Elliptical or azimuthal horologiography comprehending severall wayes of describing dials upon all kindes of superficies, either plain or curved, and unto upright stiles in whatsoever position they shall be placed / invented and demonstrated by Samuel Foster ...

12. How the Zodiac is to be limited in regard of length, and how to be described and set in its true place.

THe limitation of it must be according to the Scale of Sines by which the Ellipsis is described, which Scale is mentioned Pag 102 § 5. and Pag. 73 § 7▪

The Index or Diall plate (that is the mover) must move according to the proper Meridian of the Diall Superficies, and precisely so, as that fiducial edge of the Index must move (not elsewhere, but) in the very proper Meridian it self. This is, if the Index move. But if the Diall Superficies move, then the proper Meridian thereof (or the Superficies of the proper Meridian, namely the Superficies made by the pro∣per Meridian cutting through the Diall plate, which is of any thicknesse) must move directly upon, or through, the fiduciall edge of the Index. These things are intimated be∣fore. And that the Zodiac is to be described upon a plain,

though the Diall it selfe be not so. And further, that if the Diall plate move, (though it be not a plain it selfe, yet) it must move upon a plain, and that the proper Meridian is to be described upon the same plain, and the motion to be directed according thereunto. These things are often incul∣cated, because they are hard to be conceived, and had need of the better consideration for that reason. Now further.

1. If the Diall plate be supposed thus to move upon a plain, and on it the proper Meridian be drawn, then first of all, The angle is to be inquired that is made between the In∣dex and that part of the proper Meridian which is projected upon the plain whereon the motion is made, which how to measure will be a hard matter to give rules for, because the variety of cases and positions of one to the other will be so various. It is first to be supposed, that it makes a just right angle with it, and consequently that the Zodiac is described upon the proper horizon of the Index. And if upon this supposition the Zodiac be to be limited, then the rule will be the same with the former given in the like case, namely thus. Upon your Scale of Sines (by which you described your Ellipticall line) take from 90, to the Latitude of the Index, and count that length for a new Radius, and keepe it. Then when you have found the forenamed angle (of finding which more is said Prop. 13. following) to this new Radius finde the Secant of the complement or excesse of that angle: this length or Secant will be the Tangent of 45 gr. or the Decimall Scale by which you are to describe the Zo∣diac on both sides from the Equinoctiall point or line, ac∣cording to the numbers in the generall Tables made for this purpose, Pag. 4, 5, 6, and 7.

[For placing the Equinoctiall point in the Zodiac (upon which all the other parts of that Scale do depend)

you must set all in the same posture that they had when the Diall was described: and when you have made fit place for the Zodiac, and set on some pecu∣liar Zodiacall Index, you must note the place upon which the said Zodiacall Index pointeth, for that place is the peculiar place for the Equinoctiall, from whence all the other parts of the Suns annuall course must be set on.]

2. If the Index be made to move in any depth under the Diall superficies, then a slit must be made in the same Super∣ficies that the proper Meridian would cut, and the Index continued therein, down into one streight line till it meet with the foot whereon the Index is fixed, and which being moved, carryeth the Index along with it. And the Zodiac must be described either upon this foot (the Zodiacall Index being made to stand still while that said foot with its divisi∣ons moveth) and that also parallel to (or in) the proper Me∣ridian projected upon it: or else the foot must carry the Zo∣diacall Index, and the Zodiac must be described upon some other convenient place, as the sides (&c.) of that foremen∣tioned flat. And here, for limitation of the Zodiacs length, you must finde the Inclination of this moving foot to the In∣dex or Zenith line (which angle of inclination is mentioned before, and spoken of afterwards in the 13 Prop. following) and work directly as you did before by finding the new Ra∣dius, and the Secant of the complement (or excesse) of the angle. By which you shall finde the Tangent of 45 gr. or the length of your Decimall Scale, out of which the Zodi∣ac may be described by the Tables▪ Pag. 4, 5, &c. as is men∣tioned before in this proposition. Thus (in these cases) is the Zodiac to be set in its true place, thus it is to be limited and d••scribed.

For Occurrences of other sorts of Cases than are here mentioned (whereof there will not be many) he that can un∣derstand to do these things aright, will be able to grapple with them; and for such as do not understand what is here said, their best course is to let these difficulties alone.