H O R O 
direction, the fliadow of which ferves to point out the 
hours; as before laid, it is a portion CS of the axis of 
the fphere ; and in that cafe it Ihows the hour by the Iha- 
dow of its whole length. An upright ftyle, however, 
fuch as S Q, is l'ometimes given to dials ; but in that cafe 
it is only the lhadow of the fummit S that indicates the 
hour, becaufe this fummit is a point of the axis of the 
fphere. 
The centre of the dial is the point C where all the 
hour-lines meet. It fometimes happens, however, that 
th'efe lines do not meet. This is the cafe in dials which 
have their plane parallel to the axis of the fphere ; for it 
is evident that in fuch dials the interfeclions of the ho¬ 
rary circles mult be parallel lines. Thefe dials are called 
dials without a centre. Vertical eaft and welt dials, and 
dials turned direftly towards the fouth, and inclined to 
the horizon at an angle equal to the latitude, or which if 
produced would pafs through the pole, are of this number. 
The meridian line , as is well known, is the interfec- 
tion of the plane of the meridian with the plane of the 
dial; when the plane of the dial is vertical, it is always 
perpendicular to the horizon. The J'ubjlylar line, is that 
marked out by the plane perpendicular to the plane of 
the dial, and palfing through the ftyle. As this line is of 
great importance in declining dials, it is neceflary to have 
a very diftinft idea of it. For this purpofe, conceive a 
perpendicular let fall on the plane of the dial, from any 
point in the ftyle; and that a plane is made to pafs 
through the ftyle and the perpendicular; this plane, 
which will neceflarily be perpendicular to that of the dial, 
will cut it in a line palling through the centre, and 
through the bottom, of the perpendicular, and this line 
will be the fubftylar line. This line is the meridian of 
the plane; that is, it (hows the moment at which the ele¬ 
vation of the fun above that plane is greateft. Care how¬ 
ever muft be taken not to confound this meridian with 
the meridian of the place, or the fouth line of the dial; 
for the latter is the interleclion of the plane of the dial 
with the meridian of the place, which is the plane palling 
through the zenith of the place and the pole; whereas 
the meridian of the plane of the dial, is the interl'eftion 
of that plane with the meridian, or the horary circle palf¬ 
ing through the pole and the zenith of the plane. 
In the horizontal plane, or any other which has no de¬ 
clination, the fubftyle and the meridian of the place co¬ 
incide; but in every plane not turned direftly towards 
the fouth or the north, thefe lines form greater or lefs 
angles. Laftly, the equinoctial is the interfeftion of the 
plane of the equator with the dial; it may ealily be leen 
that this line is always perpendicular to the fubftyle. 
Thus it appears, that the plane of every dial reprefents 
the plane of iome great circle on the earth, and the gno¬ 
mon the earth’s axis ; the vertex of a right gnomon the 
centre of the earth or viiible heavens ; and the plane of the 
dial is jult as far from this centre as from the vertex of 
this ftyle. The earth itfelf, compared with its diftance 
from the fun, is confidered as a point; and therefore, if 
a fmall fphere of glafs be placed upon any part of the 
earth’s furface, fo that its axis be parallel to the axis of the 
earth, and the fphere hath fuch lines upon it, and fuch 
planes within it, as above del’cribed, it will lhow the hours 
of the day as truly as if it were placed at the earth’s cen¬ 
tre, and the (hell of the earth were as tranfparent as glafs. 
To deferibe an Equinoctial Dial .—From any point C (fig. 3), 
as a centre, -deferibe a circle AEDB; and, having drawn 
the two diameters interlefting each other at right angles 
in the centre C, divide each quadrant into fix equal parts ; 
and draw the radii C 1, C 2, C 3, and io on, as leen in the 
figure. Thefe radii will lhow the hours by means of a 
ftyle perpendicular to the plane of the dial, which muft 
be placed in the plane of the equator ; that is, in fuch a 
manner as to form with the horizon an angle equal to the 
complement of the latitude. The line A D muft coincide 
with the plane of the meridian, and the point A muft be 
LOGY >295 
direfted towards the fouth. When this equinoctial dial 
is erefted, if the hour-lines look towards the heavens, it 
is called a fuperior dial; but, if they are turned towards the 
earth, an inferior. A fuperior equinoctial dial Ihows the 
hours of the day only in the fpring and fummer; and an 
inferior one only during the autumn and winter; but at 
the equinoxes, when the fun is in the equator, or very 
near it, equinoctial dials are of no ufe, as at thofe periods 
they are never illuminated by the fun. 
It -is well known that at London the elevation df the 
plane of the equator is 38° 29', which is the complement 
of the elevation of the pole : the angle therefore which 
the plane of an equinoftial dial at London lhould form 
with the horizon, ought to be 38° 29'.—Hence it appears 
that it is eafy to conftruCl 
An UniverJ'al EquinoElial Dial, which may be adjufted to 
any elevation of the pole whatever.—For this purpofe, join 
together two pieces of ivory, or copper, or any other, 
matter, ABCDandCDEF, (fig.4,) by means of a hinge 
at C D: then deferibe on the two furfaces of the piece 
A BCD two equinoctial dials; and in the centre I place 
a ftyle extending both ways in a direction perpendicular 
to ABCD. At G, in the middle of the piece CDEF, 
fix a magnetic needle, covered with a plate of glafs, and 
towards the edge of the fame piece apply a quadrant HL 
divided into degrees, and palling through an aperture II, 
made to receive it, in the upper piece A B C D. The de¬ 
grees and minutes muft begin to be counted from the 
point L. • 
When this dial is to be ufed, place the needle in the 
meridian, making a proper allowance for the declination ; 
and cauie the two pieces A B C D and CDEF to form an 
angle B C F, equal to the elevation of the equator at the 
given place; that is, equal to the complement of the la¬ 
titude. If care be then taken to turn the quadrant to¬ 
wards the fouth, either of thefe equinoftial dials will lhow 
the hours at that place, except on the day of the equinox. 
To conjln/cl a Horizontal Dial.— Draw the meridian SM, 
(Plate II. fig. 5,) and from the point C, alfumed towards 
the middle, as a centre, deferibe the circle E T O P with 
the radius CE; then from O as a centre, with a radius 
equal to the diameter OE of the firft circle, deferibe the 
circle EAMB; and from the point E as a centre, with 
the fame radius, the circle AOBS: thefe two circles will 
cut each other in A and B, which will be the centres of 
two other equal- circles, XIEF and ZLEG. Through 
the points of interleclion F and G, draw the lines EG 
and E F; and through the points A and B the ftraight line 
XACBZ. This line, which will be the equinoftial, will 
be cut both by the above circles, and by the lines E G and 
EF, and the centre C of the firft circle, in 11 points, which 
will be thofe of the hours: they muft therefore be marked 
with the numbers 7, 8, 9, 10, n, 12, 1, 2, 3, 4, 5. 
The next thing is to find the centre of the dial, of 
which the above points are the horary divifions: this is to 
be done in the following manner: In the circle ETOP 
alfurne, towards T or P, an arc E K equal to the comple¬ 
ment of the latitude or elevation of the pole, that is, 
equal to 38° 29'if the kititude be 51 0 31', and draw CKc 
if KV be then drawn perpendicular to CK, it will cut 
the meridian in V, which will be the centre of the dial; 
fo that by drawing, from the point V, the lines V 7, V 8, 
V 9, &c. we (hall have the. hour-lines from 7 in the morn¬ 
ing till 5 in the afternoon. If a line be drawn through 
the point V parallel to the equinoftial, it will'be the line 
of 6 o’clock. The hour-lines of 7 and 8 in the morning, 
continued beyond the centre V, will give thole of 7 and 
8 in the evening; and thofe of 4 and 5 in the evening, if 
continued in the fame manner, will give 4 and 5 in the 
morning. In the laft place, if from the point V, or any 
other taken at pleafure, two circles be deferibed, they will 
ferve to terminate the hour-lines, and to contain the num¬ 
bers belonging to the different hours. 
Of the South Vertical Dial .—If the vertical dial be turned 
directly 
