168 ASTRONOMY. 
plane of the equator. In this form the hour ring forms a circle divided into 
24 hours. The shadow of a style erected perpendicularly to the centre of 
the dial face, indicates the hours whenever the twelve o’clock line of the dial 
is fixed in the meridian of the place, and the style rendered parallel to the axis 
of the earth. This equatorial dial can of course be employed to determine 
the 24 hours in those countries only where the sphere is parallel, or which 
have the pole in their zenith. In our latitude only the half circle can 
be used, and that only from vernal to autumnal equinox. 
When the plane of the dial is parallel to the plane of the horizon, it becomes 
a horizontal dial. ‘The meridian line of this dial must be in the meridian of the 
place, and the index in the direction of the pole. To construct a horizontal 
dial, draw the line of six o’clock, and, perpendicular to this and bisecting it, 
the meridian, or twelve o’clock line. At the point of intersection draw a 
line, forming, with the six o’clock line, an angle equal to the altitude of the 
pole, or the latitude of the place. Taking a moderate length on this line as 
hypothenuse, complete the right-angled triangle, by letting fall from its 
extremity a perpendicular on the six o’clock line. From the intersections of 
the first mentioned lines as centres, and with the hypothenuse, and that part 
of the six o’clock line belonging to this right-angled triangle, as radii, describe 
two semicircles on the six o’clock line. Divide each into twelve equal 
parts, and from each point of division of the inner semicircle, draw lines 
parallel to the meridian ; and from each point of the outer semicircle, lines 
parallel to the six o’clock line. Through the intersection of these two sets 
of parallels, prolong radii of the semicircles. These latter radi, twelve in 
number, will be the lines of shadow cast by the edge of the style for the 12 
hours intervening between 6 a.m. and 6 p.m.: when produced on the other 
side of the centre, they will indicate the hours from 6 p.m. to 6 a.m. Thus, 
7 a.m. produced, will indicate 7 p.m., &c. The outline of the dial plane 
may be square or circular. The style of the dial must form, with its plane, 
an angle equal to the altitude of the pole at the place of erection. If the 
style have an appreciable thickness of material, it will be necessary in the 
construction to suppose the semicircle divided into quadrants, and these 
separated by a parallel-sided space, equal in breadth to the thickness of the 
style. Since a simple index post is easily bent and moved from the required 
angle, it is preferable to employ a right-angled triangle, whose hypothenuse 
forms with the base an angle equal to the altitude of the pole. 
95. When the surface of the dial is in a vertical plane, it becomes a 
vertical dial, of which there are four forms, named after and corresponding 
to the four principal regions of the heavens: morning (oriental), noon (azi- 
muthal), evening (occidental), and midnight dials, as the vertical planes are 
turned towards the east, south, west, or north. These dials may be 
constructed mechanically by means of an equatorial dial and the rays of 
the sun. 
The surface of the dial need not necessarily be turned to any particular 
part of the heavens, nor be exactly horizontal or perpendicular, although the 
construction of these declining dials becomes more difficult, and requires a 
sreater knowledge of mathematics. Polar dials are those traced on a plane 
168 
