Horlogiographia optica. Dialling universall and particular: speculative and practicall. In a threefold præcognita, viz. geometricall, philosophicall, and astronomicall: and a threefold practise, viz. arithmeticall, geometricall, and instrumentall. With diverse propositions of the use and benefit of shadows, serving to prick down the signes, declination, and azimuths, on sun-dials, and diverse other benefits. Illustrated by diverse opticall conceits, taken out of Augilonius, Kercherius, Clavius, and others. Lastly, topothesia, or, a feigned description of the court of art. Full of benefit for the making of dials, use of the globes, difference of meridians, and most propositions of astronomie. Together with many usefull instruments and dials in brasse, made by Walter Hayes, at the Crosse Daggers in More Fields. / Written by Silvanus Morgan.

CHAP XIII.

Of the generall description and use of the preceding Tablein, the pricking down and drawing the circles of decli∣nation and Aximuths in any planes.

THe Table you see consisteth of 11 columns, the first being the minutes of the Suns altitude, and the greater figures on the top are the de∣grees of altitude, all the other columns consist of the parts of shadow, and minutes of shadow, noted above with S for shadow, and p m for parts and minutes of shadow, answerable to a gnomon divided into 12 equall parts, and it is, As the sine of a known altitude of the sun, is to the sine complement of the same altitude; so the length of the Gnomon in 10 or 12 parts, to the parts of right shadow: or for the versed shadow, as the sine complement of the given altitude of the sun, to the right sine of the same altitude; so the style in parts, to the length of the versed shadow So if we enter the Table with the given altitude of the Sun in the great figures, and if we seeke the mi∣nutes in the sides, either noted with horizontall or verti∣call shadow, according as your plane is, it shall give you the length of the shadow in parts and minutes in the com∣mon angle of meeting together. As if we look for 50 de. 40 m. the meeting of both in the Table shall be 9 parts 50 min. for the length of the right shadow on a horizontall plane: But for the versed shadow, take the complement of the altitude of the Sun, and the minutes in the right side of the Table, titled verticall shadow, and the common area of both shall give your desire. By this Table it appeareth

first, that the circles of altitude either on the horizontall or verticall planes are easily drawn, consicering they are no∣thing else but circles of altitude, which by knowing the al∣titude you will know the length of the shadow, which in the horizontall Diall are perfect circles, and have the same respect unto the Horizon, as the parallels of declination have to the Equator, but in all upright planes they wil be conicall Sections, and by having the length of the style, the altitude of the Sun may be computed by the foregoing Table with much facility, but for the more expediating of the work in pricking down the parallels of declination with the Tropicks, I have here added a Table of the altitude of the Sun for every houre of the day when the Sun enters into any of the 12 Signes.

A Table for the altitude of the Sun in the beginning of each Signe, for all the houres of the day for the Latitude of London.

Hours.	Cancer.	Gemini Leo	Taurus Virgo	Aries Libra	Pisces Scorpio	Aquar Sagitta.	Capric.
12	62	0	58	43	50	0	38	30	27	0	18	18	15	0
11	1	59	43	56	34	48	12	36	58	25	40	17	6	13	52
10	2	53	45	50	55	43	12	32	37	21	51	13	38	10	30
9	3	45	42	43	6	36	0	26	7	15	58	8	12	5	15
8	4	36	41	34	13	27	31	18	8	8	33	1	15
7	5	27	17	24	56	18	18	9	17	0	6
6	6	18	11	15	40	9	0
5	7	9	32	6	50									11	37
4	8	1	32											21	40

This Table is in Mr. Gunters Book, page 240 which if you desire to have the point of the Equinoctiall for a Ho∣rizontall

plane on the houre of 12, enter the Table of sha∣dows with 38 de. 30 m. and you shall finde the length of the shadow to be 15 parts 5 m. of the length of the style di∣vided into 12, which prick down on the line of 12 for the Equinoctiall point, from the foot of the style. So if I desire the points of the Tropick of Cancer, I finde by this Table that at 12 of the clock the Sun is 62 de. high, with which I enter the Table of shadows, finding the length of the shadow, which I prick down on the 12 a clock line for the point of the Tropick of Cancer at the houre of 12. If for the houre of 1, I desire the point through which the parallel must pass, looke for the houre of 1 and 11, in this last table under Cancer, and I finde the Sun to have the height of 59 de. 43 m. with which I enter the table of sha∣dows, and prick down the length thereof from the bottome of the style reaching till the other foot of the Compasses fall on the houre for which it was intended. Doe so in all the other houres, till you have pricked down the points of the parallels of declination, through which points they must be drawn Hyperbolically. Proceed thus in the making of a Horizontall Diall, but if it be a direct verticall Diall, you shall then take the length of the verticall shadow out of the said Table, or work it as an Horizontal plane, only account∣ing the complement of the elevation in stead of the whole elevation.

For a declining plane you may consider it as a verticall direct in some other place, and having found out the E∣quator of the plane and the substyle, you may proceed in the same manner from the foot of the style, accounting where the style stands to be no other wayes then the me∣ridian line or line of 12 in a Horizon whose pole is elevated according to the complement height of the style above

the substyle, and so prick down the length of the shadows, from the foot of the style, on every one of the Houre lines, as if it were a horizontal or Verticall plane.

But in this you must be wary, remembring that you have the height of the sun calculated for every houre of that Latitude in the entrance of the 12 signes, in that Place where your Plane is a Horizontall plane, or otherwayes, by con∣sidering of it as a horizontall or Verricallplane in another latitude

For the Azimuths, or verticall circles, shewing one what point of the compasse the sun is in every houre of the day it is performed with a great deale of facility, if first, when the sun is in the Equator, we doe know by the last Table of the height of the sun for every houre of the day and by his meridian altitude with the help of the table of shadows, find out the Equinoctiall line, whether it be a Horizontall or upright direct plane, for having drawn that line at right angles with the meridian, and having the place of the Style, and length thereof in parts, and the parts of shadow to all altitudes of the sun, being pricked down from the foot of the Style, on the Equinoctiall line, through each of those points draw parallel lines to the meridian, or 12 a clock line on each side, which shall be the Azimuths, which you must have a care how you denominate according to the quarter of heaven in which the sun is in, for if the Sun be in the easterly points, the Azimuths must be on the Western side of the plane, so also the morning houres must be on the opposite side.

There are many other Astronomical conclusions that are used to be put upon planes, as the diurnall arches, shewing the length of the day and night, as also the Jewish or old

unequal houres together with the circles of position, which with the meridian and horizon distinguisheth the upper he∣mispheare into 6 parts commonly called the houses of Hea∣ven: which if this I have writ beget any desire of the reader, I shall endeavour to inlarge my self much more, in shewing a demonstrative way, in these particulars I have last insisted upon. I might heare also shew you the exceeding use of the table of Right and versed shadow in the taking of heights of buildings as it may very wel appear in the severall uses of the quadrant in Diggs his Pantometria, & in Mr. Gunters qua∣drant, having the parts of right and versed shadow gradu∣ated on them, to which Books I refer you.