372 / 1042
D
A
l.Lct d, (Platc
LXXLfig.l.)
hc d,erun's place,
,fR,
his Jeclioatioo;
~od
in Ihe tri."'gle
JI
1..1, I'd
Ihe fum,
or Ihe diJl'creoce, of
dR,
aod
Ih~
quaJ"ot
l'11,
beiog
gi.lnby Ihe fuppoGlioo, ,s alfo the complcmcol of Ihe
J.'liwde
PI.,
~od
Ihe
"o~le
dl''L,
whid, o.eafu"s Ihe
Ihlr••ry d,iI ,oce of
d
from Ihe mcridiao; IVe
110,11
(hy
C~fe
4. of K"U's ohlique fpl"ric Trigooommy) fioJ Ihe
I"fe
Zd,
IVhieh is Ihe fuo 's JiJl.oce fromIhe zenilh, or
Ihe cllmplemenl of his .'¡tilUde.
,\od (2.) As Gne
2.1:
Goe
Pd
: :
dPZ
:
d7.P,
or
of ils fllpplcmcllI
DZS,
the niOlulhaldiJlaoce froal
th~
fomh.
Or, the Imaical rule may be as follows .
\V
rite
A
for the Ggo of Ihe fuo's altitude,
L
aod
I
for Ihe Goe and co·Goe of the Ialitude,
D
aod
d
for the
Goe and co·Goe of Ihe fuo's dechoalioo,
~od
H
for the
lioe of the horary dill?oce fromVI.
Theo Ihe rdalioo of
H
tO
A
will have time varie·
tieso
l. Wheo the declioatioo is loward the devaled pole,
and the hour of the day is betweeo
Xli
aod VI i it is
H A-LD
A=LDt HI d,
aod
= -Id
2. Wbto the hour is 'after VI, it is
A=LD
- HId
aod
LDtA
Id
3. Wheo the
declio~lioo
is toward Ihe depreífed pole,
A+LO.
we have
A=HI d_L D,
aod
lf=- -l-
•
d
Which theorems \ViII be fouod ufeful, aod expeditious
eoough for folviog Ihofe problems io geography aod dial·
iog, which depeod
00
tbe relalioo of the Cuo's allitude tO
Ihe hour of Ihe day.
E X A 111 P L E
I.
Suppofe Ihe lalilude of Ihe place to be 51
~
degrm
nonh: the time five hours dillanl from
XII,
Ihat is, an
hour afler VI ioIhe morniog, or before VI io Ihe eve·
ning;
~nd
Ihe fuo's declination 20° oonh.
Rrquired/he
funl
ol/ilude?
Theotolog.
L=
log. Go. Sl o 30' 1.89354"
addlog.
D= log.
Go. 20° o' I.S3405
Their fum
1.42759 gives
I.D
= logarithm of 0.267664, io Ihe nalural Gnes.
Aod, lO log.
H
= log. Gn.
t
1
SO
d
1-41300
add
S
log.
I
=Iog. Go.
t
38:
o;
L194
1
S
(log. á=log. Gn.
70 o 1.97300
Their fum
1.1 8015 gives
HId=
logarilhm of 0.ISI408, io the o¡tural Goes.
And thtfe IWO numbm (0.267664 aod 0. ISI408)
make 0'419072 =
A;
which, io Ihe table, is Ihe nCJfell
natural Gne of 24° 47', Ihe fuo's ahitude [lIughl.
The fome hour·dillaoce beiog aífllmed00 theolher Gde
of VI, then
LD
-
H"
is 0. 11 62S6, Ihe Gne of 6°
D
A
4()'¡ ;
which is Ihe fuo's ahiluJe
~I
V io Ihe mOloiog, or
VII
,n the
c\'eoio~,
wheo his oonh dcclioalioois 20°;
lIut wheo Ihe d!clioatioo is 20° [omh (01towards Ihede·
prelred pole) the dilrmoce
HId
-
LD
becomes oega·
live, aod IhertbyIhews
tI..
l,
~o
hour Lefore VI io the
morning, or p.¡1I VI io the eveoiog, the fuo 's center is
6° 40';' below thr horizoo.
E IX A M P L E 11.
From the f.1me
dalo
to God the fuo's
4zil/lu/h.
If
H, L
aod
D
are giveo, theo (by par. 2. of Rule
11.)
(rom
/1
h~viog
fouod the altiludeaodils complemeot
Z
¿;
aod the are
Pd
(the clinance fromthe pole) beiog giveo;
fay, As the co·fi oe of Ihe ahitude is to the Goe of the
dill~oce
from the pole, fo is lhe Gne of the hour·dillaoce
fromIhe meridiaotOIhe Goe of Ihe azimuth dillaoce {rom
themeridiano
Le!
the lalitude be 51 ° 10' nonh, the declinatioo
IS'
9 foulh, aod Ihe time
IJ
h. 24' m. in Ihe aflernooo,
wheo Ihe fuo brgios to illumioale a vertical wall, aod it is
required to fiod Ihe poGtioo of Ihe wall.
Then, by the Ioregoiog theorems, Ihe complemeol of
the ahitude will
be
81°
32'~,
and
Pd
the dillaoce from
Ihe poie beiog 109°
S',
aod the horary difiance from the
meridi~o,
or the angle
dPZ,
36°.
To log. Go. 74° 51'
Add log. Gn.
36°
o'
Aod fromIhe fum
Take Ihe log. GD. 81' 32'}
Remain,
1.75861=Jog. Go.
35°, the
~zimuth
dillaoce fought.
WhenIhe altitude is giveo, 60d fromthence the hour,
aod proceed
~s
above.
This praxis is of Gogular ufe 00 maoy occaGoos; in
Gndiog Ihe decJioatiooof vertical plaoes moreexaalyIhao
io Ihe commoo way,
efpeci~lIy
if Ihe traoGts of Ihe fuo's
ceoter is obferved by applyiog a ruler witb Gghts, eilher
plaioor telefcopical, tOthe wall or plaoe, whofe declioa.
tioo is required.-Io drawiog a meridiao lioe, aod fiodiog
the magoelic .ariatioo.- Io fiodiog thebeariogs of places
io terrellrial furveys; the traoGts of Ihe fuo over any
place, or his horizoolal dillaoce from il beiog obfervcd,
logelherwilh the ahilude and hour.-And Ihence dem·
mioiog fmal! diífereoces of loogitude.-Io obferviog Ihe
varialioo at fea, &c.
Of
Ihe
douhle horizonlal dial; amI
Ihe
Babylooian
and
Italian
tli.lr.To the
gmnmíic
projeaioo, there is fometimes addeda
jlm'grophic
projeaioo of Ihe hour·circles, aod
~he
pa·
ralleis of Ihe fuo 's declioalion, 00 the
f~me
honzoolaI
plaoe ; Ihe uprighl Gde of the goomon beiog 1I0ped iOlo
ao edge, lIaodiog perpeodicularly over Ihe
ceoler.ofIhe
projeaioo: fo that the dial, being in ilsdue poGuoo, the
Ihado,,"
• Here l'Je coofider the
1~ldillS
as IInity, aod ont
10,00000,
¡'y which, iofiead of lhe
¡mlex
9, wc have--r, as abore ;
which is of 00 fmher IIfe, than makins thc IVork alittlc ealier.
r
rhe dilllllcc of one bour from VI.
The co·latitudc of the place.
; 'fhe eu·decJillation of the fun.