1000000030

",id, lhe hour line of

XlI;

~nd

Ihil ,Ingle is CJlleJ

'!l~

diil~nce

of Ihe fubnile from lhe ",. ri(hn.

The dedining plane's diffmoce of longillloe, i$ Ihe

angle formed

the interfdl'0n of Ihe nile ,nd

pl;~,e

,he e1.,II, hy IIVO ""rid"ns ; one of wlllch

p~O~s

thrtlllr,h

the hour linc

XI!. an.1 the othe, Ih,ough the fub·

lIile.

Thi! mllch being prellliCoo concerning dials in general,

WI'

Ih.•1I1l0w p,nored

expl.in

Ihe diffcrent methods

,,1

thw conllrudion.

Ir Ihe whok mth

aPep,

(Plale LXIX. fig.

l.)

were il

tranfparenl, and hollolV, likc a fphm of glaCs, ano h,d

il; eg'lalOr di"lIled imo

~4 egll~1

pms by

many me,i·

diall Cl'lOieirdes,

,,¡,

&c. one of IVhich is

lhe

gro,~raphical

meriJian of .ny gil'en place, as London

(which is fuppoCed

Ihe point

a; )

and if the

hOllrs of

XII

IVe'e mukeJ

the equato" both upon

that meridian and the oppofite one, and all the reU of

the hours in order on Ihe rell of the meridiao!, thoCe

meridians IVould be the hour·circles of Loodon: then, if

the Iphere had ao opake axis, as

lerminating in

lhe poles

and

the {hadow of the axis ",ould fall

upon e'ery particular meriJian and hour, when the Cun

"me

the plane of the oppolite me,idian, and IVould

conCequendy (heIV the time al London, and at all other

places on the meridian of London.

If Ihi! Cphere was cut through the mi,ldle by a

Colid

rlane

ABCJ),

in the rational horizon

London, ooe

half of the axis

IVould be abo"c Ihe plane, and the

othcr half ocioIV it; and if llraight lines IVere dralVn

from the centre of Ihe plane, to lhoCe points \Vher. ils

cireumference is CUI by rhe hour·circles of Ihe Cphere,

thoCe lines \Vould be Ihe hour lines of a horizonlal dial

for London: for Ihe Ihado\V of the axis \Vould fall up.

on each panicul., hour·line of Ihe dial, IVhen it fell up·

on Ihe like hour·cirele of the fphere,

If Ihe plane ",hir.h ClltS Ihe Cphere he uprighl, as

AFee,

louching Ihe gil'en place (London) at

and direflly facing lhe meridian of London, il will Ihen

become the plane of an mtl direll Coulh dial : and if

right lioel be drawn from

ilS

center

to thoCe poi",ls

of ils circumference where Ihe hour'circles of the Cphere

CUI il, IheCe \ViII be lhe houdines of a venical or diretl

foulh dial for London,

which Ihe hours are

be fet

as in Ihe figure (contrary to lhoCe on a horizontal dial),

and Ihe lower

h.lr

of lhe axis will cal! a {hadow on

the hour of Ihe day in Ihis dial, al Ihe f.unc lime lhat it

IVould fall upon the like hou,·circlc of the fphere, if tbe

dial.plane was not in Ihe w' y.

If Ihe plJne (nill facing Ihe meridian) be made

in·

eline, or rer.line, anygil'en nllmber of degrees, Ihe hour.

",eles of tht fpherc ,'ill nill cut Ihe eJge

Ihe plane in

Ih(.r~

poinl! tO whieh Ihe hour·Jines mul! be drawn

I! "ight f",r.,

Ih~

ceo'cr; and Ihe axis of Ihe fphere ",di

c~n

O\adow on lhefe lines

Ih~

rcCpeflive houl s The

lik~

lI'ill n,ll huid, if the pldn,! be II""le

t!ecli"~

:ln Pli",::n nUlllher of

degrel's

(rom

the

lIl"rilli:\n

rtnvarcl

the ean '" ",di: pr,,.,dc,1'hp. dcdinalioo

Iels th In yo

t1egres, or Ih. r'c'in"i(,n he IJs rh.n Ih·! eu I"","de of

Ihe pllee :

~n'¡

rhe

ar.i,

of lh,: 'phcr,: wdl bc a r,nnnlUn,

or (ltle, for the di,\, Bit it ' .nr,OI be a g1omon, when

e "

·:I:nalio~

~"ile

90 Jegrm, nor when the reclina·

111'"

e'lIIal

"'C

ro·lalitude; bccauCe in Ihefe two

C,II,5,

lb.;'

;,~is

hJSnu elev.tlOn abol'e lhe planc

lhe

di,,1.

tlnrl t\;II Sit aprem, ihat Ihe plane of el'ery dial repre·

fellls

11.,'

rlAne of Ibme grcat ei rde "pon the euth; and

Ihe gnomon Ihe canh 's ax'!, whether

be a fm,lI wire,

as in Ihe ahol'e fi;;u

re! ,

or Ihe edge of a Ihin pl,lte, as in

lhe cOOlOlon horizontal dials.

The whole e""h, as

ils bulk, is bUI

poinl, if

eompdred tO ¡IS dillwce from Ihe Cun: and Ihercfore, if

a fm,lI fphere of glaCs be phced upon any pan of the

earth's lurl" e,

Ihat ils axis he pArallel to the axis

of Ihe eallh, and Ihe fpherc have fuch lincs upoo ir, and

Cuch planes wilhin il, .s above defcribed; it lI'ill (hew

Ihe hours of Ihe d"y as truly as if it IVere placcd at Ihe

earrh's ceOler, and the O,ell of the earth were

tranC·

pareO! as glaCs.

HUI becaufe it is impoOible tOha,'e a hollow Cphere of

glafs perfetlly true, blown round a (¡,lid plane ; or if it

IVas, we could not gCt at lhe plane wilhin Ihe glaCs to

Cet it in any gi ,'en pofition; lOe make ufe of awirdpherc

e~plain

Ihe principies of dialillg, by joining

feOli·

cireles logelher at Ihe poles, and pUlling a thin fiat plate

of braCs wilhin it.

eommon globe, of

inches diammr, has generally

24 meridian Cemicirelcs draIVn upon il. Iffuch a globe

be elel'ated IJ the latitude of any given place, and luro·

ed abollt untilone of Ihefemeridians CUl the horizon in Ihe

north point, where Ihe hour of XII is fuppoCed

marked; the rel! of the meridians IVill cut Ihe horizon at

the refpelli"e diflances of all lhe olhe, hours from

XII,

Then if IheCe poinls

dinaoce be

m~rked

on thehorizoo,

and Ihe globe be taken out of lhe horizon, and a nat

board or plale be pUt ioto its place, even IVilh Ihe (ur·

face of Ihe horizon; and if Ilraight lines be draIVn from

Ihe center of Iheboard, to Iho(e poinls of difiance on Ihe

horizon whieh were eUl by the

meridian Cemicireles,

thefe lines will be the hour·lines of a horizonlal dial for

Ihal lalilude, lhe edge of whoCe gnomon mun be in the

very

C,me

fituatioo that the axis of Ihe globe IVas, be·

fore il was taken OUt of Ihe horizon: Ihal is, Ihe gno·

mon mun make an angle wilh the pl,in of lhe didl, equal

the latilude of the place for whieh Ihe dial is made.

H lhe pole of lhe globe be elevated

the co·lalitude

of lhe given place, and any

m~ridian

brou~ht

lhe

nonh poinl of the horizon, Ihe ren of the meridi,os

11'111

CUl

the horizon in the reCpetlil'e dinances of all thehOllrs

from XII, for a dire,q Couth dial, whofe gnomon

mul~

be an angle wilh the plane Qf lhe dial, equal

Ihe co·

lalilude of Ihe place ; and Ihe hours ",un be ret Ihe,con.

I"'y

way on Ihis dial

\Vhal Ihey

are

on Ihe hotiZoo·

Idl.

Rut if )'our globe have Olore Ihan

mel'idian femi·

eircl~s

upon il, you nlltil I"ke Ihe following melhod for

O1~kin~

h"i:wn'

and

¡o"rh di1{¡.

EIt'vate thc pole

Ihe lalilude of yOllr place, and

turo Ihe

~lnbe

uOlil aoy particular me,idian (filppofe

the firll) comes

Ihe nmrh poinl of the horiznn, and

Ihe Orp"filC

Ill~rid"o

IVd l cut the horizon in Ihe foulh.

Then, ht tI,c

hour.in

,!cx

Ihe upperOlofl X

lIt

clrck;