The Third Book of the Cross-Staff
The common Hour-lines do commonly depend on the shadow of the Axis; but the Parallel of the Signs, and the length of the Day, the Hour-lines from Sun-rising and Sun-setting, with many others, depend on the Shadow of the top of the Style, or some other Points in the Axis, which here signifieth the Center of the World, and is represented by the Point B. And these Lines so depending are then onely useful, when they fall between the two Tropicks, and within the Horizon.
There may be several Horizontal-lines drawn upon every Plane, as I shewed before in finding the Inclination of a Plane; but the proper Horizontal-line, which is here meant, must always be in the same Plane with B the top of the Style; so that in an Horizontal Plane there can be no such Horizontal-line: but in all other Planes it may be found by applying the Horizontal Leg of the Sector unto the top of the Style, and then working as before; and the Intersection of this Line with the Meridian or Substylar-line may be found by Proportion.
- As the Tangent of 45 gr. to the Tangent of the Latitude:
- So the Height of the Style, to the Distance between the Style and the Horizontal-line.
As in the Example of the former Equinoctial Plane, extend the Compasses from the Tangent of 45 gr. unto 51 gr. 30 m. the Tangent of the Latitude, the same extent will reach in the Line of Numbers from 51 the length of the Style, unto 66, and such is the Distance between the Style and the Horizontal-line: Wherefore I take 66 parts out of a Line of Inches, and prick them down in the meridian-line from C unto H above the Style in the upper Face, but below the Style in the lower Face of the Plane; so a Right Line drawn through H, parallel to the Hour of 6, shall be the Horizontal-line.
As in the Example of the former Polar Plane, extend the Compasses from the Tangent of 45 gr. unto the Tangent of 38 gr. 30 m. the Complement of the Latitude, the same extent will reach in the Line of Numbers from 1.61 the length of the Style, unto 1.28, and such is the distance upon the Meridian between the Style and the Horizontal-line.
In all upright Planes, whether they be Direct, Vertical or Declining, or Meridian Plane, the Horizontal-line must always be drawn through A the Foot of the Style, as may appear in the Examples before.
And generally, in all Planes whatsoever, the Horizontal-line must be drawn through the Intersection of the Equator with the Hour of 6. Or if that Intersection fall without the Plane, yet if any Arks of the length of the Day be drawn on the Plane, the Horizontal-line may be drawn through their Intersections with the Hours of the Suns rising or setting.
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