368 / 1042
1)
A
Whieh differenee of longitude heing eooverted ioto
time, is
2
hours 51 mioutes.
The vertical dial declioiog lVefllVard 36 degrees at
Londoo, is Ihercfore to he drawo io all refpeéls as a
horizontal dial for fouth latitude 30¡' degrees ; fave oo·
Iy, that the reekooiog of rhe hours
IS
to antieipate Ihe
reekoning on the borizontal dial, hy
2
hours 51mioutes:
for fo mueh fooner lVill the fun come 10 the meridiao of
London, ¡han 10 the meridiao of any place IVhofe loo·
gitude is 42t degrees \Vefl from London.
2.
BUI tO he more exaél than tht globe wiJl fhelV us,
IVe fhall ufe a liule trigooometry.
Let
NE
S
W
(PlateLXX. fig.
6.)
he Ihe horizon of
Loodon, whofe zenith is
l,
and
P
rhe north pole of
the fphere; and let
Z
h
he the pofition of a vertie.1 plane
al
Z,
dedining lVefllVard from
S
(Ihefouth) by an angle
Df 36 degrees ; on IVhieh plane an ereél dial for London
ar
Z
is 10 he dtfcrihed. Make the femidiameter
Z
D
perpendicular
10
l h,
and it will cut tbe horizon in
D,
36 degre.:s well of the fouth
S.
Then aplane, ilt Ihe
tangent
H D,
tOuehing the fphere in
D,
will he parallel
10 the plane
Z
h;
and Ihe axis of Ihe fphere will he e·
<jually iAelioed to both thefe plane!.
Let
W!t,E
he Ihe equinoélial, IVhofe e1evation 2hove
the horizon of
Z
(London) is 38-\- degrees; and
PRD
he the meridi&n of Ihe plm
D,
euuing the equinoélial
in
R.
Then it is evident, thal the are
JI
D
is the lati·
tude of the plm
lJ
(where the
pl.neZ
h
1V0uld he ho·
ri'lontal) aod Ihe are
R
~
is the dift renee of longitude
of the planes
l h
and
D
H.
In the fphencal tri<ogl<
WDR,
lhe are
/{ID
is given,
for it is Ihe eomplem' nt of Ih<plane's dechnalion from
S
tOfouth; whieh eomplem<nt is 54° (viz.
900-36°: )
lhe aogle al
R,
io whieh Ihe meridian of the place
D
euls lhe equalor, is a righl angle; aod the aogle
JlWD
meafures lbe elel'alion of lhe equiooélial above Ihe hori·
zon of
l ,
oamely,' 38{- degrees. Say therefore, as ra·
dius is 10 the eo·fioe of Ihe plaoe's declinadoo from the
foulh, fo is Ihe eo·fioe of the lalitude of
l
10 Ihe/ioeof
liD
the latitude of
D:
IVhieh is of a difl'erent denomioatioo
from Ihelatitude of
l,
heeaufe
l
aod
D
are 00 dilf<fent
~des
of the equatOr.
As radius ' · • • • . 10.00000
To eo·fioe 36°
o'
=
R!t, 9.9°796
So eo·fioe
¡t0
30'
=
~Z
9.7941S
To fine 30° 14' =
DR
(9.70211 ) = the lal. of
D,
\Vhofe horizoo is parallel to the venieal plaoe
l h
al
Z.
N. B.
Wheo radius is made tite firll lerm, il may
be
omitted, and theo, hy fublraéliog il
menl~lIy
from Ihe
fum of lhe olher tIVO, lhe operation will be fhonened.
Thus, in the prefeol
c~fe,
To Ihe logarilhmi fioe of
IfIR= " S4°
o'
9.9°796
Add the logarithmiefmeof
RD
=
t
38° 30' 9.794 1S
TIeir fum- radius • • • • • • • 9 ¡02 11
~
Tbe eo·fine of
36.
o.
or of
R
. .
t Th~co·EIl~cf
JI.
·
O.orllf Z.
D
A
gil'e lhe fa
Ole
(OIUlioo as ahoye. Aod \Ve lhall keep 10
this melhod io Ihe follolVing part of lhis aniele.
To fiod the dilfereoee of longilude Of the plaees
D
aod
l,
fay, as radius is 10 Ihe co· fioe of 38} degrees,
the heighl Of lhe equiooélial at Z, fo is lhe
eO.langeo~of
36 degrees, the plane's declioalioo, to lhe eo raogeot of
the dilfereoce of longirudes. Thus,
To the logarithmic fine of •
p 0
30'
Add lhe logarilhmie rang of
t
54°
o'
9.8
9354
10. 13
874
Their fum- radius • . • • • • 10.013228
is the nearell raogeOl of
47°
8' =
WR;
which is the
cO.langent nf 42° 51' =
R~.
rhe differeoee of loogi.
rude [ought. Whieh dilfereoee, heing redueed 10 lime,
is tlVO hours 51-\- mioules.
3. And rhus hal'iog fouod lhe exaél lalilude and loo·
gitude of lhe place
D,
10 IVhofe horizoo Ihe yertieal
plane at
lis
parallel, we fh all proceed 10 the eooflrnéli·
00 of ahorizontal dial for the place
D,
whofe lalitude is
3D.
J
4'
fOUlh; hUI aOlicipatiog lite rime al
D
by 2hour!
SI minutes (oegleéliog lhe
~
mioule in praéliee) bmufe
D
is fo far wellward io loogitude from lhe meridian of
Londoo; and rhis \ViII be a true vertical dial al Loodon,
peclining lVellward 36 deglees.
Affume aoy rightline
CSL,
(PlaleLXX fig.7.) forthe
[ubllile of lhe diale, and m?ke lhe aogle
KGP
equal 10
lhe lalitude o[ Ihe place (viz. 30·
14')
To whofe hon·
zoo lhe plane of lhe dial is parallel; then
CRP
will b:
lhe axis of Ihe lIile, or edge lhat e2(!s lhe flladow 00 the
houls of liteday, in litedial. This dooe, dralV lhecoo·
, iogent lioe
E~,
cUltiog the
fubflila~,lioe
al righl aogl<s
in
K;
aod from
f(
make
KII
p,rpendicular tOIheaxis
CRP.
Then
KG (=KR)
heiog made radius, lh.t is,
equal tO Ihe ehord of
60°
or langeol Of 45° on a good
[eélor, lake 42° 51' (lhe dilfereoce of loogitude Of Ihe
places
Z
and
D)
from rhe laogeQts, 2nd haviog fel
it from
K
ro
1I1.
draw
CM
for lhe hour·line of
xr!.
Take
KN,
equal 10 Ihe tangeRl of ao aoglc lers by IS o
degrees lhao
KM;
thal is, lhe laogenl 27°
51';
and
lhrough the point
N
dralV
CN
for rhe hour·line of
l.
The laogenl of 12°
51'
(lVhich is ISo lef! lhan 27°
51')
fel olf the fame IVay, will givea POiOI betweeo
K
aud
N, .
throug~
which lhe hour·lioe of
J[
is 10 be dralVo. The–
langent of 2° 8' (lhe dilfcreoce helween
45°
and 42°
S2')
plaeed 00 the orher fide of
CL,
will determine the
point through which lhe hour·line Of
III
is tObe dralVn!
10 which 2° 8', if the laogent of ISo be added, it wllI
make I7° 8'; aod Ihis ftl olf from
K
tOlVa rds
~
00 lhe
line
E~,
will gil'e a POiOI for Ihe hour·line of 1m: and
[o of the rell.- The foreoooo hour lioes are drawn'lhe
[ame lVay, hy lhe contioual addilion of lhe laogeots ISo,
;0°,
45°,
&c.
10 42°
51'
(=the tangeot Of
KM)
for
Ihe hours of XI, X, IX,
&c.
as far as oeeeffary; thal
is, until Ihere be nl'e honrs 00 eaeh fide Of lhe fubfltle.
The fixlh hour, aceoooted from lhal hour or pan of
th~
houronIVhieh thefuhllilefalls, \ViII he alwaysin aline per–
peodicuJartothefuhaile, arui dralVo through the eCOIer
C.
~
The co·fine of
38.
jO.
or of
f{lf) R.
t
The
~o·
aogeot of
36.
o, or of
DIfI.
4'