DIAL. 
If, then, the block be fo placed, as that the plane 
MN KL looks to the fouth, and the plane of the meridian 
bife& it in the line in the horizontal dial 
MN KL, all - hours of the 
day will be indicated by feveral planes at o 
TALS, Secondary, are all = drawn on n the planes of 
other circ'es, befides the horizon, prime vertical, equinoc 
ial, and polar aie 3 or thofe ao either Saline, caeae, 
elie, or deinclin 
ALS, wee. are ere or vertical dials, which de- 
cline rae any of the cardinal points; or they are fuch as 
cut either the Li of the prime vertical, or of the horizon, 
at oblique an 
The ufe 7 delving dials is very frequent; as the walls 
ials are ufually drawn, commouly de- 
al points. 
ining das there are feveral kinds, which are de- 
1 points; which they feem moft 
they have a real declination: 
OF decli 
nominated from the cardina 
but fro ich 
lly. 
elevation of the 
pole of the place, being given; to find ie angle formed in 
the centre of the dial, by the meridian and fubftyle. 
Canon. As the whole fine is to the tangent of the com- 
plement of the height of the pole of the place G F (fig. 21.) 
fo is the fine of the angle of the declination of the plane 
GF D, to the tangent GD, of the angle required GA D. 
he declination of the plane being given, and the 
elevation of the pole of the place, to find the angle formed 
in the centre of a vertical declining dial, by the fubftyle 
and axis. 
Canon. As the whole fine ‘is to the fine of the comple- 
ment of the elevation of the GF; fo is the fine of the 
complement of the seas of the plane DG F, to the 
fide D F, the fine of thea A.B required. 
3. The Sari - a one. and the elevation of the 
pole, ee. 3 to > he difference of longitudes, that 13, 
the arc of the auctor comprehended between the meri- 
dian of lis alee and the meridian of the plan 
Can As the whole fine is to the fine of ite height of 
the poles of the pike, foi is es tangent of the complement o 
the declination of the plane, ‘to the ten of the comple- 
the difference of se ngitudes 
. Theangle of the difference oflongitaes, and that of the 
axis with the fubftyle, being given; to find the angles formed 
in the centre 1 a vertical declining dial, bee the fubftyle 
and hour. lin 
arne admits of oa eae for the hour-lines, 
whofe ane are fought, may be T e 
meridian and fubfty] 
angle of the difference of longitudes found by the laft a 
blem; and in the third cafe, the fum of thofe two angles is 
to be taken, and the following canon ufed. 
Canon. As the whole fine is to the fine of the angle be- 
tween the axis and fubftyle, fo is the tangent of the differ- 
ence of the fun’s diftance from the meridian, and the differ- 
ence of longitudes, or of the ae of thofe two angles, to 
the se of the angle requi 
he angle formed by diets bityle, with the hour-lines, 
and ‘that of the {ubftyle with the meridian, given ;. to find 
the angles formed between the meridian and hour-lines in 
the centre of vertical declining dials. 
1. The angles of the hour-lines between the meridian and 
fubityle are found by fubtra&iing the angle formed by the 
fubilyle with the er from the angle formed by the 
fubftyle with the me 
. The angles beyond he fubftyle, and on the fide oppo- 
fite to-that of the meridian, are found by adding thofe two 
angles. 
3. Thofe on ie oe fide of the meridian are found by 
taking their di 
To deferibe a eee Dra; ai from the fouth to the 
or weft geometrically. — Fin ecliaation of the p i 
as an taught, under the ar a te 
er an horizontal dial, fuopofing i: line of 
line 1 K, making 
the dectination of the 
G H reprefents the interf{: €tion of the 
, LK will be the interfec- 
; whence we alfo 
Draw a right line pal to the horizon on the given plane, 
or wall, to anfwer to 1 K; and affuming a point therein an- 
fwering to E, fet off from the right line I K on the paper the 
ante horary ; diftances E 1, E2 Then from the 
t E ereét a perpendicular E C, equal to the diftance of the 
bate of the horizontal dial, from its line of contingency. 
Draw lines aan to the feveral points of the hour-lines Er, 
E 2, E3, &c. let fall a perpendicular A rom the centre 
of the tier dial A, to the line of contingency Ik, 
and transfer the diftance ED, from the point E upon the 
wall: then will C D be the fublty lar line. 
Wherefore, joining AD and DC at right angles, the 
hypothenufe A C will be an slat index, to be faftened 
on the wali inthe point C, aceording to the angle 
confiru a vertical riers ae is Pike the joub, to~ 
the zenith. 
degrees of declination in the 
wards the north, and bring the ica: end of th 
that degree of declination, at ha the reckoning | ends. Then 
ring any meridian (¢. gr. the firft under the 
A ae edge of the upper part of the brazen neater 
and fet the hour index to XII at noon. ‘Turn the globe 
eaftward on its axis, the quadrant of altitude being kept to 
the degree of a in the horizon, and obferve aa de- 
e fir meridian in the eo . altitude, 
oXTI,X; 
IX, &c. i and the degrees, ied nee in the 
quadrant by the firft fee are the refpective diftances of 
the forenocn hours from XII on the plane of the dial. For 
the afternoon hours, turn the quadrant of altitude round the 
zenith till it comes to the degree in the horizon oppolite 10 
that where it was placed before, or as far from the weft 
‘point towards the fouth as it was at fir from the eaft to- 
wards the north; and turn the globe weitward on its axis, 
till the firft meridian comes to the brazen meridian, and the 
hour index to XII; then turning the globe weftward to the 
afternoon hours I, IL, ILI, &c. the firft meridian wili cut the 
uadrant of altitude in the re{peGtive number of degrees from 
the zenith, that each of thefe hours is from XII on the dial; 
-and the limit of this dial will be determined by the hour- 
4 index, 
