Mathematical Instruments
Book VIII.

# Remarks and Definitions appertaining to Dialling.

Sun-Dials take their Name from the principal Circles of the Sphere to which they are parallel: as, a Horizontal-Dial is one parallel to the Equinoctial-Dial one parallel to the Equinoctial; a Vertical-Dial one that is parallel to a Vertical Circle; and so of others.

There are two sorts of Styles placed on the Surfaces of Dials; one is called a Right Style, which is a pointed Iron-Rod, that shews the Hour or Part on a Dial by the Shadow of its Extremity; and the other is called an oblique or inclined Style, or else the Axis, which shews the Time of Day upon a Dial by the Shadow of the whole Length thereof.

The Extremity of the right Style of any Dial, represents the Center of the World and Equator, and the Plane of a Dial is supposed to be as far distant from the Center of the Earth, as is the Length of the right Style. For because the Sun’s Distance from the Center of the Earth is do great, and the Distance of any Point in the Earth’s Superficies from the Center is so small, compared with the Sun’s Distance; therefore any Point on the Earth’s Surface may without any sensible Error be taken for its Center: and so the Extremity of the Style of any Dial may be taken for the Center of the Earth; and a Line parallel to the Axis of the World, which passes thro’ the Extremity of the Style, may be considered as the Axis of the World.

The Hour-Lines, which are drawn upon Dial-Planes, are the Intersections of the said Planes made by the Hour-Circles of the Sphere.

The Center of a Dial, is the Intersection of its Surface with the Axis of the Dial passing thro’ the Extremity of the Style parallel to the Axis of the World; and in this Center all the Hour-Lines meet each other.

All Dial-Planes may have Centers, except East, West, and Polar ones; for on these the Hour-Lines are all parallel between themselves.

The Vertical Line of a Dial-Plane, is a Perpendicular drawn from the Extremity of the Style to the Foot thereof; but the Vertical Line of the Place wherein the Dial is, is a right Line perpendicular to the Horizon drawn thro’ the Extremity of the Style.

Dials have likewise two Meridians; one of which is the substylar Line or proper Meridian of the Dial-Plane, because its Circle passes thro’ the Vertical Line of the Dial-Plane; and the other, which is the Meridian of the Place, hath its Meridian Circle passing thro’ the Vertical Line of the Place.

When a Dial declines neither to the East or West, the substylar Line, or Meridian of the Plane, coincides with the Meridian of the Place or Hour-Line of 12, let the Surface of the Dial be Vertical, Horizontal, or even inclined upwards or downwards.

The Horizontal Line of a Dial-Plane, is the common Section of the said Plane, and a horizontal or level Line passing thro’ the Extremity of the Style; and the Equinoctial Line is the common Section of the Dial-Plane and Equinoctial Circle: and this Line is always perpendicular to the substylar Line; and consequently if the Position of the substylar Line be known, and a Point of the Equinoctial Line be given, we may likewise have the Position of the Equinoctial Line: and contrariwise, if the Equinoctial Line be given, we may have the substylar Line, which is perpendicular thereto. Note, This substylar Line must pass thro’ the Foot of the Style and the Center of the Dial.

The Hour-Line of six always passes thro’ the Intersection of the Horizontal and Equinoctial Lines in declining Dials; and so the said Point of Intersection is one Point of the Hour-Line of six. Note, The Point wherein the Substyle and Meridian Lines meet, is the Center of the Dial.

When a Dial is to be drawn upon a Plane, you must first find the Position of the said Plane, or of the Wall it is to be set up against, with regard to the Sun and the principal Circles of the Sphere: And this may be done, in observing several Times the same Day, at every 3 or 4 Hours interval, where the Shadow of the Extremity of a Style falls upon the Dial-Plane: for by this means the Position of the Dial-Plane may be determined, and afterwards all the Hour-Lines, &c. may be drawn thereon in the manner we shall hereafter shew. Note, The Exactness of a Dial very much depends upon these Points.