The Third Book of the Cross-Staff

CHAP. III.
To draw the Hour-lines in a Meridian Plane.

A Meridian Plane is that which is parallel to the Meridian Circle in the Fundamental Diagram, represented by SZN; it hath two Faces, one to the East, and the other to the West; in each of them the Style will be parallel to the Plane, and the Hour-lines parallel one to the other, as in a Polar Plane; the difference being only in the placing of the Equator, and in numbering of the Hours.

For in these Meridian Planes having drawn an occult Vertical Line CZ, and an occult Horizontal Line CN, crossing one the other at Right Angles in the Point C, the Equator AC will cut the Vertical with an Angle ZCA, equal to the Latitude of the Place; then may we cross the Equator at Right Angles with the Line CB for the Hour of 6, and from this set the Hour-points in the Equator, as in the former Prop.

For, supposing the length of the Style CB to be 10 Inches, the length of the Tangent Line belonging to the first Hour will be 2 In. 68 p. the length of the second 5 In. 77 p. as in the Table. Then the Tangent of 15 gr. being prickt down in the Equator on both sides from 6, shall serve for the Hour of 5 and 7, and the Tangent of 30 gr. for the Hours of 4 and 8; and so the rest.

This done, if we draw Right Lines through each of these Points, crossing the Equator at Right Angles, they shall be the Hour-lines required: And if we set a Style over the Hour of 6, so as the edge of it may be parallel to the Plane, and the height of it may be equal to the distance between the Hours of 6 and 9 in the Equator, it shall represent the Axis of the World, and be truly placed for the casting of the Shadow upon the Hour-lines in a Meridian Plane.