dial to be justly set either upon the post, or upon the Meridian, Look what a clock is it by the outward dyal, and observe what point of the upright shadow falleth upon the very same minute in the inner dial, and through that same point imagine a parallel circle for the sun's course; that imaginary circle in the Ecliptic shall cut the day of the month.  
These Instrumental dial's are made in brass by Elias Allen dwelling over against St. Clement's Church without Temple-bar.   
FINIS.