365 / 1042
D
A
" 1,00 Ihe lioe
lb;
coolinuingIhehOllr·lioes of
Vil
and
VI![ ¡hrollgh ¡he center
a
tO ¡he oth" lide of the dial, for
Ihe like hOHr! (lf
Ih~
eveoing; alld
C~¡
the hours 10 Iheir
r~fpe.qive
Iines, as io Ihe figure. Laflly, make Ihe goo·
mon Ihe
C.me",ayas taugl1l abol'e for the horizootal dial,
aod the whole will be fio;llled.
To make an eretl fo¡ah dial, take Ihe co·)atitude of
your place from the Ctale of latitudes, aod Iheo proceed
io alJ refphqs for ¡he hour.lines, as io Ihe horizontal di. l;
only
revcrfin~
the hours, as io fig.
4.
aod makiog ¡he
angleof ¡he Hile's height equal ¡O ¡he co·la¡i¡ude.
BUl lell the youog dialill !hollld have nei¡her globe nor
wooden fcale, \Ve !hall now
01~\V
him how he may make a
dial withoUl any of theft: helps. On!y, if he has not a
lioeof chords, he mull divide
a
quadraot into 90 equal
pansordegrees for t.¡king thepro)'.r an&le of ¡he flile's ele·
va¡ion; which is eafily done.
\Vllh
any openiog of ¡he comparres, as
Z
L,
deCcribe
Ihe IWO fcmicircles
LF
kaod
L!?.R,
upoo ¡he ceo¡m
Z
aod
=,
whtre ¡he fix o'e1oek lioe crolres ¡he double meri·
diao lioe, and divide each Cemicircle in¡o 12 equal .pam,
beginning al
L
(¡hough, f1rillly fpeakiog, ooly the qu.·
dra"" from
L
to ¡he fix o'clock lioe oeed be divided;) then
coontll ¡he divifioos which are equidiHan¡ from
L,
by the
rarallelli~cs
KIlf,
IN,
HO, CP,
and
Ff¿
Draw
VI.
for the hypo¡heoufe of ¡he Ilile, making ¡h. aogle
filE
equa) ¡O¡he latitu¿eof your place ; aod contioue theIioe
Vl
¡O
R.
Dr.w the lioe
Rr
par:t1le1
lO
the fix o'dock
lioe, and fet off thedlff.loce
a
K
Crol:)
l
10
r, tho·dillance
h
Ifrom
Z
to
X,
e.J1
from
Z
to
11',
dC
from
Z 10
T,
aod ,
F
from
Z
to
S.
Theo draw ¡h. lines
Si, TI,
W.",
Xx,
andr],
e.ehr.rallci lo
R,.
S~lolflhe
dill.nce] r
from
a
10 11, aod fromflo 1; ¡he diflance
xX
from
b
10
19,
and from
g
10
2 ;
.vII'
from
e
10
9,
~nd
fro'o
h
10
3;
,r
from
d
10
8,
20d frolO
i
10
4;
IS
from (107, and
frolO
n
10
5.
Thcn laying a ruler
10
Ihe ccoler
Z,
draw
Ihe forenooo hour·lines Ihrough the poiots 11, 10,9.8,
7;
and layin,g il 10 ¡he center
z,
dra\V Ihe ¡f¡eroooo lines
through Ihe points 1, 2,
3, 4, 5;
conliouiog Ihe fore–
noon lines of VIl aod VIl! lhrough lhe cenler
Z,
10lhe
oppofile lide of lhe dial, for Ihe like aflernoon hours; aod
Ihe af¡ernoon lioes m I aod
y
Ihrough the eeoler
z,
10
Ihe oppofi¡e fide, for Ihe like morolOg hours. Sel the
hours 10 Ihefe lioes as in lhe figure, and theo ereét lhe
filie or gnomon, aod lh. horizontal dial will be lioiOt·
ed.
To confirull
a
fouth dial, draw Ihe lioe
VZ,
making
an angle wi¡h
lh~
meridian
Z
L
equal
lO
Ihe co·latÍlUde
of your place; and proeeed in
. 11
re[peéts
dS
io the abol'e
ho~izontal
dial for ¡he
[,me
la¡i:nd~,
rcverfiog the hours
as
10
fig.
4.
aod mnkiOg Ihe elen¡ion of Ihe
gnom~o
e·
qual lO ¡he co·J.ttilude.
Pcrhapl it may no¡ be unacceptJble 10 explnin Ihe me·
Ihod of
coollru{ti~'6
¡he
¿¡..
Iiog hoc>, aod
tom~
lllhm ;
which is as follo,,"s.
Wi¡haoyopetlingof Ihecompalíe" (PI",e
LXX.
fig.
l.)
as
~.
A,
aecordin~
tOIhe inlended lenr,th uf Ihe 1"lt, de·
r~tlbc
¡hecirele
AJ)C/I,
and
~ruls
11
a¡
lil!l"
a,,~I·,
hy ¡he
dl"mlters
CE
."
nnd
D í:; O.
J)llIde ¡he '1'I.i(Ir"ol
,¡
a
flfO iuo 9 e'iu,1ram, and thtn ¡'.eh ra1t In¡o 10; fo
111,11
¡he c¡u.tdrant
L~
ulvided iOlo 90 crl"al I
aIIS Of
de·
D
A
grees. Draw Ihe righl lioe
AFO
(or Ihe eI,old of Ilris
qu.adraol, and Cetling ooe fool of ¡he comp,rrtS in ¡he
POlO¡
A,
eXlend ¡he olher 10 Ihe fel'eral diviGons of ¡he
quadrant, and traosfer Ihefe divifions lOlhe lioc
AFO
by
Ihe ares 10,1 0, 20, 20,
ee.
and ¡his will he a line of
chords, dividcd iOlo 90 unequal pms ; " hich, if tranf.
f~rred
from Ihc lioe back ag,io 10 Ihe quadranl, \ViII di.
Vide 11 equally.
It
is plain by ¡he figu re, Ihat Ihediltaoce
from
110
60 in
I~e
line of chords, is jull equal 10
AE,
lhe radlU! of lhe mcle fromwhich that lioe is made' for
if ¡he arc 6o, 60 be coolioued, of whieh
A
is Ih6
ce~ler
il goes exaétly Ihrough Ihe cenler
E
of Ihe are
AO.
'
Aod Iherefore, in laying down any number of degrees
on a cirele, by lhelioe of ehords, you mull firn open Ihe
comparres
Co,
as ¡O takc in jull 60 degrees upoo ¡hal Eoe,
as from
A
10 60: aod Ihen, ",ilh ¡hat eXtenl, as aradius,
defcribt a cirele, which \Vi II be exallly of Ihe fame fize
witb Ihat from which Ihe lioe \Vas divided: which done,
fel ooe fool of lhe
comp~rres
in Ihe begioning of theehort!
line, as al
A,
aod extend Ihe o¡her 10 ¡lte oumber of d(–
Wees
you.wa~1
upon the
lin~;
which eXlent, applied ¡O Ihe
c"e1e, wllI IOclude lhe hke number of degrees upun
il.
Divide Ihe quarlranl
CD
iOfO 90 equal pam, aod fr(lm
eaeh poiOl of divifion draw righl lines, as
i,
J,
/,
cre. lo
Ihe Ilne
CE;
all perpendicular 10 ¡hal line, aod parallcl 10
D E,
which \ViII divide
EC
iOlo a line of fines' and .1.
though lhefe are feldom pUl "moog Ihe dialiog lin.s 00 a
fcale, yCllhey allifi io drawing lhe Iioe of
l~tÍlude!.
For
if a ruler be laid npon¡he poinl
D,
aod om eaeh rlivifi–
on in Ihe lioe of fines, it IVdl dil'ide Ihe
quadr.ntCD
in.
10 90 unequ,d pms, as
Ba, Oú, (,c.
O,ewn by ¡he righf
line: lOA,
20h, 30C,
&e.
drawo along ¡he edge .of ;he
ruler. If Ihe righl lioe
OC
be drawn, fubleudino Ibis
qu.dranl, and Ihe oealdl dlllances
Da, Bh, Be.
ó:.
be
laken io ¡he compaOes from
B,
ind Cet uroo lhis lioe in
lhe fame manoer as direéled fo r Ihe lioe of chords il wdl
make a line of laliltldcs
llC,
equ;¡ inleoglh fO lit; line of
chords
AB,
and of an equal oumber of divifioos, but
very unequal as
10
Iheir leogdls.
Draw Ihe rigllt Iioe
D
(;
A,
fubtending the quadrant
DA;
and parallcl lo il, draIV Ihe rigilt llOe
r
i ,
lOuch.
ing lhe quadraol
D A
al lhe oumml figure
3.
Divide
this quadranl iOlO fix equal pam, as 1, 2,
3,
&e.
~od
Ihrough theCe poiots of divifion e1raw righ l lines fromthe
centre
E
'tO the lille
/'J,
whieh will divide il allh, POiO¡9
wbere lhe lix hours are 10 be plnced, as in Ihe figure.
lf
el'ery fix¡h par! of Ihe quad"nl be fubdiviJcd iOlo
four ellual pam, righl lioes drawo from Ihe centre
lhrou&h ¡heCe poinls of divifioo, aod cOOlinued to ¡he
lioc
r
1,
\ViII divide eaeh hour upon il ioto quarterl.
lu
Fig, ~.
Plate LXX. we hal'e Ihe repreCenu¡ion
of a ponable diJI, whirh may be eafily drawo 00
a
cdl'd
aod carmd 10 a pocke¡·book. The lines
a
d, "b,
aol
he
01'
die gnumon mufi be
CIII
quite Ihrol/gh Ihe eaeJ.
and al ¡he cnd
11
b
of
th~
go?mon is rai!ed
occaGooalJ~
a~u\
e
lhe plane of ¡he d"I,
11
m",s I/piln lhe Uoelll lir.c
ed
as 00 a hinge. l'he line
JOII~d
,-/0
muf! be ilil
'Iulle ¡hrough lite eard, and Ihe ¡hi tad
r:
mull be pUt
¡hro,,~1t
the Oil, .ud h,\\', a kllOI ticd bdlilld, lOkeep Ir
(rom belog e.fily dr.lwlI OUI.
<..'n
¡he
o::I~r
CIlJ
of ¡hi,
IIH.·.J