t-angled at A, the side pA, equal to ZP,
is the co-latitude of the place, that is, the difference between the
latitude and 90 deg.; and the successive angles ApB, ApC, &c., are 15
deg., 30 deg., &c., respectively. Then

tan AB = tan 15 deg. sin _co-latitude_;

or more simply,

tan AB = tan 15 deg. cos _latitude_,
tan AC = tan 30 deg. cos _latitude_,
&c. &c.

and the arcs AB, AC so found are the measure of the angles AEB, AEC,
&c., required.

In this ease the angles diminish as the latitudes increase, the
opposite result to that of the horizontal dial.

_Inclining, Reclining, &c., Dials._--We shall not enter into the
calculation of these cases. Our imaginary sphere being, as before
supposed, constructed with its centre at the centre of the dial, and
all the hour-circles traced upon it, the intersection of these
hour-circles with the plane of the dial will determine the hour-lines
just as in the previous cases; but the triangles will no longer be
right-angled, and the simplicity of the calculation will be lost, the
chances of error being greatly increased by the difficulty of drawing
the dial plane in its true position on the sphere, since that true
position will have to be found from observations which can be only
roughly performed.

In all these cases, and in cases where the dial surface is not a
plane, and the hour-lines, consequently, are not straight lines, the
only safe practical way is to mark rapidly on the dial a few points
(one is sufficient when the dial face is plane) of the shadow at the
moment when a good watch shows that the hour has arrived, and
afterwards connect these points with the centre by a continuous line.
Of course the style must have been accurately fixed in its true
position before we begin.

_Equatorial Dial._--The name equatorial dial is given to one whose
plane is at right angles to the style, and therefore parallel to the
equator. It is the simplest of all dials. A circle (fig. 5) divided
into 24 equal ares is placed at right angles to the style, and hour
divisions are marked upon it. Then if care be taken that the style
point accurately to the pole, and that the noon division coincide with
the meridian plane, the shadow of the style will fall on the other
divisions, each at its proper time. The divisions must be marked on
both si